Applied Science, Faculty of
Biomedical Engineering, School of
DSpace
UBCV
Fele-Paranj, Ali
Master of Applied Science - MASc
University of British Columbia
In this thesis, we developed a computational framework using physiologically based pharmacokinetic (PBPK) models to study radiopharmaceutical kinetics in the body. To handle the complexity of PBPK models (over 100 differential equations), a scalable modeling notation called the "reaction graph" is introduced. Implemented in Matlab's Simbiology module and shared in the systems biology markup language (SBML) format, this notation enables easy model reproduction. Referred to as the physiologically based radiopharmacokinetic model (PBRPK), it is fine-tuned specifically for radiopharmaceuticals. Using the PBRPK model and literature-based parameters, we addressed three key questions in radiopharmaceutical therapy. First, we systematically studied the interaction between hot and cold species and its impact on absorbed dose in tumors and organs at risk (OARs) and we found out that tumor receptor density and volume influence the degree of competition and the average absorbed dose in tumors and OARs in a way that lower receptor density (or lower tumor volume) leads to more dominant competition between hot and cold species that is the absorbed dose by tumor highly depends on the number of cold ligands injected to the patient. Next, the effect of injecting radiopharmaceuticals in smaller portions and with specific timing is investigated. We found that bolus injection leads to non-efficient receptor binding and sub-optimal delivered doses to the tumor and organs at risk. However, we found that injecting in several smaller portions leads to a higher absorbed dose by tumors and organs at risk. So multi-bolus injection can be thought of as a tool that increases the delivered dose to the tumor and OAR without any differential effect (delivering mode dose to the tumor and sparing OAR) Finally, the PBRPK model is used to simulate the impact of albumin affinity on radiopharmaceutical kinetics. Varying albumin affinity of the radiopharmaceuticals reveals changes in blood residence time, with lower dissociation rates resulting in longer residence times. Generally, lower dissociation rates increase tumor absorbed dose and decrease OAR dose, which makes the albumin binding a potential tool to achieve differential enhancement in targeting tumors and sparing OAR.
Use of Physiologically Based RadioPharmacoKinetic(PBRPK) Models to Simulate RadiopharmaceuticalTherapiesbyAli Fele-ParanjBSc in physics, Sharif University of Technology, 2021A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of Applied ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Biomedical Engineering)The University of British Columbia(Vancouver)December 2023© Ali Fele-Paranj, 2023The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:Use of Physiologically Based RadioPharmacoKinetic (PBRPK) Modelsto Simulate Radiopharmaceutical Therapiessubmitted by Ali Fele-Paranj in partial fulfillment of the requirements for the de-gree of Master of Applied Science in Biomedical Engineering.Examining Committee:Arman Rahmim, Professor, Radiology and Physics, UBCSupervisorCarlos Uribe, Clinical Assistant Professor, Radiology, UBCSupervisory Committee MemberRoger Tam, Associate Professor, Biomedical Engineering, UBCSupervisory Committee MemberiiAbstractIn this thesis, we developed a computational framework using physiologicallybased pharmacokinetic (PBPK) models to study radiopharmaceutical kinetics inthe body. To handle the complexity of PBPK models (over 100 differential equa-tions), a scalable modeling notation called the ”reaction graph” is introduced.Implemented in Matlab’s Simbiology module and shared in the systems biologymarkup language (SBML) format, this notation enables easy model reproduction.Referred to as the physiologically based radiopharmacokinetic model (PBRPK), itis fine-tuned specifically for radiopharmaceuticals.Using the PBRPK model and literature-based parameters, we addressed threekey questions in radiopharmaceutical therapy. First, we systematically studied theinteraction between hot and cold species and its impact on absorbed dose in tumorsand organs at risk (OARs) and we found out that tumor receptor density and volumeinfluence the degree of competition and the average absorbed dose in tumors andOARs in a way that lower receptor density (or lower tumor volume) leads to moredominant competition between hot and cold species that is the absorbed dose bytumor highly depends on the number of cold ligands injected to the patient.Next, the effect of injecting radiopharmaceuticals in smaller portions and withspecific timing is investigated. We found that bolus injection leads to non-efficientreceptor binding and sub-optimal delivered doses to the tumor and organs at risk.However, we found that injecting in several smaller portions leads to a higher ab-sorbed dose by tumors and organs at risk. So multi bolus injection can be thoughtof as a tool that increases the delivered dose to tumor and OAR without any differ-ential effect (delivering mode dose to the tumor and sparing OAR)Finally, the PBRPK model is used to simulate the impact of albumin affinityiiion radiopharmaceutical kinetics. Varying albumin affinity of the radiopharmaceuti-cals reveals changes in blood residence time, with lower dissociation rates resultingin longer residence times. Generally, lower dissociation rates increase tumor ab-sorbed dose and decrease OAR dose, which makes the albumin binding a potentialtool to achieve differential enhancement in targeting tumors and sparing OAR.ivLay SummaryIn this thesis, we developed a computer program to study radiopharmaceuticals fortreating prostate cancer. These medicines, containing radiation, bind to tumors andorgans. We focused on three key questions.First, we examined the impact of different amounts of radioactive and non-radioactive medicines on tumor and organ doses. Increasing the number of radioac-tive molecules and reducing the non-radioactive molecules for injection improvedtumor cell destruction.Next, we investigated injecting the medicine in smaller portions instead of a“all-at-once” injection. Small injection portions increased tumor cell death butalso affected healthy organs.Lastly, we explored how the medicine binds to the blood protein albumin. Mod-ifying this binding influenced the medicine’s duration in the blood. Also, we ob-served higher binding affinity to the albumin leads to higher tumor cell killing andlower healthy organ cell damage.Our findings optimize radiopharmaceutical use, enhancing tumor treatmentwhile minimizing harm to healthy organs.vPrefaceThe material presented in this thesis have been presented in different conferences,as well as a peer-reviewed scientific paper as below:Physiologically Based RadioPharmacoKinetic (PBRPK) Modeling toSimulate and Analyze Radiopharmaceutical Therapies: Studies of Non-Linearities, Multi-Bolus Injections, and Albumin BindingAli Fele-Paranj, Babak Saboury, Carlos Uribe, Arman Rahmim,EJNMMI Radiopharmacy and Chemistry, Accepted for Publication, 2024Some parts of the material covered in Chapter 2 and Appendix A were presentedat the Society of nuclear medicine and molecular imaging (SNMMI) conference2022 [1]:Modular Model Architecture for Radiopharmaceutical Therapy Plan-ning: Physiologically-Based RadioPharmacoKinetics (PBRPK) Im-plementation.Ali Fele-Paranj, Julia Brosch-Lenz, Carlos Uribe, Arman Rahmim, Babak SabouryJ. Nucl. Med., vol. 63 (suppl. 2): 3197, 2022The studies described in Chapter 3 were presented in another work for the SNMMIconference of the same year [2]:Non-linearities in the Transition from Imaging Radiotracers to Thera-peutic Radiopharmaceuticals.Ali Fele-Paranj, Julia Brosch-Lenz, Carlos Uribe, Babak Saboury, Arman RahmimJ. Nucl. Med., vol. 63 (suppl. 2): 2821, 2022vias well as another submission to the European Association of Nuclear Medicine(EANM) :Open-source, modular, high-computational-throughput physiologicallybased pharmacokinetics (PBPK) modeling fine-tuned for optimizationof radiopharmaceutical therapy.Ali Fele-Paranj, Carlos Uribe, Babak Saboury, Arman RahmimEur. J. Nucl. Med. Mol. Imaging, vol. 49 (suppl. 1): S398, 2022.Moreover, the material covered Chapter 4 were presented at the SNMMI con-ference 2023 [3]:In silico investigation of the effect of multi-bolus injections in ab-sorbed doses to organs and tumors in radiopharmaceutical therapiesAli Fele-Paranj, C. Uribe, H. Abdollahi, E. Mollaheydar, N. Zakariaei, M. S. RahimSiddiqui, B. Saboury, A. RahmimProc. SNMMI Annual Meeting, 2023Also, the material presented in Chapter 5 is accepted as a “top-rated oral presenta-tion” in the European Association of Nuclear Medicine (EANM) 2023:Theranostic Digital Blueprint Predicts Higher Therapeutic EfficacyUsing Radiopharmaceuticals with Higher Albumin Affinity.Ali Fele-Paranj, Carlos Uribe, Francois Benard, Arman Rahmim, Babak SabouryProc. EANM Annual Meeting, 2023The overall theme of my research helped my PIs to open new lines of research inthe lab that are summarized in the following article [4]:Theranostic digital twins for personalized radiopharmaceutical thera-pies: Reimagining theranostics via computational nuclear oncology.A. Rahmim, J. Brosch-Lenz, A. Fele-Paranj, F. Yousefirizi, M. Soltani, C. Uribe, B.SabouryFrontiers in Oncology, vol. 12, pp. 1062592, 2022This new line of research and my preliminary results have been helping my super-visors to write a research grant for further investigations in this exciting field, aswell as some conference papers presented by my colleagues [5, 6]:viiUsing the cluster gauss newton algorithm to estimate theranostic phar-macokinetic model parameters.N. Zakariaei, A. Fele-Paranj, H. Abdollahi, A. RahmimyProc. SNMMI Annual Meeting, 2023andTowards non-tracer kinetic modeling: Our past returning through thefuture.A. Rahmim, H. Abdollahi, A. Fele-Paranj, K-N. Lee, B. Saboury, C. UribeProc. SNMMI Annual Meeting, 2023viiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii1 Introduction to Molecular Biology of Cancer . . . . . . . . . . . . . 11.1 DNA Damage: The Molecular Cause of Cancer . . . . . . . . . . 21.2 Interaction of Radiation with Living Matter . . . . . . . . . . . . 51.2.1 Different Timescale of the Effect of Ionizing Radiation . . 61.2.2 Radiation-induced damage and the DNA damage response 71.3 Approaches to Treatment of Cancer . . . . . . . . . . . . . . . . 101.4 Nuclear Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . 121.4.1 A Brief History of Nuclear Medicine . . . . . . . . . . . 13ix1.4.2 Radiopharmaceutical therapy, the triumph of nuclear medicine 162 Modeling the Kinetics of Radiopharmaceuticals Using Physiologi-cally Based RadioPharmacoKinetic (PBRPK) Models . . . . . . . . 222.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Background and Previous Models . . . . . . . . . . . . . . . . . 252.3 Improving the PBPK Models: Towards PBRPK . . . . . . . . . . 282.4 Systems Biology Markup Language and Model Reproducibility . 312.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 In-silico Investigation of the Competition Between Hot and Cold Ra-diopharmaceuticals . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 373.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 Exploring the Effects of Multi-Bolus Injection in Radiopharmaceu-tical Therapy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 Studying the Effect of Albumin Binding on the Kinetics of Radio-pharmaceuticals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 Conclusions And Closing Remarks . . . . . . . . . . . . . . . . . . . 61x6.1 Summary of the thesis . . . . . . . . . . . . . . . . . . . . . . . 616.2 Limitations of the Current Modeling Approach . . . . . . . . . . 626.3 Possible Clinical Applications . . . . . . . . . . . . . . . . . . . 646.4 Contribution to the Field . . . . . . . . . . . . . . . . . . . . . . 64Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67A Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 85A.1 Naming Convention for Variables . . . . . . . . . . . . . . . . . 85A.2 Structure of the model . . . . . . . . . . . . . . . . . . . . . . . 86A.2.1 Internal Structure of the Organs in PBRPK . . . . . . . . 87A.3 S-Values and Dose Calculation . . . . . . . . . . . . . . . . . . . 93A.4 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . 95B Model Details in Simbiology . . . . . . . . . . . . . . . . . . . . . . 97xiList of TablesTable 1.1 Some examples of ligands used for radiopharmaceutical therapy(See [7] for a more detailed discussion). . . . . . . . . . . . . 19Table 3.1 The range of parameter values on injected hot, injected cold,and tumor receptor density to study the competition betweenhot and cold species. . . . . . . . . . . . . . . . . . . . . . . . 36Table 4.1 The range of parameter values utilized for evaluating the effectof injection profile (multi-bolus injection) . . . . . . . . . . . 46Table 5.1 The range of parameter values used to study the effect of albu-min binding on the kinetics of radiopharmaceuticals . . . . . . 54Table A.1 The list of different organs in the PBRPK model. The organscan be classified into receptor-negative and receptor-positive or-gans which are organs that have and do not have radiopharma-ceutical uptake respectively. . . . . . . . . . . . . . . . . . . . 86Table A.2 Self-absorbed fraction for different gamma-ray energies and var-ious organs (table from [8]). . . . . . . . . . . . . . . . . . . . 95Table A.3 S-Values for tumor and salivary glands . . . . . . . . . . . . . 96Table A.4 S-Values used for kidney dose calculation. Table adapted from[9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96xiiList of FiguresFigure 1.1 Oxidation of Guanine under the oxidative stress . . . . . . . . 2Figure 1.2 Relation between oxidative stress and human health . . . . . . 3Figure 1.3 Base loss damage . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 1.4 Experimental methods to detect DSB . . . . . . . . . . . . . 6Figure 1.5 Time scales of the interaction of radiation with a living matter 8Figure 1.6 Dose calculation in radiopharmaceutical therpay . . . . . . . 20Figure 1.7 The clinical practice in radiopharmaceutical therapy. . . . . . 21Figure 2.1 Different organs in a PBRPK model . . . . . . . . . . . . . . 25Figure 2.2 Substructures of the organs in our PBRPK model . . . . . . . 27Figure 2.3 The compartmentalized structure of organs in the PBPK model. 29Figure 2.4 The interaction graph: The interactions between different speciesin a PBRPK model. . . . . . . . . . . . . . . . . . . . . . . . 29Figure 2.5 The detailed structure of the PBRPK for selected organs . . . 31Figure 2.6 Full structure of the PBRPK model in Simbiology . . . . . . . 33Figure 3.1 Dependence of the delivered dose to organs on the injected hotamount and injected cold amount . . . . . . . . . . . . . . . 38Figure 3.2 The effect of tumor receptor density on the competition be-tween hot and cold species. . . . . . . . . . . . . . . . . . . . 39Figure 3.3 The effect of tumor volume on the competition between hotand cold species. . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.4 The effect of tumor receptor density on the competition degree(i.e. twist) between hot and cold species. . . . . . . . . . . . 41xiiiFigure 3.5 The effect of the tumor volume on the competition degree (i.e.twist) between hot and cold species. . . . . . . . . . . . . . . 42Figure 3.6 The effect of tumor receptor density on the average absorbeddose by tumor . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 4.1 Effect of receptor density on the effectiveness of multi-bolusinjection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 4.2 Effect of tumor volume on the effectiveness of multi-bolus in-jection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 4.3 Effect of receptor density on injection fractionation. . . . . . . 49Figure 4.4 Effect of tumor volume on the effectiveness of multi-bolus in-jection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Figure 4.5 Effect of injection coefficient on fractionation . . . . . . . . . 51Figure 5.1 The effect of albumin affinity on the blood residence time ofactivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 5.2 Dependence of dose on the dissociation constant of the albumin-ligand reaction. . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 5.3 Dependance of enhancement factor on the dissociation rate ofalbumin-ligand interaction. . . . . . . . . . . . . . . . . . . . 59Figure A.1 Compartmentalized structure of the receptor-negative organs. . 87Figure A.2 Compartmentalized structure of the receptor-positive organs. . 88Figure A.3 Compartmentalized structure of the kidney. . . . . . . . . . . 89Figure A.4 The interactions between different species in a PBRPK modelrepresented by a reaction graph. . . . . . . . . . . . . . . . . 90xivList of AbbreviationsATM Ataxia-Telangiectasia Mutated ProteinBER Base Excision RepairCT Computed TomographyDDR DNA Damage ResponseDNA Deoxyribonucleic acidDSB Double Strand BreakDSBR Double Strand Break RepairICL interstrand cross-linkMMR Mismatch repairNER Nucleotide Excision RepairOAR Organ at RiskODE ordinary differential equationPBPK Physiologically Based PharmacokineticsPBRPK Physiologically Based RadiopharmacokineticsPET Positron Emission TomographyPSMA Prostate Specific Membrane AntigenRPT Radiopharmaceutical TherapySBML Systems Biology Markup LanguageSPECT Single Photon Emission Computed TomographyxvSSB Signel Strand BreakSSBR Single Strand Break RepairUV UltravioletxviAcknowledgmentsI would like to extend my heartfelt gratitude to those who have been instrumen-tal in my journey throughout my master’s thesis. Their unwavering support anddedication have been invaluable to me.First and foremost, I want to express my deepest appreciation to my lovelywife, Elahe. Her unwavering support, patience, and encouragement have been mypillars of strength. Without her, this achievement would not have been possible.I am also profoundly grateful to my family for their continuous encouragementand belief in my abilities. Their love and support have been a constant source ofmotivation.I owe a tremendous debt of gratitude to my supervisors, Arman, Carlos, andBabak. Their guidance, expertise, and tireless dedication to my academic growthhave been truly exceptional. Their mentorship has not only enriched my knowledgebut also shaped me as a researcher.I want to extend my appreciation to all my fellow lab members. Your cama-raderie and friendly support have made my time in the lab truly enjoyable. Thecollaborative spirit within our lab has been a crucial factor in my growth as a re-searcher.In closing, I want to express how much I have cherished my time in the lab.It has been an enriching experience, filled with learning and growth, and I lookforward to carrying the knowledge and skills gained here into my future endeavors.xviiDedicationIn heartfelt memory of Seyed Ali Yazdani, an 11-year-old warrior who bravelybattled cancer with unwavering strength and resilience. His remarkable journeyand unwavering spirit have forever changed us, serving as a profound reminderof the urgency to conquer cancer. Seyed Ali is our beloved teacher and a con-stant inspiration in our pursuit of a world free from the clutches of this devastatingdisease.xviiiChapter 1Introduction to MolecularBiology of CancerCancer, the second leading cause of death worldwide, poses a significant threat tothe health of human societies [10]. Its prevalence has been on the rise, exemplifiedby the staggering numbers in the United States alone. By 2022, approximately233,900 individuals were affected by cancer in Canada, with 85,100 succumbingto the disease [11]. Addressing this issue is challenging due to the complex na-ture of cancer, which manifests as a diverse array of diseases at the tissue level.The heterogeneity of cancer poses a major challenge in terms of both therapy anddiagnosis [12].In terms of specific cancer types, prostate and lung cancers have the highestincidence in men, while breast and lung cancers are predominant in women [13].Among children, blood cancers and cancers affecting the brain and lymph nodesrank highest in terms of prevalence [14]. The development of cancer begins witha series of genetic mutations that alter normal cellular functions. This disruptionultimately leads to the dysfunction of crucial genes, resulting in uncontrolled cellproliferation [15].A key aspect of this uncontrolled growth is the absence of tumor suppressorgenes, which normally regulate cell division [16]. Consequently, cancer cells pro-liferate unchecked, leading to the progression of the disease. Understanding themolecular aspects of cancer is essential for devising effective strategies for diag-1nosis and treatment [15]. By reviewing cancer from a molecular perspective, wecan gain valuable insights into its mechanisms and develop targeted approaches tocombat this complex disease [17].In this chapter, we will describe the molecular events that ultimately cause can-cer and the strategies that a particular cell utilizes to overcome any modificationto its genetic material, along with a discussion of the most recent clinical treat-ments and technologies to cure cancer. Also, we will discuss the field of nuclearmedicine, providing a short history and finally, we will introduce the concept ofradiopharmaceutical therapy which is the major theme of this thesis.1.1 DNA Damage: The Molecular Cause of CancerIn the realm of molecular biology, deoxyribonucleic acid (DNA) damage repre-sents a common occurrence that arises from various sources, encompassing bothenvironmental factors and the intricate metabolic processes taking place within thecell. On a daily basis, a cell can encounter a staggering range of 1,000 to 1,000,000DNA lesions (any structural change in its structure) due to such damages [18]. Nu-merous types of DNA damage have been identified, each contributing to the overallcomplexity of maintaining genomic stability. In this section, we will review thedifferent biochemical processes that lead to the DNA damage within a living cell.Figure 1.1: The formation of 8-oxoG from guanine through the oxidative pro-cess. Guanine is one of the susceptible species to oxidation by hydroxylradicals (Figure from [19]).2Oxidative processes can lead to significant cellular damage, including oxidativedamage to DNA. Reactive oxygen species (ROS), such as hydroxyl radicals (.OH),are highly reactive and can cause oxidative damage. ROS can be generated fromvarious sources, including ultraviolet and ionizing radiation, as well as enzymaticreactions [20]. Guanine, one of the nucleic acid bases in DNA, is particularly sus-ceptible to oxidation by hydroxyl radicals due to its low ionization potential. Thisoxidation process converts guanine into 8-oxo-dG, which is considered one of themost abundant DNA lesions and a biomarker of oxidative stress. It is estimated thataround 100,000 8-oxo-dG lesions can occur per cell per day. Moreover, 8-oxo-dGhas a lower reduction potential than guanosine, making it prone to further oxidationand the formation of secondary oxidation products [21]. The relationship betweenoxidative stress and human health is significant. Oxidative stress, caused by animbalance between ROS production and antioxidant defenses, can lead to cellulardamage, DNA mutations, and various diseases, including cancer, cardiovasculardiseases, neurodegenerative disorders, and aging processes [22].Figure 1.2: different effects of oxidative stress-induced damage on humanhealth and its relation with common diseases (Figure from [19]).DNA crosslinking is yet another form of DNA damage, characterized by thecovalent linkage of two DNA strands or the formation of interstrand crosslinks[23]. This hinders the separation and unwinding of DNA during replication and3repair, impeding vital cellular functions. DNA crosslinking occurs when exoge-nous or endogenous agents react with two nucleotides of DNA, forming a cova-lent linkage between them [24]. Crosslinks can occur within the same strand (in-trastrand) or between opposite strands of double-stranded DNA (interstrand). Forexample, UVlight can induce crosslinks between pyrimidine residues, commonlytwo thymine residues, and is a primary cause of melanomas in humans [24].Alkylation of bases is another type of DNA damage that can occur due to ex-posure to alkylating agents found in the environment or produced as by-productsof cellular metabolism. Alkylation can result in the formation of lesions in DNAor RNA bases. These lesions can be cytotoxic, blocking replication and inter-rupting transcription, or mutagenic, causing mutations in the newly synthesizedDNA [25]. Common alkylated products include N7-methylguanine (7meG), N3-methyladenine (3meA), O6-methylguanine (O6meG), and methyl phosphotriesters(MPT).Base loss can occur when apurinic/apyrimidinic sites (AP sites), also known asabasic sites, are formed in DNA. It is estimated that around 1000 apurinic and 500apyrimidinic sites are generated in a cell each day [26]. In E. coli, adenine is pref-erentially inserted across from AP sites during DNA repair processes. Hydrolysis,a process wherein water molecules break chemical bonds, can lead to base lossand subsequent DNA damage. The hydrolysis of bases within the DNA moleculecompromises its integrity and can contribute to genomic instability [27].Additionally, the formation of bulky adducts represents another mechanism ofDNA damage. These adducts, formed by the covalent binding of certain moleculesto DNA, can distort the helical structure of the DNA molecule, affecting its repli-cation and transcription processes [28]. Bulky adduct formation involves the co-valent linkage of chemicals, such as benzo[a]pyrene, with DNA and proteins.Benzo[a]pyrene is a procarcinogen found in tobacco smoke, coal tar, and grilledmeats. It undergoes metabolic activation, forming a reactive metabolite that canform bulky adducts preferentially with guanine residues in DNA [29].Understanding the diverse array of DNA damage types is crucial for compre-hending the mechanisms by which DNA repair processes operate within the cell.These repair mechanisms are indispensable for maintaining genomic stability andpreventing the accumulation of mutations that could potentially lead to the devel-4opment of diseases, including cancer [30]. By elucidating the intricate pathwaysinvolved in DNA damage and repair, researchers aim to uncover novel therapeuticstrategies and interventions to mitigate the detrimental effects of DNA damage onhuman health [30].Figure 1.3: Base loss is the situation in which apurinic/apyrimidinic sites (APsites) are formed in DNA (Figure from [19]).Measuring DNA strand breaks is important for assessing DNA damage. Tra-ditional methods include sucrose gradient sedimentation, alkaline and neutral fil-ter elution, and nucleoid sedimentation [31]. However, current methods such aspulsed-field gel electrophoresis (PFGE) and the comet assay are widely used [32,33, 34]. PFGE separates DNA fragments based on their size, allowing the visual-ization of radiation-induced breaks. The comet assay, also known as single-cell gelelectrophoresis, assesses DNA damage at the individual cell level by observing themigration of fragmented DNA in an electrophoresis gel [35].Radiation-induced nuclear foci are accumulations of proteins at the site ofDNA damage caused by ionizing radiation. Proteins such as γH2AX, 53BP1,ATM, RPA, RAD51, and BRCA1 form foci and can be used as markers to detectand study DNA damage and repair processes [36]. These methods and markersplay crucial roles in understanding the extent of DNA damage, evaluating the ef-fectiveness of repair mechanisms, and assessing the impact of various agents andenvironmental factors on DNA integrity.1.2 Interaction of Radiation with Living MatterIn the field of nuclear physics, understanding the stability of nuclides is crucial.Unstable radionuclides undergo radioactive decay by emitting electromagnetic ra-5Figure 1.4: Different Experimental methods to measure DNA strand breaksA) Pulsed-field gel electrophoresis assay to measure the DNA damagedue to radiation, B) comet assay to assess DNA damage at the individualcell level. (Figure from [34])diation or charged particles as they approach stability. The stability of a nuclide isdetermined by the interplay between attractive strong forces and repulsive electro-magnetic forces. This balance is disrupted when the forces are disturbed, leadingto the nuclide becoming unstable and radioactive. Nature contains about 259 stablenuclides, highlighting the significance of studying the stability of nuclides.Apart from the interesting dynamics of radioactive elements from a physicalpoint of view, the interaction of this radioactive material with living matter is ofparticular interest. That is because most radioactive elements exist naturally andany living organism on earth is exposed to that. On the other hand, these moleculescan have biological applications in delivering high amounts of energy to the cellthat we don’t want to be alive (like cancerous cells). In this section, we will reviewthe effect of radiation on living organisms from a biochemistry point of view.1.2.1 Different Timescale of the Effect of Ionizing RadiationThe time scale of the processes in the interaction of radiation with living matterspans several orders of magnitude. To capture that in more detail, it is convenientto categorize the effects into three phases: physical phase, chemical phase, andbiological phase [18]. When the ionizing radiation first enters the body, its interac-tion with electrons of atoms causes ionizations and excitation events. The ionizedelectron can lead to a subsequent cascade of ionization events. For 1 Gy (1 Gy =61J1Kg ; see Section A.3 for more details) of absorbed dose, there are in excess of 105ionizations with the volume of every cell of diameter 10 m [37]. These events hap-pen in the time scale of femtoseconds to nanoseconds and are all considered in thephysical phase. In the chemical phase, the ionized atoms and electrons react withmolecules present in the environment (like water molecules) and break them apartinto unstable species. These unstable species which are highly reactive react withother molecules and create the so-called free radicals which are themselves alsovery reactive [38]. All of these events are complete within 1 ms of radiation expo-sure. The free radicals can be inactivated with sulphydryl compounds or can causestable chemical changes in biologically important molecules in the body (throughthe fixation reaction) [39]. The biological phase includes events from several sec-onds to many years. These events include the DNA damage mechanisms and theDNA damage response by the cell (which includes steps like sensing the damageby molecules and proteins, transducing the appropriate signals, and finally activat-ing the DNA damage response effectors like apoptosis, cell cycle arrest, etc), DNArepair, and etc [40]. The formation of misrepairs of DNA lesions and chromosomeaberration all happen at this phase in the time scale of several seconds to severalhours [41]. The progress of gene instability within cells with damaged DNA caneventually lead to the formation of detectable tumors which can happen in a fewweeks up to several years. The late reactions also can appear after months/yearsof being exposed to radiation that include fibrosis and telangiectasia of the skin,spinal cord damage, and blood vessel damage [37].1.2.2 Radiation-induced damage and the DNA damage responseRadiation-induced damage is a consequence of ionization, which occurs when radi-ation ejects electrons from molecules within cells. The damaging effects primarilyarise from the radiation’s ability to cause ionization in the DNA molecule [42]. Celldeath is predominantly a result of radiation affecting the DNA, as demonstrated byexperiments showing that high doses of radiation delivered to the cell membraneand cytoplasm do not cause cell death to the same extent as radiation affecting theDNA [43].As discussed before, various natural sources can cause damage to DNA, includ-7Figure 1.5: The interaction of ionizing radiation with living matter spans sev-eral orders of magnitude (Figure from [37]).ing oxidation and alkylation due to metabolism, ingested chemicals, and UVradiation.To counteract these types of damage, different repair mechanisms are in placewithin the cell. Base excision repair (BER) repairs damage to bases, single strandbreak repair (SSBR) fixes single strand breaks, double strand break repair (DSBR)handles double strand breaks, interstrand cross-link (ICL) repair deals with cross-links, mismatch repair (MMR) corrects base pair mismatches, and nucleotide ex-cision repair (NER) repairs bulky lesions or DNA adducts formed by UVlight andcertain drugs [44].Radiation exposure can lead to various types of DNA damage, with 1 Gy ofradiation causing approximately 105 ionizations, around 1000 single strand DNAbreaks (SSB), and 20-40 double strand DNA breaks (DSB) [34]. DSBs are con-sidered the most lethal type of lesion as they can cause issues during chromosomesegregation in mitosis [45]. DSBs can arise from primary radiation lesions as wellas replication-induced lesions, which occur during DNA replication and can appearhours after irradiation [46].The repair process involves various events, including the unfolding of chro-matin to expose the damaged DNA, recruitment of appropriate proteins, cessa-tion of transcription and cell-cycle progression, and monitoring of the repair [47].This coordinated response to DNA damage is known as the DNA damage response8(DDR). The DDR consists of different components, including sensors that activelysurvey the genome for damage, transducers that transmit the signal from sensorsto effectors, effectors themselves, such as programmed cell death and DNA repairpathways, and checkpoints that temporarily or permanently halt cell cycle progres-sion [48].The DDR system also has adaptive effects on gene transcription, mRNA trans-lation, and protein modification and degradation. Additional proteins can functionas activators or adaptors to amplify and regulate the signal within the DDR [49].One of the key signaling proteins in the DDR is the ataxia-telangiectasia mu-tated protein (ATM). It is activated in response to DNA double-strand breaks [50].ATM is a kinase that phosphorylates itself, as well as other proteins involved inDNA repair and cell cycle control, including CHK2, p53, and H2AX. Mutations inthe ATM gene lead to the development of ataxia-telangiectasia syndrome, which ischaracterized by radiosensitivity and a high risk of developing cancer due to im-paired DSB repair [51]. Also some other key damage sensors and their functionsinclude:• Specific glycosylases: These enzymes recognize and remove damaged basesin DNA, such as oxidized or alkylated bases. They act as damaged basedetectors and initiate the repair process [18].• Poly (ADP-ribosylation)-polymerases (PARPs): Loss of bases or phosphodi-ester bonds within DNA activates PARPs. They are involved in DNA repairand play a role in signaling DNA damage [52].• MRN complex: The MRN complex consists of MRE11, RAD50, and NBS1proteins. It acts as a sensor for double-strand breaks (DSBs) in DNA. NBS1,the product of the Nijmegen breakage syndrome gene, has a critical role inrepairing DSBs [53].• Ku proteins: Ku70 and Ku80 proteins recognize and bind to the ends ofDSBs, facilitating the repair process [54].• RPA complex: The Replication Protein A (RPA) complex binds to and cov-ers single-stranded DNA regions generated during replication or DNA repair,protecting them and facilitating the repair process [55].9These sensors detect specific types of DNA damage and initiate signaling trans-ducers to activate downstream effector pathways.Overall, damage sensors and signaling transducers work together to recognizeDNA damage and activate the appropriate cellular responses, including DNA re-pair, cell cycle checkpoints, and cell death mechanisms, to maintain genomic in-tegrity [56].1.3 Approaches to Treatment of CancerWithin the realm of cancer treatment, various methods have been employed tocombat the disease and enhance patient outcomes. These strategies encompassa range of approaches, including palliative care, curative care, preventive care,supportive care, survivorship care, and end-of-life care. Each of these methodsaddresses different aspects of the disease and aims to improve patients’ quality oflife, manage symptoms, and provide appropriate treatment interventions [57].Palliative care is centered around relieving symptoms, pain, and stress associ-ated with cancer, with a focus on enhancing patients’ overall quality of life. Thisapproach includes providing emotional support to patients and their families, ad-dressing psychological aspects, and alleviating the burden of the disease [58].Curative care, on the other hand, aims to achieve a complete cure for cancer.This is typically pursued through a combination of treatment modalities such assurgery, radiation therapy, chemotherapy, and immunotherapy. Curative care isoften recommended for patients with a higher life expectancy or those diagnosedwith early-stage and localized cancer [59].Preventive care plays a vital role in cancer management by focusing on pre-venting the development of cancer or detecting it at an early stage when treatmentis most effective. This includes regular cancer screenings like mammograms, Papsmears, colonoscopies, and genetic testing, allowing for early intervention and im-proved outcomes [60].Survivorship care involves long-term monitoring and control of cancer sur-vivors after completing their primary treatment. It encompasses regular follow-upvisits, health screening, surveillance for late effects, and monitoring for cancer re-currence. The goal is to ensure optimal health and well-being in the post-treatment10phase.End-of-life care is provided for patients with advanced or terminal cancer,where curative treatment is no longer effective or needed. The primary focus ison improving comfort and quality of life during the final stages of the illness. Painmanagement, symptom control, and emotional support for both patients and theirfamilies are integral components of this type of care [61].In addition to the broad categories of cancer treatment, it is important to exam-ine the specific treatments and technologies employed for these purposes. Variousapproaches have been developed to combat cancer, including chemotherapy, im-munotherapy, radiation therapy, and surgery, among others [62]. Each of thesemethods encompasses distinct subcategories that differ from one another. For ex-ample, external beam radiotherapy and radiopharmaceutical therapy both fall underthe umbrella of radiation therapy; however, they exhibit significant differences intheir approaches and mechanisms of action.Chemotherapy, a widely used treatment modality, employs various mecha-nisms of action to combat cancer. It can target specific molecular pathways es-sential for cancer cell survival and growth, leading to disruption of cell divisionor induction of programmed cell death [63]. Additionally, some chemotherapyagents induce DNA damage in cancer cells, resulting in DNA cross-links, breaks,or mutations that activate cell death pathways [64]. Chemotherapy can be curative,adjuvant (given after surgery or radiotherapy to remove remaining cancer cells),neoadjuvant (administered before surgery or radiotherapy to shrink tumors), orpalliative (aimed at managing symptoms and improving quality of life in advancedor metastatic cancer) [65].Radiation therapy, considered one of the most successful cancer treatmentmethods, utilizes various techniques such as external beam radiotherapy, brachyther-apy, and radiopharmaceutical therapy (RPT) [66]. These approaches involve theuse of ionizing radiation to target and destroy cancer cells while sparing healthytissues. Radiation therapy can be employed as a standalone treatment or in con-junction with surgery or chemotherapy, depending on the specific cancer type andstage [67].Immunotherapy has emerged as a promising approach to cancer treatment, har-nessing the power of the immune system to recognize and attack cancer cells [68].11Immune checkpoint inhibitors, for instance, enhance the anti-tumor immune re-sponse by blocking receptors on T-cells or tumor cells that inhibit T-cell activity[69]. Adoptive cell transfer involves collecting and genetically engineering thepatient’s own immune cells, such as T-cells, to specifically recognize and targetcancer cells. Tumor vaccines aim to stimulate the immune system to recognize andattack cancer cells, either preventively or therapeutically [70]. Oncolytic viruses,genetically engineered to selectively target and destroy cancer cells, represent an-other avenue of immunotherapy [71].Surgery plays a vital role in cancer treatment, particularly for early non-metastatictumors. It involves the removal of cancerous tumors along with a margin of healthytissue [72]. Diagnostic surgery, prophylactic surgery, debulking surgery, and re-constructive surgery are among the different surgical approaches used based onthe specific circumstances [73]. Sentinel lymph node biopsy, a surgical procedure,helps determine if cancer has spread to nearby lymph nodes [74].1.4 Nuclear MedicineNuclear medicine encompasses the scientific and technological utilization of ra-diolabeled compounds for diagnostic and therapeutic purposes. This field also ex-plores the concept of theranostics, which integrates both diagnostic and therapeuticfunctionalities which are described in detail in [75]. To initiate the process, ligandsare labeled with specific radioisotopes.In terms of imaging mechanisms, radionuclides emit positrons (which eventu-ally form gamma pairs) or gamma rays. As these gamma rays interact with thebody (through scattering or absorption), some exit without any interaction. De-tecting these gamma rays using gamma cameras and subjecting the data to vari-ous processes such as signal processing, corrections, and reconstruction, enablesthe generation of an image depicting the distribution of radionuclides, and conse-quently, the ligands [76].Two main types of imaging techniques exist: single photon imaging and positronemission imaging [77]. Single photon imaging involves the use of radionuclidesthat decay through gamma-ray emission. By capturing an image of the radionu-clide distribution from a specific angle, a planar image is obtained (which is called12scintigraphy). Although lacking depth information, this image can still contributeto the diagnostic process. However, by acquiring images from multiple angles, atomographic image can be constructed (which is called SPECT or single photonemission computed tomography), offering cross-sectional insights into the patient[78].In positron emission imaging, radionuclides emit positrons during the decayprocess. These positrons have a short half-life and annihilate with electrons, re-sulting in the emission of two nearly anti-parallel 511 keV gamma rays. A gammaimaging system detects these gamma pairs via coincidence detection, facilitatingthe creation of a radioactivity map within the body [8].Nuclear medicine techniques can measure a wide range of biological processes,including tissue perfusion, glucose metabolism, somatostatin receptor status in tu-mors, dopamine receptor density in the brain, and gene expression [79]. The highsensitivity of radiation detectors and the ability of radiochemists to label com-pounds with high specific activity enable the formation of high-quality images evenwith very low concentrations of compounds, such as nanomolar or picomolar levels[80]. This allows for the safe injection and tracking of trace amounts of compoundsover time without disturbing the biological system. Similar to CT scans, nuclearmedicine studies involve a small radiation dose, which varies depending on the ra-dionuclide and the distribution of the radiolabeled compound being studied. Thesafe dosage for human studies is determined through careful dosimetry for eachnewly approved radiopharmaceutical used in humans [81].1.4.1 A Brief History of Nuclear MedicineThe history of nuclear medicine is a complex subject involving numerous scien-tists, engineers, technologists, and physicians. While a comprehensive overviewis beyond the scope of this thesis, there are several key highlights that providecontext for the development of nuclear medicine. The origins of nuclear medicinecan be traced back to the late 19th century with the discoveries of radioactivity byHenri Becquerel in 1896 and radium by Marie Curie in 1898. These discoveriesclosely followed Wilhelm Roentgen’s discovery of X-rays in 1895. X-rays and ra-dium were quickly adopted for medical use, particularly in creating shadow images13where radiation passed through the body onto photographic plates [82].The discovery of X-rays allowed physicians to visualize the inside of the hu-man body for the first time, particularly for imaging bones. X-rays quickly becamethe preferred method for producing radiographs due to their speed and improvedcontrast compared to radium or other naturally occurring radionuclides available atthe time [83].The foundations of nuclear medicine were established between 1910 and 1945.In 1913, Georg de Hevesy developed the principles of the tracer approach and ap-plied them to study the absorption and translocation of radioactive lead nitrate inplants. The first human study using radioactive tracers was conducted in 1927,measuring the transit time of blood using radon injected intravenously [84]. Theinvention of the cyclotron in the 1930s expanded the range of biological processesthat could be studied by artificially producing new radionuclides. De Hevesy pio-neered the use of these radionuclides in studying biological processes in plants andred blood cells. Following World War II, nuclear reactor facilities developed duringthe Manhattan Project were utilized to produce sufficient quantities of radioactiveisotopes for medical applications [85].In the 1950s, technological advancements allowed for imaging the distribu-tion of radionuclides throughout the human body instead of limited measurementpoints. Key milestones included the development of the rectilinear scanner in 1951by Benedict Cassen and the Anger camera in 1958 by Hal Anger, which served asthe precursor to modern nuclear medicine single-photon imaging systems [86]. In1951, the use of positron emitters and their advantageous imaging properties weredescribed by Wrenn and colleagues [87].In the early years of nuclear medicine, which lasted until the early 1960s, thefield mainly relied on the use of iodine-131 (131I) for studying and diagnosingthyroid disorders. Additionally, various other radionuclides were employed, buteach was suitable for only a limited number of specific organs [75].The introduction of Technetium-99m (Tc-99m) for medical imaging in 1964by Paul Harper and colleagues was a significant milestone in the advancementof nuclear medicine [88]. Tc-99m emitted gamma rays that were highly suitablefor imaging purposes and offered great flexibility for labeling various compounds,enabling the study of virtually every organ in the body. Moreover, Tc-99m could be14generated in a long-lived form using generators, ensuring a readily available supplyof the radionuclide. Today, Tc-99m is the most commonly used radionuclide innuclear medicine [89].Another crucial development was the mathematical algorithms used to recon-struct tomographic images from a series of angular views around the patient. Thistransformative technique revolutionized medical imaging as a whole, leading tothe creation of CT, PET, SPECT, and MRI. It replaced the two-dimensional repre-sentation of the three-dimensional radioactivity distribution with an accurate three-dimensional representation [90]. This breakthrough facilitated the development ofSPECT (e.g. by Kuhl and colleagues [91]) and PET (e.g. by Phelps and colleagues[92]), marking the onset of the modern era of nuclear medicine.The widespread use of positron-emitting radionuclides in PET imaging re-quires either an onsite accelerator or delivery of PET radiopharmaceuticals fromregional radio pharmacies due to their short half-lives. In the United States, thereis now a PET radiopharmacy within 100 miles of around 90% of hospital bedsto meet this demand. The growth of clinical PET has been driven by the utilityof 18F-fluorodeoxyglucose, a metabolic tracer with applications in cancer, heartdisease, and neurological disorders [93, 75].While the underlying physics of nuclear medicine remains unchanged, thereare ongoing advancements in the technology used to produce radioactive tracersand obtain images of their distributions. Major improvements in nuclear medicinetechnology are expected through the integration of developments in detector andaccelerator physics, electronics, signal processing, and computer technology. Theaccurate quantification of tracer concentrations in specific structures, measurementof biological processes, and effective communication of this information to physi-cians in a clinically meaningful and biologically relevant format are important chal-lenges for the future.Furthermore, the refinement of dosimetry models will enhance the character-ization of radiation exposure, making nuclear medicine even safer than it alreadyis. Physics will continue to play a vital and ongoing role in delivering high-quality,cost-effective, quantitative, reliable, and safe biologic assessments in living hu-mans [94, 95, 96].151.4.2 Radiopharmaceutical therapy, the triumph of nuclear medicineRadiopharmaceutical therapy (RPT) has emerged as a promising and successfultargeted approach for combatting various forms of cancer (see Figure 1.7 for avisual demonstration of RPT in a vclinical setting). Through the use of pharma-ceuticals, radiation is administered either systemically or locally, specifically tar-geting cancer cells or accumulating through natural processes. The radionuclidesemployed in RPT emit detectable photons, allowing for non-invasive visualizationof the therapeutic agent’s distribution within the body. RPT has exhibited consider-able effectiveness while minimizing detrimental side effects, distinguishing it fromalternative systemic cancer treatments. The recent approval of multiple RPT agentsby the FDA has highlighted the extraordinary potential of this innovative treatment.This comprehensive examination delves into the fundamental characteristics, clin-ical advancements, and the associated obstacles encountered in the realm of RPT(See Sgouros et al. [7] for a more detailed discussion).Basic Overview of RPTThe core mechanism of RPT involves the obliteration of cells through radiation-induced elimination. Extensive research into the consequences of radiation ontissues and tumors commenced shortly following the revelation of radiation andradioactivity. RPT capitalizes on the considerable reservoir of expertise acquiredfrom radiotherapy [97]. Nevertheless, RPT deviates from conventional radiother-apy, necessitating a comprehension of the distinctive components that shape itstherapeutic impact.An essential question about RPT focuses on the agent’s location and how longit stays, which can be modeled mathematically (see Chapter 2). By delving intothe subject of ”Dosimetry,” we can gain a better understanding of the absorbeddose that distinguishes tumor cells from healthy tissue (see Section A.3 and Sec-tion 1.4.2). This information acts as a metric for evaluating the potential effective-ness of the treatment (see [7]).Within the realm of photons, in a very general sense, we can say that we en-counter two distinct ”flavors”: X-rays and γ-rays. X-rays generally stem fromelectron transitions within orbits and generally possess lower energy levels com-16pared to γ-rays (it can also stem from the acceleration of a charged particle underthe influence of the electric field of the nucleus which is called Bremsstrahlungradiation). While radionuclide photon emissions serve as valuable tools for vi-sualizing the distribution of RPT, they are not suited for localized administrationof cytotoxic radiation. The imaging of photon energies covers a broad spectrum(ranging from 70 to 400 keV), yet optimal results for all nuclear medicine imag-ing devices such as γ-cameras and single-photon emission computed tomography(SPECT) cameras are achieved within the energy range of 100 to 200 keV. Addi-tionally, certain radionuclides also emit positrons, which, in turn, generate 511-keVphotons detectable by positron emission tomography (PET) cameras.Electron emissions encompass a spectrum of energy levels and decay types,including Auger electrons, β -particles, and monoenergetic electrons, which holdsignificance in the context of RPT. Auger electrons, arising from suborbital transi-tions, manifest as emissions with a limited range, typically spanning 1–1000 nm,contingent upon their energy of release. If the RPT drug localizes within the nu-cleus of a cell, these emissions possess the potential for potent cytotoxicity [98, 99].Despite the substantial therapeutic efficacy exhibited in preclinical investigations,the widespread adoption of Auger electron-emitter RPT remains limited in humanstudies [100].β -Particles represent electrons discharged from the nucleus, offering a rela-tively greater tissue penetration range (approximately 1–5 mm), making them aprevalent emission type for RPT agents. This preference can be attributed, inpart, to the extensive accessibility of β -particle-emitting radionuclides, many ofwhich also emit detectable photons within a conveniently imaged energy range.Over the past four decades, notable introductions in the field include samarium-153, lutetium-177, yttrium-90, and iodine-131 (see Sgouros et al. [7] for more de-tails). These radionuclides which are commonly called medical radioisotopes canbe generated using particle accelerators or generators which are discussed in de-tail by Chandra and Rahmim [8]. Among these, iodine-131 has gained significantrecognition and employment in the treatment of thyroid cancer. Several other β -emitting radionuclides have undergone investigation or consideration. However,factors such as limited availability, challenging radiochemistry procedures, andforemost, the lack of commercial justifications to surmount regulatory and financial17obstacles, have hindered their widespread adoption [101].Possible Targets for Radiopharmaceutical TherapyThe potential of RPT extends to any cancer that meets the necessary targeting re-quirements for radionuclide delivery. However, comprehensive investigations intoRPT have been limited to specific cancer types. The selection of these cancer typesaligns with factors such as the evolution of available targets, the accessibility ofRPT agents designed for those targets, and the proficiency and focus of clinicalresearchers within academic institutions.RPT has historically exerted a significant influence on thyroid malignancies,a trend that endures to this day. The exploration of hematological malignanciesstarted in the early 1990s and remains an area of ongoing fascination. Hepaticmalignancies and prostate cancer have experienced the most notable surge in RPTresearch since the 1980s. This surge coincides with the development of novel RPTagents, such as 90Y-loaded microspheres for hepatic malignancies and β -emitter-labeled and α-emitter-labeled small-molecule constructs targeting the prostate-specific membrane antigen (PSMA) [7]. Notably, the approval of the α-emitter223Ra by the FDA (happened in May 2013 [102]) has substantially bolstered in-terest in RPT for prostate cancer. While solid cancers like colorectal and breastcancer continue to attract attention, they have yet to witness the breakthrough ad-vancements observed in hepatic and prostate cancer research. Neuroendocrine can-cer in which the expression of the somatostatin receptor increases significantly, hasremained a consistent subject of investigation, culminating in the FDA’s approvalof 177Lu-labelled DOTATATE, marking a significant milestone in RPT targetingthese particular cancers [103, 104].The development of RPT requires expertise in various disciplines, includingradiochemistry, radiobiology, oncology, pharmacology, medical physics, and ra-dionuclide imaging. However, RPT has been an underexplored and less recognizedtreatment modality in the past. The recent approval of RPT agents targeting neu-roendocrine cancers, phaeochromocytomas, and bone metastases of prostate can-cer, as well as promising results with other alpha-particle-emitting radionuclides,has renewed interest in RPT [105, 106, 107]. Pharmaceutical companies are now18RPT agent Indication Properties[131I]mIBGAdrenergicreceptor and tumoursActive uptake mechanism viathe adrenaline transporterand storage in presynapticneurosecretory granules131I-labelledaCD45Bone marrowtransplantpreparation131I-based antibody targetingCD45+ cells for bonemarrow ablation beforetransplantation177Lu-labelledDOTA-JR11NeuroendocrinetumoursSSR-mediated binding andinternalization177Lu-labelledDOTATATENeuroendocrinetumoursSSR-mediated binding177Lu-labelledPSMA-617Prostate cancer,tumour neovasculaturePSMA-mediated binding177Lu-labelledNeoBOMB1GRPR+ tumours GRPR binding177Lu-labelledDOTA-JR11NeuroendocrinetumoursSSR-mediated binding andinternalization177Lu-labelledPSMA-R2Prostate cancer,tumour neovasculaturePSMA-mediated binding andinternalizationXofigo(223Radium dichloride)Prostate cancer First alpha therapy approveI-131 Thyroid cancer Biological uptakeTable 1.1: Some examples of ligands used for radiopharmaceutical therapy(See [7] for a more detailed discussion).recognizing its potential and investing in its development.DosimetryAccurate anticipation of treatment response and potential toxicity is critical for theoptimal administration of cancer therapy. Radiopharmaceutical therapy operatesthrough a well-defined physical parameter known as absorbed dose (D), denotingthe energy absorbed per unit mass of tissue and governing its biological effects.Extensive experience in radiotherapy has established absorbed dose as a reliablepredictor of biological response [108]. However, in chemotherapy, targeted bio-19logical therapy, and immunotherapy, there lacks an equivalent dosimetry concept.In the context of RPT, dosimetry serves as a means to conduct real-time pharma-codynamic studies on treated patients. By incorporating dosimetry analysis intopatient treatment, it becomes possible to calculate the absorbed dose in tumor ver-sus normal organs, thereby estimating the likelihood of treatment success.Dose, in simple words, is basically the amount of energy (in Joule) deliveredto 1 kg of matter. In other words:D=∆E∆m,in which D is the dose in Gray, ∆E is the absorbed energy in Joule and ∆m is themass of the matter that absorbed the radiation. However, for radiopharmaceuticaltherapy purposes, this formalism should be written as:D(T ← S) = A˜(S)S(T ← S).in which D is the absorbed dose by the “target” organ irradiated from the “source”organ, A˜(S) is the area under the time-activity curve (which is called time-integratedactivity), and S(T ← S) is the S-factor which determines the dose to the target perdecay of the radionuclide in the source (see Figure 1.6). For a detailed discussionabout the concept of S-factor and dose calculation see Section A.3.Figure 1.6: Dose calculation in radiopharmaceutical therapy. Note that in bthe S-factor coefficient has been written explicitly showing the individ-ual terms making it up. In this formula, ∆ represents the total energyemitted from the source organ, φ is the fraction of energy that is ab-sorbed in the target organ (see Section A.3), and M is the mass of thetarget organ (Figure is from [109]).20Figure 1.7: The clinical practice in radiopharmaceutical therapy. Specific lig-ands are labeled with radioactive elements and then injected into the pa-tient to target the cancer cells within the body.21Chapter 2Modeling the Kinetics ofRadiopharmaceuticals UsingPhysiologically BasedRadioPharmacoKinetic (PBRPK)ModelsA method is more important than adiscovery since the right methodwill lead to new and even moreimportant discoveries.Lev LandauImportant Note: Elaborate technical details of the PBRPK modelare described in Appendix A which should be studied along with thischapter.In recent years, modeling and simulation methods (e.g. physiologically basedpharmacokinetic (PBPK) models) have gained increasing recognition as valuable22tools within the pharmaceutical industry. These techniques offer a range of bene-fits, including the identification and validation of drug targets, prediction of drugefficacy, and assessment of crucial factors such as ADMET which stands for Ab-sorption, Distribution, Metabolism, Excretion, and Toxicity (see [110] for moredetails). By enabling effective integration and extraction of knowledge from data,modeling aids in better decision-making and plays a pivotal role in predicting hu-man dosage, developing new formulations, designing clinical trials, and guidingregulatory decisions.This chapter introduces a unique type of physiologically-based pharmacoki-netic (PBPK) model tailored specifically for simulating the kinetics of radiophar-maceuticals within the body. The development of this specialized model holdssignificant promise as it allows for simulations to be conducted prior to the costlyundertaking of designing and executing large-scale clinical experiments. By em-ploying this model, researchers can gain valuable insights into the behavior of ra-diopharmaceuticals, providing a cost-effective means of optimizing experimentaldesign and informing subsequent clinical investigations.2.1 IntroductionPhysiological modeling, also known as physiology-based mathematical modeling,integrates knowledge of physiological processes with physicochemical attributesor other relevant information to predict or simulate complex biological properties.The level of detail in these models can vary depending on the desired predictions,available knowledge, and required accuracy. They can focus on cellular processes,tissues, organ systems, or entire organisms, providing a mechanistic understand-ing of biological systems. Although the size, complexity, and parameterizationchallenges of physiological models have historically limited their widespread ap-plication in pharmaceutical companies, recent advancements in high-performancecomputing have overcome these constraints. The availability of biological pathwayinformation, genetic data, molecular mechanisms, and improved biological mea-surements has facilitated the parameterization of these models. Modern physio-logical models can address intricate questions and account for the interdependenceof component models, making them valuable tools in pharmaceutical research and23development.In recent years, the significance of in-silico, computational, and virtual modelsand clinical trials has gained considerable attention, as highlighted in our recentTDT grant. Building upon this premise, our study aims to delve into the expand-ing realm of physiologically-based pharmacokinetic (PBPK) models, which havealready provided valuable insights into crucial factors and optimal solutions at thepopulation level [111, 112]. In this context, we propose the utilization of physi-ologically based radiopharmacokinetic (PBRPK) models to assess and predict thebehavior of various radiopharmaceuticals prior to their administration to patients.This approach holds great promise for personalizing and designing optimal treat-ment plans for radiopharmaceutical therapy (RPT) recipients, ensuring tailored so-lutions for each individual.Furthermore, these computational models offer an opportunity to streamlinethe selection process of novel radiopharmaceuticals for clinical translation. Bysimulating their behavior within a ”virtual environment,” we can identify the mostpromising candidates without allocating extensive resources to conventional clin-ical trials. This aligns seamlessly with the overarching theme of in silico/compu-tational/virtual clinical trials, which are gaining momentum in contemporary re-search [113, 114]. The importance of computational models and trials has alsobeen recognized by regulatory bodies. The Food and Drug Administration (FDA)has provided increasing guidance on the integration of such models in regulatorysubmissions, acknowledging their value in informing decision-making processes[115, 116]. Moreover, the European Union’s REACH (Registration, Evaluation,Authorization, and Restriction of Chemicals) legislation emphasizes the adoptionof in silico methods to reduce the reliance on animal testing [117]. Notably, the2023 FDA legislation represents a significant milestone, enabling new drugs toprogress to human trials after successful rounds of ”non-clinical tests,” which ex-plicitly include computer modeling.By embracing computational models and their application in clinical research,we aim to highlight their growing importance and showcase their potential in revo-lutionizing drug development and treatment planning in a more efficient and ethicalmanner.242.2 Background and Previous ModelsPhysiologically based pharmacokinetic (PBPK) models are primarily constructedbased on key physiological assumptions regarding the system of the body. In thecontext of simulating the kinetics of radiopharmaceuticals, PBPK models incorpo-rates a comprehensive representation of organs crucial to the modeling objective.Figure 2.1: The modeled organs in ourPBRPK model. The red and bluetubes represent the arteries andveins respectively.There have been previous attemptsin modeling the kinetics of radiophar-maceuticals ([118, 119, 120, 121, 122,123, 124, 125, 126, 127]). How-ever, their structures were designed ina way that was not easily scalable. Tobe more specific, the previous modelswere using the concept of “parallel”tracks to keep track of different speciesin the body like the labeled and unla-beled radiopharmaceuticals (see [111]as an example). The prior attempts hada number of challenges, the most im-portant of which was the fact that theywere not easily scalable. For instance,adding the concept of albumin interac-tion to the model (a new attempt pur-sued in our work) would require addingseveral other “parallel tracks” to themodel which makes it very hard andcomplicated to implement. In this thesis, we performed some major upgrades onthe previous modeling frameworks that are summarized in Section 2.3 and Sec-tion 6.4.Figure 2.1 illustrates the inclusion of specific organs in this model, which canbe classified into three distinct subgroups based on their characteristics and inter-actions with radiopharmaceuticals. The first subgroup comprises organs that do notpossess prostate-specific membrane antigen (PSMA) enzymes, commonly referred25to as receptor-negative organs. These include the brain, lungs, heart, adipose tis-sue, skin, bone, bone marrow, and muscle. As these organs lack PSMA receptors,their interactions with radiopharmaceuticals differ from those in PSMA-expressingtissues.The second subgroup consists of organs expressing PSMA enzymes but ex-hibiting non-specific binding with radiopharmaceuticals, commonly known as or-gans at risk. This subgroup encompasses the salivary glands, kidneys, spleen,prostate (in the case of prostate cancer imaging or therapy), liver, gastrointestinal(GI) tract, and tumor tissues. Understanding the behavior of radiopharmaceuticalsin these organs is crucial, as they may experience specific binding and potentialuptake, necessitating careful assessment of their impact and associated risks.By incorporating these organ subgroups into our PBPK model for radiophar-maceutical kinetics, we can gain a comprehensive understanding of the distribu-tion, metabolism, and elimination of these agents within the body. This modelingapproach enables us to investigate and predict the behavior of radiopharmaceuti-cals prior to costly clinical trials, providing valuable insights and optimizing studydesign for more efficient and informed research.Examining a magnified view of these organs reveals their internal structures,as summarized in Figure 2.2. This illustration, for the time being, disregards thepresence of radiopharmaceuticals and focuses on four major structures within theorgans:• Vasculature Structure: The network of blood vessels, including veins andarteries, through which the radiopharmaceuticals will circulate after beinginjected into the patient.• Interstitial Structure: The interstitial space, situated between cells withinthe organs, where the radiopharmaceuticals will enter from the vasculaturestructure. This space provides an opportunity for interactions with the PSMAenzymes expressed on the cell surfaces.• PSMA Enzymes: These enzymes are present on the cell membranes andare responsible for binding with the radiopharmaceuticals, forming ligand-enzyme complexes.26• Internal Volume of Cells: Once the ligand-enzyme complexes are formedin the interstitial space, they have the potential to enter the cells through aprocess known as internalization. Subsequently, degraded PSMA ligands arereleased from the cells.Figure 2.2: Different structures inside the tissue. These structures includevasculature structure, interstitial volume, PSMA enzymes expressed onthe cells and internal volume of the cells.After injection, the radiopharmaceuticals traverse the bloodstream via the veinsand arteries, eventually reaching the organs. Once inside the organs, they enterthe vasculature structure, enabling them to move into the interstitial space betweencells. It is within this interstitial space that the radiopharmaceuticals have an oppor-tunity to interact with the PSMA enzymes expressed on the cell surfaces, leadingto the formation of ligand-enzyme complexes. These complexes may then undergointernalization, allowing them to enter the internal volume of the cells. Eventually,the degraded PSMA ligands are released from the cells through various clearanceprocesses.To illustrate the various mechanisms described above, compartments can beemployed, as depicted in Figure 2.3. These compartments are interconnected usingordinary differential equations (ODE), enabling the representation of the dynamicinteractions within the body. In addition to incorporating physiological factors, itis crucial to model the diverse interactions that radiopharmaceuticals may undergo27within the body which are discussed in Section 2.3.2.3 Improving the PBPK Models: Towards PBRPKAs we discussed in Section 2.2, the previous implementations of the PBPK mod-els for radiopharmaceuticals had some challenges. However, we resolved the mainchallenges of the previous models and developed the concept of reaction graphs(see Section 2.3, and Section 6.4 for a detailed discussion) to make the model scal-able, and utilized the most recent notations in the community of scientific comput-ing to easily manage the huge number of variables and parameters in the model(see Section A.1). In this section, we will go through the details of the new im-proved model. The elaborate details for model re-implementation can be found inAppendix A.In general, five distinct species circulate throughout the body: hot and coldspecies (as shown in Figure 2.4), AlbHot (albumin-hot complex), AlbCold (albumin-cold complex), and albumin itself. Albumin, a highly abundant protein in theserum, plays a critical role in regulating the kinetics of various molecules withinthe body. For example, hormones bind to albumin, allowing them to circulate uni-formly and be released as needed. Given albumin’s significant influence on thekinetics of circulating molecules, researchers have explored its potential in en-hancing radiopharmaceutical therapy. Moreover, due to the leaky nature of tumorvasculature, albumin can potentially infiltrate the interstitial space of tumors. Thischaracteristic makes albumin a potential tool for improving the targeting efficiencyof tumors in radiopharmaceutical therapy. However, these factors have not beenincluded in previous PBPK models as applied to RPTs which we pursue in thiswork (see Chapter 5 for more details).By incorporating these species and their interactions into the model, a compre-hensive understanding of the behavior and potential therapeutic impact of radio-pharmaceuticals can be obtained. This approach not only captures the complexdynamics of radiopharmaceuticals within the body but also offers insights intoleveraging albumin’s properties for enhanced targeting and therapy in the contextof radiopharmaceutical treatment.The reaction graph is in fact a concise way of showing the following set of28Figure 2.3: The compartmentalized structure of organs in the PBPK model.All of the biological details discussed in Figure 2.2 can be modeled ascompartments with certain inputs and outputs.Figure 2.4: Interactions of the different species with each other. The yellowcircles represent the reactions between species and those circles labeledwith a two-way arrow indicate that the reaction is a two-way reaction.The reactions that are not two-way are the decay process of radiophar-maceuticals.29chemical reactions:H+Albkalbon−−⇀↽−kalboffAHC+Albkalbon−−⇀↽−kalboffACH λ−−→ CAH λ−−→ ACin which AH, AC is the same as AlbHot and AlbCold in Figure 2.4 and representsthe ligand-albumin complex, while H and C represent the hot and cold speciesrespectively (see Figure 1.7), and λ is the decay constant of the radioisotope con-nected to the ligand.The interplay between the aforementioned species can be mathematically rep-resented by the following system of differential equations:dHdt=−λH− kalbon H ∗ [Alb]+ kalbo f fAH (2.1)dCdt= λH− kalbon C ∗ [Alb]+ kalbo f fAC (2.2)dAHdt=−λAH+ kalbon H ∗ [Alb]− kalbo f fAH (2.3)dACdt= λAH+ kalbon C ∗ [Alb]− kalbo f fAC (2.4)Alb= Alb0−AH−AC (2.5)in which H and C represent the hot and cold species respectively (see Figure 1.7),kalbon and kalbon are the rate constant of the ligand-albumin reaction in forward andreverse direction respectively, [Alb] is the concentration of albumin, AH is thealbumin-hot complex, λ is the decay constant of the radioisotope, and finally Alb0is the initial concentration of albumin.The ”chemical” interactions among the species can be integrated with the phys-iological structure of the body, as illustrated in Figure 2.5, to form a comprehen-sive physiologically-based pharmacokinetic (PBPK) model. This amalgamation30enables the representation of the entire system using a set of differential equations(for the details of the ODE system see Appendix A.)Figure 2.5: The detailed structure of PBPK for tumors, receptor-positive or-gans, and receptor-negative organs. Note the leakage of albumin andalbumin-bound radiopharmaceuticals to the interstitial space of the tu-mor.2.4 Systems Biology Markup Language and ModelReproducibilityThe Systems Biology Markup Language (SBML) is a widely adopted XML-basedformat that serves as a means of communication and storage for computationalmodels of biological processes. As an open standard freely available to the scien-tific community, SBML has gained substantial recognition and support. Its exten-sive software ecosystem and a dedicated community of users and developers havecontributed to its widespread use in the field of systems biology. SBML offers31the versatility to represent various types of biological phenomena, including butnot limited to metabolic networks, cell signaling pathways, regulatory networks,and infectious diseases. Due to its comprehensive features and wide-ranging ap-plicability, SBML has been proposed as the prevailing standard for representingcomputational models in systems biology. Its usage ensures interoperability, fos-ters collaboration, and facilitates the exchange of models and data across differentresearch groups, thereby promoting the advancement of scientific knowledge in thefield.In order to ensure the reproducibility of the model and its associated results,we implemented our PBRPK model within the SimBiology toolbox in MATLAB,as depicted in Figure 2.6. Additionally, the model was exported as an SBML ex-tension, allowing it to be loaded into any software that supports SBML as an input.This facilitates easy simulation of the model in various computational environ-ments. Furthermore, to enhance the ease of result regeneration, all population-measured parameters were included within the SBML file, streamlining the processof reproducing the obtained results.2.5 SummaryIn summary, we made some improvements to the previous PBPK models and madethem more scalable (in the sense that more complicated scenarios can be simulatedwithout challenging implementation problems), and we developed the concept ofPBRPK models. In the PBRPK model, we developed the concept of a reactiondiagram to capture the interaction of radiopharmaceuticals with different species inthe body. We then implemented the whole system in Simbiology Matlab and sharedthe SBML implementation of the model to enable easy model re-implementation.For more discussion about our contribution see Section 6.4.32Figure 2.6: Structure of the model implemented in Matlab Simbiology. The boxes indicate the compartments and blueovals represent species. Yellow circles represent the reactions between species and the solid lines connecting thespecies to reaction circles determine which elements react with each other.33Chapter 3In-silico Investigation of theCompetition Between Hot andCold Radiopharmaceuticals3.1 IntroductionIt is often a common intuition in external beam radiotherapy that increasing theamount of irradiation leads to a proportional increase in the dose delivered to thetumor (and other organs at risk). However, in the case of radiopharmaceuticaltherapy, because of the competition between hot and cold species, increasing theinjected amount does not necessarily lead to a proportional change in the deliv-ered dose to the tumor (or OAR). Three factors playing important roles in thisphenomenon are the receptor density of the target (which itself can depend on thevolume), the amount of injected hot molecules, and the amount of injected coldmolecules. We have used our PBRPK model to study this phenomenon in moredetail and explore any chance to utilize this phenomenon to increase therapeuticefficacy.The interaction between hot and cold species happens only in the receptor-positive organs (those organs that express the target receptor; see Chapter 2). The34interaction is as follows:H+R−−⇀↽− HRC+R−−⇀↽− CRin which H, C, HR, CR represent the hot, cold, receptor-hot complex, and receptor-cold complex species respectively (see Figure 1.7). Note that since the number ofreceptors is limited, then we observe the competition between hot and cold speciesin binding to the receptors. In other words, either hot or cold species occupy thefree receptors, limiting the number of available receptors for the other species. Soin a nutshell, the competition can be reduced to the following algebraic constrainton the system:R= R0−HR−CRin which R is the number of free receptors, and R0 is the initial number of receptors.This constraint causes the hot and cold species not to behave like an ideal gas, butto have interaction with each other (through the common limited resources thatis the number of receptor sites). This simple constraint causes the ODE systemdescribing the mode to be nonlinear (see Appendix A) and some other interestingbehaviors which will be discussed in this chapter.3.2 MethodsFor this study, we used the PBRPK model already presented in Chapter 2 (For thetechnical and the mathematics details of the model see Appendix A) to simulate thekinetics of 177Lu-PSMAI&T (see [9]). In short, the PBRPK model is a compart-mentalized modeling approach in which we build different organs and their innerstructures as compartments and add the dynamics by connecting the compartmentsto each other via a system of ordinary differential equations (ODEs). We utilizedthe realistic population-measured values along with the PBRPK model (see Ap-pendix B) to accurately capture the kinetics of radiopharmaceuticals.We swept the value of the injected hot amount, the injected cold amount, recep-tor density, and the volume of the tumor in the realistic ranges (see Table 3.1) andcomputed the delivered dose to organs over the Cartesian product of those ranges.35Parameter Range of Values unitinjected hot amount 10 linear samples from the interval [5,100] nmolinjected cold amount 10 linear samples from the interval [25,800] nmoltumor receptor density 10 linear samples from the interval [10,890] nmol/littumor volume 10 linear samples from the interval [40,2100] mlTable 3.1: The range of parameter values on injected hot, injected cold, andtumor receptor density to study the competition between hot and coldspecies.Since there are a finite amount of receptors and two species that both are will-ing to attach to the receptors (i.e. hot and cold species), we expect to observe acompetition between these two species in binding to the receptors, we calculateda new quantity that can measure the degree of competition between hot and coldspecies. For this purpose, we calculated the iso-dose curves (using the s-valueslist in Table A.3) on the ”injected hot amount” × ”injected cold amount” set (notethat × represents the Cartesian product). In simple terms, we created plots of in-jected cold vs injected hot and on these plots, we highlighted different isodoses.The values of other parameters are as listed in Appendix B. Then we picked theiso curves corresponding to the lowest iso-dose value and highest iso-dose valuesand calculated the angle between these two curves (we approximated these curveswith straight lines). We repeated the same calculation considering different recep-tor densities for the tumor. This angle between the lowest iso-dose line and thehighest iso-dose line, which we call ”twist“, is a good measure of the competitionbetween hot and cold species. This will be clear when we discuss the results in Sec-tion 3.3. Note that there are many ways to quantify the degree of competition andthe one that we have used here is a simple geometric measure of the dose manifold.Also, we looked at the average dose to tumor (averaged over different hot andcold combinations as shown in table Table 3.1) as a function of receptor density oftumor and also tumor volume. We varied the size of the tumor in a realistic interval(as discussed in [111]).Finally, since the concept of specific activity is widely used in clinics, we needto elaborate on its meaning here. Specific activity, in simple terms, is the amountof activity, i.e. λN in which λ is the decay constant, normalized by the total mass36of the radionuclide-ligand solution. In other wordsSA=λHMHH+MCCin which λ is the decay constant of the radionuclide, H is the hot amount, C is thecold amount, and finally, MH and MC are the molar mass of hot and cold species.However, because of the relatively small molar mass of radionuclides (comparedto the PSMA ligands), we usually assume that MH ≈MC. Specific activity (as dis-cussed above) and injected activity (which is simply λH) are two quantities thatare commonly used in clinics to characterize a particular injection. However, sincethese quantities are not totally independent, in the computational research commu-nity of nuclear medicine, people have been working with independent quantitiessuch as the number of hot and cold molecules (see [9] for instance). This is thereason we have reported all of our results in the language of “hot amount” and“cold amount” instead of working on injected activity and specific activity.3.3 Results and DiscussionOur results revealed the competition between hot and cold species and the non-proportional dependence of the delivered dose to the tumor (and OAR) on the in-jected activity amount.Figure 3.1 shows the delivered dose to tumors and organs at risk as a functionof injected hot and injected cold amount. It shows that in order to deliver thesame dose to the tumor and OAR, an increased amount of injected cold should beaccompanied by an increased amount of injected hot amount. The lines and thebands in Figure 3.1 show the iso-dose curves.We hypothesized that this phenomenon is due to the competition between hotand cold species in the body. In other words, increased levels of cold moleculeswill block some of the available receptors and the availability of the receptors willdecrease for the hot molecules. The effect of competition between hot and coldspecies can be visualized in several ways, two of which will be discussed here.The first argument is that the two red dots in the Figure 3.1 are both located ona single iso-dose curve (corresponding to about 20 Gy). However, the red dot in37Figure 3.1: Dependence of the delivered dose to organs on the injected hotamount and injected cold amount. Moving from the left side of each plotto the right side, we observe that the iso-dose lines get tilted, suggest-ing more competition between hot and cold species (see Section 3.3formore details). Also, two dots on the 20 Gy iso-dose curve reveals thatwe can achieve the same absorbed dose in the tumor by even lower in-jected activity if accompanied by lower cold amount (i.e. higher specificactivity).the upper right corner of the plot is achieved with about 90 nmol of hot and 780nmol of cold injection. At the same time, the dot in the lower left corner of thesame plot has the same dose but is achieved through 45 nmol of hot and 50 nmolof cold injection. So with approximately half the amount of injected activity, wecan achieve the same absorbed dose in the tumor. But the catch is that the injectedcold amount is about 15-fold less, indicating the significance of the competitionbetween hot and cold species.Another way of looking at this is to consider the injections with the same in-jected activity (see the vertical dashed line in Figure 3.1). It is clear that althoughthe amount of injected radioactivity is constant, as we increase the amount of in-jected cold (i.e. lower specific activity), the absorbed dose in the tumor decreases.For instance, at about 80 nmol injected hot amount, a 10-fold increase in the num-ber of injected cold molecules yields a 2-fold decrease in absorbed dose in thetumor.Figure 3.2 and Figure 3.3 show the effect of tumor receptor density and tu-mor volume on the competition between hot and cold molecules. One thing tonote is that the iso-dose curves become more vertical with higher tumor volumeor higher tumor receptor density. This fact can be captured by the “twist” of the38Figure 3.2: The effect of the tumor receptor density on the competition be-tween hot and cold species for 20 ml for the tumor volumeiso-dose curves (see Section 3.2). The change in twist as a function of tumor re-ceptor density and tumro volume is shown in figures Figure 3.5 and Figure 3.4.These results suggest that radiopharmaceutical therapy for tumors with low recep-tor density should be done with a very high specific activity (which translates to alow number of cold molecules and a high number of hot molecules at the injectiontime).Furthermore, as it is evident in Figure 3.5, increasing the tumor receptor den-sity does not change the twist value of the OAR (salivary glands and kidney) whileincreasing the tumor volume decreases the twist of the organs at risk as well asthe twist of the tumor. This means increased tumor receptor density decreases thecompetition between hot and cold molecules just in the tumor compartment and hasno effect on the organs at risk. However, increased tumor volume causes less ra-diopharmaceutical uptake in the organs at risk (due to the tumor sink effect (where39Figure 3.3: The effect of the tumor volume on the competition between hotand cold species. The value of tumor receptor density is set to 40nmol/lit for these plots.radiopharmaceuticals are preferentially absorbed by larger or more metabolicallyactive tumors, reducing the availability for other organs) as discussed by Tuncelet al. [128]) which leads to lower competition between hot and cold species inOAR as well as tumor.The other observation is the effect of tumor receptor density on the averageabsorbed dose by the tumor. This is shown in Figure 3.6. The absorbed dose bythe tumor increases almost linearly with tumor receptor density.The simulations presented in this chapter reveal the competition between hotand cold species and to the best of our knowledge, this competition has not beenstudied in much detail in the community of nuclear medicine before. That is be-cause the field of radiopharmaceutical therapy is experiencing a tremendous re-naissance. In this paradigm, the intention is to use radiopharmaceuticals, not in40Figure 3.4: The effect of tumor receptor density on the competition degree(i.e. twist) between hot and cold species (with 20 ml for the tumorvolume). Higher tumor receptor leads to less competition (thus lesstwist) in the tumor, while the competition level remains the same (For adetailed discussion see Section 3.3).tracer amounts that do not perturb biological systems (and also the competition be-tween hot and cold species is not significant), but in fact to cause cellular damage.However, since the competition between hot and cold species increases with lowerreceptor density in the tumor as well as lower tumor volume, radiopharmaceuticaltherapy will be most efficient when the receptor density in the tumor is very high orthe tumor volume is large. Otherwise, the amount of injected cold should be verylow relative to the injected hot amount (which translates to high specific activity).As a final note, PBRPK has its own limitations as a mathematical model andcan represent reality in a limited range of values. As such, when we extend thevalues of hot and cold injection to more than the current clinically used values,we assume that the model is still valid. Since there are no reasons that the modelcan go wrong with higher values of injected hot and cold values, it is still a quitesafe assumption. However, this reasoning is not enough and all of these extensionsshould be accompanied by real experiments to test the model prediction. This is41Figure 3.5: The effect of the tumor volume on the competition degree (i.e.twist) between hot and cold species (tumor receptor density set to 40nmol/lit). Higher tumor volume leads to less competition (thus lesstwist) in the tumor as well as in the kidney and salivary glands. Thedecrease in OAR twist is due to the tumor sink effect which is discussedin the main text.one of our major goals as our future steps.3.4 ConclusionIn this chapter, we studied the competition between hot and cold species in radio-pharmaceutical therapy. We showed that this competition can lead to a decreaseddelivered dose to tumors and sub-optimal treatment. In addition, we quantifiedthe degree of competition by measuring a simple geometric property of the dosingmanifold (which we called ”twist”). This helped us to infer that the competitionbecomes more serious when the receptor density in the tumor is very low, whichsuggests that the patients with low receptor density should be treated with a highspecific activity injection.42Figure 3.6: The effect of tumor receptor density on the average absorbed doseby the tumor. The average absorbed dose by the tumor linearly dependson the tumor receptor density. The tumor volume is 20 ml.43Chapter 4Exploring the Effects ofMulti-Bolus Injection inRadiopharmaceutical Therapy4.1 IntroductionIt is very common in the world of external beam radiotherapy to deliver the doseto the tumor in several fractions. It has been shown that fractionation can lead tolower normal tissue complications [129]. Since the cell-killing mechanism is thesame between external beam radiotherapy and radiopharmaceutical therapy, thenwe can expect the same kind of effect for fractionating the injections in radiophar-maceutical therapy. However, because of the different mechanisms of irradiatingthe targets (one is targeted externally and the other one is governed by the kineticsof the body), the effect of fractionation needs to be studied more carefully in RPTsince it has a kinetic side as well. In this chapter, we utilized the PBRPK tool (seeChapter 2) to explore the effect of fractionating the injection of radiopharmaceu-ticals and its impact on the delivered dose to tumors and organs at risk. In otherwords, instead of a single bolus injection as commonly performed in practice, weexplored injection of the same content in several smaller bolus injections.The potential impact on the absorbed dose by tumors or organs at risk (OAR)44due to fractionated injection arises from a series of compartments (arteries, organ’svascular compartment, interstitial compartment, and the bound compartment, asdetailed in Chapter 2) that a ligand (active or inactive) must traverse to reach its re-ceptors. Each compartment is characterized by distinct input and output rates (referto Figure 2.3), indicating that ligand transport is time-dependent and governed byspecific time constants related to these rates. This can be analogized to charginga capacitor in an RC circuit, where the capacitor’s charge accrues over a certainperiod, determined by the circuit’s characteristic time scale (τ = 1RC ). Unbound ra-diopharmaceuticals, or those not internalized by cells, are cleared by the kidneys.Therefore, a slower injection of radiopharmaceuticals could potentially enhancereceptor binding and reduce renal clearance, a hypothesis that will be explored inthis chapter.4.2 MethodsFor this study, we tested different injection strategies (single bolus, and multi-bolus) on different patients with different numbers of receptors on the tumors andthen measured TIA and Dose (see Chapter 2 and Appendix A for the details of thePBPRK model used). In simple terms, PBRPK model treats different organs andtheir inner structures as compartments that are connected to each other with ordi-nary differential equations. The radiopharmaceutical of interest in this study was177Lu-PSMAI&T (see [9]) and we injected the patients with 10c nmol of hot and100c nmol of cold ligands, in which c is the injection coefficient that enables us toinject a higher or lower total amount of hot and cold molecules. The parameterscharacterizing each injection were the total number of injections and also the timebetween injections which are summarized in Table 4.1.Next, to quantify the effect of multi-bolus injection in contrast to the singlebolus injection, we found the injection strategy yielding the highest delivered doseto tumor and OAR and then calculated the relative change compared to the bolusinjection (we call it the maximum relative dose change or MRDC). We repeated thesame calculation considering different tumor receptor densities and also differenttumor sizes to see if these parameters have any effect on the effectiveness of theinjection fractionation.45Parameter Range of Values unitnumber of injections {1,2,3,4,5,6,7,8,9,10} dimensionlesstime between injections {10,50,100,200,300,400,500,750,1000} minutestumor receptor density 10 linear samples from the interval [43,342] nmol/littumor volume 10 linear samples from the interval [1,100] milliliterinjection coefficient {1,2,3,4,5,6} dimensionlessTable 4.1: The range of parameter values utilized for evaluating the effect ofinjection profile (multi-bolus injection)In addition, to quantify the effect of the total injected amount of hot and coldmolecules on the effectiveness of the injection fractionation, we calculated theMRDC considering different injection coefficients. For instance, if the injectioncoefficient is 3, then it means that the total injected hot is 3×10 nmol and the totalinjected cold is 3×100 nmol.Note that for each injection strategy (that is a collection of injections with acertain timing between them), the amount of hot and cold ligands is the same ateach injection adding up to 10c nmol of hot and 100c nmol of cold ligands in total,in which c is the injection coefficient as discussed above. In simple words, thetotal injected hot and cold are kept the same for all experiments (for a given valueof injection coefficient), but injected in smaller portions. This is, however, quitehard and challenging to achieve in real life which is discussed in more detail inSection 4.4.As a final note, all of the simulations are done using the Simbiology softwarein Matlab [130]. Since the SBML implementation of the model is shared (seeSection 6.4), the results can easily be reproduced by simply importing the modelinto the software and running the appropriate pre-designed studies.4.3 ResultsFigure 4.1 and Figure 4.2 show the effect of tumor receptor density on the effec-tiveness of a multi-bolus injection. Each subfigure represents the dose delivered tothe tumor as a function of the time between injections and the number of injectionsin total. Furthermore Figure 4.3 and Figure 4.4 show the change in fractionationefficacy as a function of tumor receptor density and tumor volume respectively.46We observe that the relative effectiveness of the multi-bolus injection in de-livering dose to the tumor, compared to the single bolus injection, increases withlower receptor densities in tumors or smaller tumor volume. However, the samequantity remains almost constant for organs at risk like kidneys and salivary glands(see Figure 4.3). That is because higher receptor density in tumors has a very loweffect on the behavior of radiopharmaceuticals in the organs at risk. However, weobserved that the larger volume of the tumor reduces the effectiveness of the multi-bolus injection in delivering the dose to the tumor, kidney, and salivary glands (seefigure Figure 4.4).Comparing Figure 4.3 and Figure 4.4 reveals that the effectiveness of dosedelivery to OAR decreases with higher tumor volume but remains constant withhigher tumor receptor density. That is because a larger tumor size leads to loweruptake in other organs (known as tumor sink effect as discussed in Tuncel et al.[128]), thus decreasing the saturation level of receptors in OAR which leads toless effectiveness of multi-bolus injection. Keep in mind that if we had an infiniteamount of receptors in organs, then there would be very minor effectiveness atfractionating the injection (i.e. with fractionating the injection, we would observeno significant change in the dose delivered to the organs compared to the case inwhich we inject everything at once).Figure 4.5 shows the efficacy of fractionated injection as a function of tumorreceptor density under different scenarios (i.e. different injection coefficient). Thisfigure shows that higher injected cold amounts and hot amounts (for instance upto a 6-fold increase) will still preserve the effectiveness of the multi-bolus injec-tion, meaning that injecting higher amounts of hot and cold molecules, is betterdone in smaller portions to increase the absorbed dose by the tumor. However,Figure 4.5 shows that with the higher injected amount (hot and cold combined),the effectiveness of fractionation in delivering dose to OAR is still small and isnot very significant (reflected by the zero slop of the red and yellow curves in Fig-ure 4.5). Also, this figure shows another interesting phenomenon: the delivereddose by the kidney and salivary glands gets closer to each other as the amount ofhot and cold injections increases (despite their structural differences as discussedin Appendix A). The reason for this behavior is still unknown to us and will be oneof our main objectives in our future research.47Figure 4.1: Effect of receptor density on the effectiveness of multi-bolus in-jection. These plots suggest that the receptor density plays the main rolein increasing the uptake due to injection fractionation.In a nutshell, We found that fractionating the injection (i.e. distributing theinjection into several smaller injections) increases the uptake in the tumor and alsoother organs. This suggests that by injecting the radiopharmaceuticals all at once,the availability of receptors decreases more rapidly and some radiopharmaceuticalsget no chance to bind to any receptor and get cleared from the body through thekidney. This hypothesis is tested by plotting the maximum relative dose change orMRDC with respect to tumor receptor density (Section 4.2).4.4 DiscussionOur results suggest that the fractionation in injection has a less significant effect(in delivering more doses to the organs) when the tumor receptor density or tumorvolume is large. That is because if radiopharmaceuticals can not bind to any re-ceptor, then they will clear out from the body very rapidly, thus receptor bindingis the only way to preserve radiopharmaceuticals from rapid clearance. So, for48Figure 4.2: Effect of tumor volume on the effectiveness of multi-bolus injec-tion. These plots suggest that tumor volume can be a crucial factor indetermining the effectiveness of injection fractionation.Figure 4.3: Effect of receptor density on injection fractionation. We can ob-serve that at low receptor densities, the effect of fractionation is moresignificant.49Figure 4.4: Effect of tumor volume on the effectiveness of multi-bolus injec-tion. With smaller tumor size, fractionating the injection will help indelivering more dose. However, this increase in dose delivery, will notbe in a differential manner (i.e. delivered dose to both tumor and OARincrease with the same rate).patients with low receptor density, or low tumor perfusion, it is best to inject theradiopharmaceuticals in many smaller portions.Based on the predictions of the presented PBRPK model, multi-bolus fraction-ating becomes very important when we are willing to inject higher amounts of hotand cold molecules into the patients (which can be a possible strategy for futureradiopharmaceutical therapies. Our results suggest that injecting radiopharmaceu-ticals in smaller portions will allow us to inject more radiopharmaceuticals (evenin the cases where tumor receptor density is low) and still avoid the rapid clearanceof radiopharmaceuticals (see Figure 4.5 for more details).Another important aspect of this study that needs further discussion is thePBRPK model itself and its limitations which are discussed in more detail in Sec-tion 6.2. Another aspect worth discussing is the fact that for all simulations, wehave assumed that fractionation means injecting a specific amount of hot and cold,for instance, 10 nmol of hot and 100 nmol of cold, in several smaller portions with50Figure 4.5: Effect of injection coefficient on fractionation. These plots sug-gests that fractionating the injection in therapies that require higher in-jected activity (i.e. hot amount) will help in delivering more dose.certain timing between them, for instance in 5 injections with 200 minutes betweeneach injection which translates to 2 nmol of hot and 20 nmol of cold at each in-jection. This however can be very hard and challenging to achieve in the real-lifesituation. That is because in real life, a certain amount of activity is created throughan accelerator (see [131]) or a generator (see [132]) and then attached to the appro-priate ligands (see Table 1.1). So if we decide to inject the synthesized solution in5 injections with 200 min between each injection, then we will inject the last por-tion about 1000 minutes later by which some of the radiation will undergo physicaldecay decreasing the number of hot molecules and increasing the number of coldmolecules.Lastly, the presented results strongly depend on the setting of the parametersand can wildly change when different conditions apply, for instance when theradiopharmaceuticals have a strong affinity with the albumin (which will be dis-51cussed in Chapter 5), or when different hot and cold combinations are injected tothe patient (which is discussed in Chapter 3). However, any arbitrary combinationof parameters can be used to simulate the system using the PBRPK model imple-mentation that we have shared in SBML format (see Section 2.4) in Section 6.4.We suggest importing the model in the Simbiology app in Matlab (see [130]) andthen simulating the model with any arbitrary model parameters and settings.4.5 ConclusionIn this chapter, we explored the multi-bolus injection strategy and investigated itseffect on the kinetics of radiopharmaceuticals. We characterized each multi-bolusinjection with two quantities: the number of injections, and the time between eachinjection. In order to study the effect of the injection profile in isolation, we setthe injected activity and specific activity to be constant throughout all simulations.We found that injecting the radiopharmaceuticals in smaller portions would lead tohigher delivered doses to both tumors as well as OAR. We found that the expla-nation behind this phenomenon is receptor binding and the fact that the radiophar-maceuticals that are not bound to any receptor, would get cleared from the bodyvery quickly, and injecting the radiopharmaceuticals in smaller portions would givethem enough chance to bind to available receptors. In other words, the smaller in-jection portions result in a reduced saturation level in receptors.52Chapter 5Studying the Effect of AlbuminBinding on the Kinetics ofRadiopharmaceuticals5.1 IntroductionAlbumin is one of the most abundant proteins in the serum that serve very importantroles in regulating the kinetics of different molecules across the body [133, 134].For instance, hormones get a chance to circulate evenly around the body by bindingto the albumin so that they can be released on demand [135]. Because of the pro-found effect of albumin on the kinetics of molecules circulating around the body,There has been an interest in the community of radiopharmaceutical therapy toutilize it to enhance radiopharmaceutical therapy [136, 137]. Also, since albumincan leak into the interstitial space of the tumors (because of the leaky nature ofthe tumor vasculature [7]), albumin can possibly increase the targeting efficiencyof tumors in RPT. To our knowledge, there are no mathematical models ever pro-posed to model the kinetics of radiopharmaceuticals with an albumin-binding arm.However, we expanded the idea of PBPK models to include the albumin bindingpossibility as well (as described in the model development section in the methodssection). In this study, we evaluated the effect of different albumin binding on the53delivered dose to the tumor and also OARs.5.2 MethodsPBPK model improvements (discussed in Section 2.3 and Appendix A) were thecrucial elements for the simulations explained here. For instance, the developmentof the concept of ”reaction graph“ (see Figure 2.4 in Chapter 2) enabled us toinclude the albumin reaction in a concise way.For this study, we did a parameter sweep on the different values of KalbD , loga-rithmically sampled from the range [5, 106] nmol/lit. For each of those simulations,we injected the patients with 10 nmol hot ligands and 100 nmol cold ligands. Foreach value of KD, we calculated the blood residence time (time-integrated activityin the vein compartment divided by the injected activity) as well as the delivereddose to the organs under study. The blood residence time (BRT) can be written asBRT =∫ tend0 Avein(τ)dτA0in which Avein(τ) is the activity in the vein compartment which is simply Avein(τ) =λphysHvein with Hvein representing the hot ligands in the vein, and A0 is the injectedactivity that is simply A0 = λphysH0 with H0 representing the injected hot amount.Parameter Range of Values unitKalbD 20 logarithmically spaced values from [5, 105] nmol/litTable 5.1: The range of parameter values used to study the effect of albuminbinding on the kinetics of radiopharmaceuticalsOur objective in optimized therapy is to increase the absorbed dose to the tu-mor while decreasing the delivered dose to OAR. Thus any increase/decrease inthe delivered dose to the tumor is less important and it is required to evaluate anyincreased/decreased dose to the tumor relative to OAR. For this purpose, we cal-culate a quantity called ”enhancement factor“ using the following formulaEF(KalbD ) =TumorDose(KalbD )/OrganDose(KalbD )TumorDose(∞)/OrganDose(∞),54in which EF is the enhancement factor, TumorDose(KalbD ) represented the tumorarborbed dose as a function of KalbD , and similarly OARDose(KalbD ) represents thedose to organ at risk. Intuitively speaking, EF quantifies the effectiveness of albu-min binding in delivering differential dose to tumor (relative to OAR). For instance,for a given value of KalbD , EF = 4 means that enabling albumin binding with thegiven KalbD , devlivered 4 times more dose to tumor relative to OAR, compared tothe situation where albumin binding was off (i.e. KalbD = ∞).The key assumptions that we made for these simulations are summarized be-low:1. Stoichiometry coefficient of albumin-radiopharmaceutical interaction:The interaction between albumin and radiopharmaceuticals can be writtenas:nX + Albkalbon−−⇀↽−kalbo f fXAlbin which X represents the radiopharmaceuticals (it can be hot or cold) andAlb represents the albumin, XAlb represents the albumin-radiopharmaceuticalcomplex, kalbon and [kalbo f f represents the forward and backward reaction rate re-spectively. A very important constant characterizing this reaction is calledthe dissociation constant which characterizes the equilibrium behavior of thesystem. This value is defined asKalbD =kalbo f fkalbo f f.Due to the relatively large size of albumin (about 70 kilodalton) comparedto the radiopharmaceuticals (around 1 kilodalton), the radiopharmaceuticalscan bind to albumin through different sites, hence the stoichiometry coeffi-cient n. However, to our best knowledge, this has not been measured exper-imentally yet. So for our simulations, we assume the lower bound for thisvalue n= 1.2. Dissociation due to the radiation kick: When the albumin-bound hot ra-diopharmaceuticals undergo physical decay, the kinetic energy of the radio-55pharmaceutical can overcome the binding energy between the radiopharma-ceutical and albumin and lead to dissociation. However, since there havebeen no experiments supporting this dissociation, we assumed that there isno such dissociation and the only type of dissociation is thermal.5.3 ResultsFigure 5.1 shows the blood residence time as a function of albumin-ligand disso-ciation constant. We observe that with higher albumin affinity (which translates tolower values of KD), the residence time of radioactivity in the blood compartmentincreases. This finding supports the biological observations discussed at [138].The intuitive explanation for this observation is that since the albumin-bound ra-diopharmaceuticals can not enter the interstitial space of most of the organs (seeSection 2.3), they remain in the blood compartment, hence increasing the delivereddose to both tumor and OAR slightly.Figure 5.2 shows the delivered dose to tumor and OARs as a function of dis-sociation constant of albumin-ligand interaction. There are different regions in theplot separated via solid line, dashed line and dotted-dashed line, each of which hasits own biological explanation as follows. The blue region, in which higher albumininteraction has lead to sligtly higher dose to tumor and OAR, corresponds to theincreased residence time of radiopharmaceuticals as a results of increased albuminaffinity (i.e. lower dissociation constant). However, due to the porous vascula-ture structure in the tumor microenvironment and the leakage of albumin-boundradiopharmaceuticals into the interstitial space of the tumor [139], we observe anincreased amount of dose to the tumor and decreased dose to OAR (see the greenregion in Figure 5.2).Furthermore, for the very low values of KD, we observe a decrease in the deliv-ered dose to the tumor (see the red region in Figure 5.2). That is because of the factthat the albumin-bound radiopharmaceuticals can not bind to the PSMA enzymesbecause of their huge size compared to the target enzymes. So overpopulatingthe tumor microenvironment with albumin-bound radiopharmaceuticals will leadto fewer peptide-receptor complexes and that will lead to a slight decrease in thedelivered dose to the tumor. However, the decrease in dose to organs at risk with56higher values of albumin affinity is due to the fact that the albumin-bound radio-pharmaceuticals can not enter the interstitial space of organs, and thus we observea rapid decrease in the delivered dose to organs at risk with a higher population ofalbumin-bound radiopharmaceuticals.Figure 5.1: The effect of albumin affinity on the blood residence time of ac-tivity. We can observe that the increased albumin affinity (lower KD)will increase the blood residence time.Figure 5.3 shows the enhancement ratio as a function of dissociation constant.This plot shows that with the higher albumin affinity, the differential delivery tothe tumor is increased. As long as we are considering the differential delivery, itwill be improved with higher albumin affinity (which is supported by biologicalstudies). This fact is true even if we have lower KD values compared to the onecorresponding to the dashed line in Figure 5.2 (in which delivered dose to bothtumor and OAR starts decreasing). That is because although both tumor and OARdose decreases, the decrease in OAR dose is much more rapid that the decrease intumor dose.57Figure 5.2: Dependence of dose on the dissociation constant of the albumin-ligand reaction. With higher albumin affinity (i.e. lower values of thedissociation constant), we observe that the dose to OAR and tumor bothstart to increase (see the solid line) which is due to the increased res-idence time of the radiopharmaceuticals. However, for further lowerdissociation value, (see the dotted-dashed line), the dose to OAR startsdecreasing while dose to tumor still increasing, which starts decreasingfor lower values of KalbD (see the dashed line).5.4 DiscussionOur results suggest that albumin binding can enhance the differential dose deliveryto tumors compared to the OAR. This becomes crucial when the patient has lowtumor receptor density or limited tumor perfusion. Also, albumin binding can sparethe OAR; so for patients with sensitive salivary glands or kindly, we can preventOAR from extensive damage by enabling albumin binding. However, it is veryimportant to note that we have solely been looking at the effect of albumin bindingon the kinetics of radiopharmaceuticals. For instance, very low KalbD (i.e. very highalbumin affinity), can be very harmful to bone marrow and can destroy it altogether(see [140]) which is not reflected in our PBRPK model.A very crucial limitation of the current model is that we assume only one ligandcombines into only an albumin molecule (see Section 5.2 for more details) which is58Figure 5.3: Dependance of enhancement factor on the dissociation rate ofalbumin-ligand interaction. Lower values of KalbD lead to higher en-hancement ratio meaning that higher albumin affinity will help in deliv-ering more dose to the tumor and sparing (to some degree) the OAR.not necessarily true as albumin is a huge molecule with multiple potential bindingsites. To our best knowledge, there are no studies in the field for this phenomenon.As such, one of our primary goals for the future steps is to model the interactionof radiopharmaceuticals with albumin utilizing statistical physics and moleculardynamics tools.An addition, one of the assumptions that critically affects the result of the sim-ulation is the assumption that albumin leaks into the interstitial space of tumors butnot organs at risk (see Section 5.2). However, there is limited literature support forthe characteristics of such behavior. For instance, we are not aware if it dependson the tumor volume or tumor type, or other tumor characteristics. Incorporatingmore details of albumin penetration into the interstitial structure of the tumor isone of our future aims.As a connection to the biological observation, our latest literature review showsthat albumin-binding moieties have shown promise in augmenting therapeutic out-comes through better tumor uptake. This improvement is largely attributed to the59extended blood residence time offered by these entities, allowing for more pre-cise control over the pharmacokinetics of the radiopharmaceuticals. Moreover,Research has shown that varying the albumin-binding affinity can significantly in-fluence the distribution and uptake of radioactivity in tumors, suggesting a potentialfor enhanced therapeutic effectiveness. [141, 142, 143, 136, 144].5.5 ConclusionIn this chapter, we utilized the modified PBRPK model (see Section 2.3) to simu-late the effect of albumin binding on the kinetics of radiopharmaceuticals. For thispurpose, we made some assumptions, such as the stoichiometry coefficient of theradiopharmaceuticals in interaction with albumin to be 1, among other ones (seeSection 5.2). We observed that albumin binding increases the blood residence timeof the radiopharmaceuticals which is due to the fact that albumin can not enter theinterstitial space of healthy organs. We also found that, due to the leakage of thealbumin to the interstitial space of the tumor, the differential delivered dose to thetumor increases (compared to OAR). We conclude that albumin binding can ef-fectively deliver more doses to tumors and spare the OARs which is the ultimateobjective of radiopharmaceutical therapy optimization.60Chapter 6Conclusions And ClosingRemarksI remember my friend Johnny vonNeumann used to say, with fourparameters I can fit an elephant,and with five I can make himwiggle his trunk.“A meeting with Enrico Fermi”“Nature” 427: p. 297.6.1 Summary of the thesisIn the presented thesis, we developed a PBRPK model to accurately simulate thekinetics of radiopharmaceuticals in the body. Such a simulation framework couldenable us to better predict the outcome of therapy before performing any real one.Thus, this model has the potential to fine-tune the therapy parameters and achieveoptimal one without doing high-risk, costly, and invasive experiments.In Chapter 2, we presented a scalable and modular structure to model the ki-netics of radiopharmaceuticals in the body (PBPRPK). Introducing the notion of a“reaction graph” and a scalable organization of model variables into compartments.enables the new structure to model much more complicated systems.61In Chapter 3, we systematically studied the presence of hot and cold species,their interactions with each other (i.e. competition in binding to the available re-ceptors), and the consequences of such interactions. We found that this competitioncan result in a reduced dose delivered to tumors and less effective treatment out-comes. By measuring a geometric property called ”twist” in the dose manifold,the extent of competition was quantified, which suggested that the competition be-comes more significant in cases of low receptor density in the tumor, highlightingthe need for high specific activity injections in patients with low receptor density.Chapter 4 was focused on exploring the effect of injection profile on the kinet-ics of radiopharmaceuticals. We examined two key factors that define each multi-bolus injection: the number of injections and the time intervals between them. Toisolate the specific effects of the injection profile, we maintained a constant levelof injected activity and specific activity throughout all our simulations. Our find-ings unveiled a remarkable outcome: dividing the radiopharmaceutical injectionsinto smaller portions resulted in significantly higher doses reaching both tumorsand organs at risk (OAR). This intriguing phenomenon can be attributed to theinteraction between the injected substances and their binding to receptors. Un-bound radiopharmaceuticals were rapidly eliminated from the body, yet employingsmaller injection portions allowed for increased opportunities to bind to availablereceptors. In simpler terms, smaller injection portions effectively reduced receptorsaturation levels, leading to improved treatment outcomesFor the albumin study in Chapter 5, we found that albumin binding can improvethe targeted delivery of radiation to tumors, especially in cases where the patienthas low tumor receptor density or limited tumor blood flow. This approach alsohelps protect sensitive organs, such as salivary glands or kidneys, from excessivedamage.6.2 Limitations of the Current Modeling ApproachApart from certain assumptions that we disccsed separately in each chapter, Thereare certain assumptions that we made in developing the whole model that can leadto possible limitations. The very first obvious assumption is the hard wiring of themodel that accounts for the “PB” section of the word “PBRPK”. For instance, we62assumed that the tumor compartment is not very different from other organs exceptthe fact that it has higher receptor density. However, this is not true in reality. Thereis significant literature discussing the heterogeneity in the tumor microenvironmentand its significant impacts on the outcome of certain cancer treatments [145, 146,147, 148, 149, 150, 151, 152, 153, 154, 155, 156], but the whole concept is ignoredin the current PBRPK model.Apart from the physiological limitations of the model, there are certain math-ematical challenges with the model that can possibly shrink its validity domain inthe real world. The PBPK model has lots of parameters some of which are derivedfrom other ones. This causes several problems listed below.1. Parameter contamination through the propagation of measurement er-rors: In the PBPK model, there are several instances in which one parameteris defined based on another one. For instance, an experimentally measuredparameter, hematocrit, is used to calculate VP which is the plasma volume.Then VP is utilized to calculate the vascular volume and the interstitial vol-ume of several organs (see Appendix B). This kind of longitudinal depen-dence of one parameter on another one, will cause the experimental error inmeasuring the first parameter to propagate in the system and “contaminate”other parameters. If a parameter with high sensitivity (the parameter that theoutput of the system highly depends on the value of that parameter), then theprediction of the model would be ruined.2. Model degeneracy: Our developed PBRPK model contains more than 200parameters among which 10 of them are free parameters that are determinedthrough fitting [111]. However, there are other parameters that are related tothese free parameters longitudinally (i.e. these free parameters are used todefine those parameters), the total number of free parameters is in fact higherthan 10. The high number of free parameters can give a model some sort of“god power”, in the sense that it can fit almost any type of data.3. The challenges in personalization of the model: As discussed above, thePBRPK model has lots of parameters and this will yield yet another problem.The problem is that the model can not predict anything at the individual level63(personalized treatment), and its predictions will only apply to the popula-tion average. The problem with the individualization of the model is a hugenumber of measurements that needs to be performed which is nearly impos-sible with the current technological and economical setting in the clinics.4. Radiobiology: As we discussed many times throughout the thesis, the cur-rent PBRPK model only models the kinetics of radiopharmaceuticals andthere are no radiobiological models implemented in it. In other words, ourPBRPK model can only predict the concentration of radiopharmaceuticals indifferent organs throughout the treatment but there are no models to predictthe survival fraction of the cells in the course of treatment.6.3 Possible Clinical ApplicationsAs we discussed before (see item 3 in Section 6.2), the large number of parametersin the model, makes the individualization of the model very challenging. However,this does not mean that this model can not be used in regular clinical practicefor radiopharmaceutical therapy. For instance, we can still run the model withpopulation-measured values for different populations (like a male, female, pregnantfemale, children, etc) and get quite accurate predictions and run experiments thatare very challenging to set up in real-world (due to the financial, technological,and ethical challenges) as we discussed some of them in Chapter 3, Chapter 4, andChapter 5.6.4 Contribution to the FieldWe are likely in the golden age of scientific computing, with important applicationsin different fields. The newly emerging field of radiopharmaceutical therapy is noexception to this. As we reviewed in Section 2.2, the previous attempts for PBPKmodeling for radiopharmaceutical therapy was not quite aligned with the recentmovements in the scientific computing community (for instance see [157, 158, 159,160]). Thus we pursued a major effort in aligning the previous attempts with thecurrent standards. For instance, we introduced the concept of reaction graphs (see64Section 2.3) instead of the parallel-track method to capture the kinetics of differentspecies. This new approach is easily scalable compared to the old one. Also, wehave shared our new implementation with the RPT research community in SBMLfile format which eases the result reproducibility (see my GitHub page))Along with the contributions discussed above, to our best knowledge, therehave been no systematic studies in the past, to uncover the competition betweenhot and cold species as well as the effect of multi-bolus injection(instead of single-bolus injection) in the world of RPT. These two topics are discussed in Chapter 3and Chapter 4 respectively.Given our new scalable design, we added a new dimension to the PBPK modelto capture the kinetics of radiopharmaceuticals that to our best knowledge have notbeen modeled before. These results were in agreement with some animal data (seeSection 5.3). These new investigations and the computational support for the effec-tiveness of albumin binding in delivering differential doses to tumors (compared toOAR) can help the RPT community to design more directed experiments.As a summary, our contributions to the field can be summarized as follows:• Scalable model development for albumin simulation (see Section 2.3, andChapter 5)• Replacing the concept of the parallel structures for hot and cold and replac-ing it with the concept of reaction graph (see Section 2.3, and Appendix A)• Utilizing the SBML conventions for the compartments (see Section A.1, andSection 2.4)• Sharing the SBML implementation for easier reproduction (see my GitHubpage).• Systematic study on the reaction between hot and cold species in the radio-pharmaceutical therapy and its consequences (see Chapter 3).• Studying the effect of fractionated injection profile on the kinetics of radio-pharmaceuticals (see Chapter 4).• Exploring the kinetic effects of different albumin affinity of the radiophar-maceuticals as discussed in Chapter 5.65In conclusion, this research endeavors to lay a foundational stone in the evolv-ing landscape of personalized cancer treatments, particularly through the use ofradiopharmaceutical therapy. By meticulously developing and applying physiolog-ically based radiopharmacokinetic (PBRPK) models, this thesis not only addressescomplex biological interactions and kinetic behaviors of radiopharmaceuticals butalso opens new avenues for in-depth studies. Our findings, particularly concerningthe nuances of receptor density and volume, bolus injection strategies, and the piv-otal role of albumin affinity, highlight the potential for significantly improving theprecision and efficacy of radiopharmaceutical therapy. It is my aspiration that thiswork serves as a catalyst, inspiring further research and innovation in the field, andultimately leading to more effective, tailored, and patient-centric approaches in thefight against cancer.66Bibliography[1] A F Paranj, J Brosch-Lenz, C Uribe, A Rahmim, and others. Modularmodel architecture for radiopharmaceutical therapy planning:Physiologically-Based RadioPharmacoKinetics (PBRPK) implementation.2022. → page vi[2] A F Paranj, J Brosch-Lenz, C Uribe, B Saboury, and others. Non-linearitiesin the transition from imaging radiotracers to therapeuticradiopharmaceuticals. 2022. → page vi[3] Ali Fele Paranj, Carlos Uribe, Hamid Abdollahi, Elaheh Mollaheydar,Niloufar Zakariaei, Md Shahriar Rahim Siddiqui, Babak Saboury, andArman Rahmim. In silico investigation of the effect of Multi-Bolusinjections in absorbed doses to organs and tumors in radiopharmaceuticaltherapies. J. Nucl. Med., 64(supplement 1):P1422–P1422, June 2023. →page vii[4] Arman Rahmim, Julia Brosch-Lenz, Ali Fele-Paranj, Fereshteh Yousefirizi,Madjid Soltani, Carlos Uribe, and Babak Saboury. Theranostic digitaltwins for personalized radiopharmaceutical therapies: Reimaginingtheranostics via computational nuclear oncology. Front. Oncol., 12:1062592, December 2022. → page vii[5] Niloufar Zakariaei, Ali Fele Paranj, Hamid Abdollahi, and ArmanRahmim. Using the cluster gauss newton algorithm to estimate theranosticpharmacokinetic model parameters. J. Nucl. Med., 64(supplement 1):P1449–P1449, June 2023. → page vii[6] Arman Rahmim, Hamid Abdollahi, Ali Fele Paranj, Kyung-Nam Lee,Babak Saboury, and Carlos Uribe. Towards Non-Tracer kinetic modeling:Our past returning through the future. J. Nucl. Med., 64(supplement 1):P1447–P1447, June 2023. → page vii67[7] George Sgouros, Lisa Bodei, Michael R McDevitt, and Jessie R Nedrow.Radiopharmaceutical therapy in cancer: clinical advances and challenges.Nat. Rev. Drug Discov., 19(9):589–608, September 2020. → pagesxii, 16, 17, 18, 19, 53[8] Ramesh Chandra and Arman Rahmim. Nuclear Medicine Physics: TheBasics. Lippincott Williams & Wilkins, October 2017. → pagesxii, 13, 17, 95[9] Peter Kletting, Christiane Schuchardt, Harshad R Kulkarni, MostafaShahinfar, Aviral Singh, Gerhard Glatting, Richard P Baum, and Ambros JBeer. Investigating the effect of ligand amount and injected therapeuticactivity: A simulation study for 177Lu-Labeled PSMA-Targeting peptides.PLoS One, 11(9):e0162303, September 2016. → pages xii, 35, 37, 45, 96[10] Rebecca L Siegel, Kimberly D Miller, Hannah E Fuchs, and AhmedinJemal. Cancer statistics, 2022. CA Cancer J. Clin., 72(1):7–33, January2022. → page 1[11] Sid Lee. Cancer statistics at a glance. https://cancer.ca/en/research/cancer-statistics/cancer-statistics-at-a-glance?gclid=CjwKCAjw2K6lBhBXEiwA5RjtCb9jwx fKTQmefLxkT XlinwtNxmn1Q4diUhtGtJ XCWK0nhzEKjRoC4rUQAvD BwE. Accessed:2023-7-10. → page 1[12] Jon Zugazagoitia, Cristiano Guedes, Santiago Ponce, Irene Ferrer, SoniaMolina-Pinelo, and Luis Paz-Ares. Current challenges in cancer treatment.Clin. Ther., 38(7):1551–1566, July 2016. → page 1[13] Rebecca L Siegel, Kimberly D Miller, Nikita Sandeep Wagle, andAhmedin Jemal. Cancer statistics, 2023. CA Cancer J. Clin., 73(1):17–48,January 2023. → page 1[14] Line Elmerdahl Frederiksen, Luzius Mader, Maria Feychting, HannaMogensen, Laura Madanat-Harjuoja, Nea Malila, Anniina Tolkkinen,Henrik Hasle, Jeanette Falck Winther, and Friederike Erdmann. Survivingchildhood cancer: a systematic review of studies on risk and determinantsof adverse socioeconomic outcomes. Int. J. Cancer, 144(8):1796–1823,April 2019. → page 1[15] Sanford D Markowitz and Monica M Bertagnolli. Molecular origins ofcancer: Molecular basis of colorectal cancer. N. Engl. J. Med., 361(25):2449–2460, December 2009. → pages 1, 268[16] Anthony A Mercadante and Anup Kasi. Genetics, cancer cell cycle phases.In StatPearls. StatPearls Publishing, Treasure Island (FL), August 2022. →page 1[17] Wentao Dong, Mark A Keibler, and Gregory Stephanopoulos. Review ofmetabolic pathways activated in cancer cells as determined throughisotopic labeling and network analysis. Metab. Eng., 43(Pt B):113–124,September 2017. → page 2[18] Michael C Joiner and Albert van der Kogel. Basic Clinical Radiobiology,Fifth Edition. Taylor & Francis, June 2016. → pages 2, 6, 9[19] CH450 and CH451: Biochemistry - defining life at the molecular level.https://wou.edu/chemistry/courses/online-chemistry-textbooks/ch450-and-ch451-biochemistry-defining-life-at-the-molecular-level/, July2019. Accessed: 2023-7-2. → pages 2, 3, 5[20] John R Jefferson, William H Elliott, and Daphne C Elliott. Biochemistryand Molecular Biology. Oxford University Press, 2018. → page 3[21] David L Nelson and Michael M Cox. Lehninger Principles ofBiochemistry. W. H. Freeman, January 2017. → page 3[22] Reginald Garrett and Charles M Grisham. Biochemistry. Nelson EducationLimited, 1995. → page 3[23] Kurt Housh, Jay S Jha, Zhiyu Yang, Tuhin Haldar, Kevin M Johnson, JiekaiYin, Yinsheng Wang, and Kent S Gates. Formation and repair of aninterstrand DNA Cross-Link arising from a common endogenous lesion. J.Am. Chem. Soc., 143(37):15344–15357, September 2021. → page 3[24] Gerald Karp, Janet Iwasa, and Wallace Marshall. Karp’s Cell andMolecular Biology. John Wiley & Sons, February 2020. → page 4[25] Yihan Peng and Huadong Pei. DNA alkylation lesion repair: outcomes andimplications in cancer chemotherapy. J. Zhejiang Univ. Sci. B, 22(1):47–62, January 2021. → page 4[26] Hans E Krokan and Magnar Bjøra˚s. Base excision repair. Cold SpringHarb. Perspect. Biol., 5(4):a012583, April 2013. → page 4[27] J O Blaisdell and S S Wallace. Abortive base-excision repair ofradiation-induced clustered DNA lesions in Escherichia coli. Proc. Natl.Acad. Sci. U. S. A., 98(13):7426–7430, June 2001. → page 469[28] Bo Hang. Formation and repair of tobacco carcinogen-derived bulky DNAadducts. J. Nucleic Acids, 2010:709521, December 2010. → page 4[29] Bin Ma, Irina Stepanov, and Stephen S Hecht. Recent studies on DNAadducts resulting from human exposure to tobacco smoke. Toxics, 7(1),March 2019. → page 4[30] Nimrat Chatterjee and Graham C Walker. Mechanisms of DNA damage,repair, and mutagenesis. Environ. Mol. Mutagen., 58(5):235–263, June2017. → page 5[31] Gabriela Figueroa-Gonza´lez and Carlos Pe´rez-Plasencia. Strategies for theevaluation of DNA damage and repair mechanisms in cancer (review).Oncol. Lett., 13(6):3982–3988, June 2017. → page 5[32] Yunfeng Lin, Anh Ha, and Shan Yan. Methods for studying DNASingle-Strand break repair and signaling in xenopus laevis egg extracts. InLata Balakrishnan and Jason A Stewart, editors, DNA Repair: Methods andProtocols, pages 161–172. Springer New York, New York, NY, 2019. →page 5[33] D W Fairbairn, P L Olive, and K L O’Neill. The comet assay: acomprehensive review. Mutat. Res., 339(1):37–59, February 1995. → page5[34] Eric J Hall and Amato J Giaccia. Radiobiology for the Radiologist. WoltersKluwer, June 2018. → pages 5, 6, 8[35] F A Nascimento, D de Melo E Silva, H F Nunes, and M R Parise.Evaluation of DNA damage and toxicological methodology development:A bibliometric study. Hum. Exp. Toxicol., 39(6):870–880, June 2020. →page 5[36] Se´bastien Penninckx, Eloise Pariset, Egle Cekanaviciute, and Sylvain VCostes. Quantification of radiation-induced DNA double strand breakrepair foci to evaluate and predict biological responses to ionizingradiation. NAR Cancer, 3(4):zcab046, December 2021. → page 5[37] Michael C Joiner and Albert J van der Kogel. Basic Clinical Radiobiology.CRC Press, August 2018. → pages 7, 8[38] Ifigeneia V Mavragani, Zacharenia Nikitaki, Spyridon A Kalospyros, andAlexandros G Georgakilas. Ionizing radiation and complex DNA damage:70From prediction to detection challenges and biological significance.Cancers, 11(11), November 2019. → page 7[39] Julie A Reisz, Nidhi Bansal, Jiang Qian, Weiling Zhao, and Cristina MFurdui. Effects of ionizing radiation on biological molecules–mechanismsof damage and emerging methods of detection. Antioxid. Redox Signal., 21(2):260–292, July 2014. → page 7[40] J S Bertram. The molecular biology of cancer. Mol. Aspects Med., 21(6):167–223, December 2000. → page 7[41] Marco Durante and Silvia C Formenti. Radiation-Induced chromosomalaberrations and immunotherapy: Micronuclei, cytosolic DNA, andInterferon-Production pathway. Front. Oncol., 8:192, May 2018. → page 7[42] Gissela Borrego-Soto, Rocı´o Ortiz-Lo´pez, and Augusto Rojas-Martı´nez.Ionizing radiation-induced DNA injury and damage detection in patientswith breast cancer. Genet. Mol. Biol., 38(4):420–432, December 2015. →page 7[43] Nguyen T K Vo, Marwan Shahid, Colin B Seymour, and Carmel EMothersill. Effects of dose rate on the reproductive cell death and earlymitochondrial membrane potential in different human Epithelium-Derivedcells exposed to gamma rays. Dose Response, 17(2):1559325819852508,May 2019. → page 7[44] Rania Nakad and Bjo¨rn Schumacher. DNA damage response and immunedefense: Links and mechanisms. Front. Genet., 7:147, August 2016. →page 8[45] Ralph Scully, Arvind Panday, Rajula Elango, and Nicholas A Willis. DNAdouble-strand break repair-pathway choice in somatic mammalian cells.Nat. Rev. Mol. Cell Biol., 20(11):698–714, November 2019. → page 8[46] Stephen P Jackson. Sensing and repairing DNA double-strand breaks.Carcinogenesis, 23(5):687–696, May 2002. → page 8[47] J Ross Chapman, Martin R G Taylor, and Simon J Boulton. Playing the endgame: DNA double-strand break repair pathway choice. Mol. Cell, 47(4):497–510, August 2012. → page 8[48] Akhtar Ali, Wei Xiao, Masroor Ellahi Babar, and Yanzhen Bi.Double-Stranded break repair in mammalian cells and precise genomeediting. Genes, 13(5), April 2022. → page 971[49] Constantinos G Broustas and Howard B Lieberman. DNA damageresponse genes and the development of cancer metastasis. Radiat. Res.,181(2):111–130, February 2014. → page 9[50] Krystyna Mazan-Mamczarz, Patrick R Hagner, Yongqing Zhang, BojieDai, Elin Lehrmann, Kevin G Becker, Jack D Keene, Myriam Gorospe,Zhenqui Liu, and Ronald B Gartenhaus. ATM regulates a DNA damageresponse posttranscriptional RNA operon in lymphocytes. Blood, 117(8):2441–2450, February 2011. → page 9[51] Alo Ray, Chessica Blevins, Gulzar Wani, and Altaf A Wani. ATR- andATM-Mediated DNA damage response is dependent on excision repairassembly during G1 but not in S phase of cell cycle. PLoS One, 11(7):e0159344, July 2016. → page 9[52] Julio Morales, Longshan Li, Farjana J Fattah, Ying Dong, Erik A Bey,Malina Patel, Jinming Gao, and David A Boothman. Review of poly(ADP-ribose) polymerase (PARP) mechanisms of action and rationale fortargeting in cancer and other diseases. Crit. Rev. Eukaryot. Gene Expr., 24(1):15–28, 2014. → page 9[53] Brandon J Lamarche, Nicole I Orazio, and Matthew D Weitzman. TheMRN complex in double-strand break repair and telomere maintenance.FEBS Lett., 584(17):3682–3695, September 2010. → page 9[54] Victoria L Fell and Caroline Schild-Poulter. Ku regulates signaling to DNAdamage response pathways through the ku70 von willebrand a domain.Mol. Cell. Biol., 32(1):76–87, January 2012. → page 9[55] Alexandre Mare´chal and Lee Zou. RPA-coated single-stranded DNA as aplatform for post-translational modifications in the DNA damage response.Cell Res., 25(1):9–23, January 2015. → page 9[56] Alberto Ciccia and Stephen J Elledge. The DNA damage response: makingit safe to play with knives. Mol. Cell, 40(2):179–204, October 2010. →page 10[57] Dejene Tolossa Debela, Seke Gy Muzazu, Kidist Digamo Heraro,Maureen Tayamika Ndalama, Betelhiem Woldemedhin Mesele,Dagimawi Chilot Haile, Sophia Khalayi Kitui, and Tsegahun Manyazewal.New approaches and procedures for cancer treatment: Current perspectives.SAGE Open Med, 9:20503121211034366, August 2021. → page 1072[58] Rajiv Agarwal and Andrew S Epstein. The role of palliative care inoncology. Semin. Intervent. Radiol., 34(4):307–312, December 2017. →page 10[59] A Kitta, A Hagin, M Unseld, F Adamidis, T Diendorfer, E K Masel, andK Kirchheiner. The silent transition from curative to palliative treatment: aqualitative study about cancer patients’ perceptions of end-of-lifediscussions with oncologists. Support. Care Cancer, 29(5):2405–2413,May 2021. → page 10[60] I Valle, D Tramalloni, and N L Bragazzi. Cancer prevention: state of the artand future prospects. J. Prev. Med. Hyg., 56(1):E21–7, June 2015. → page10[61] Robin B Rome, Hillary H Luminais, Deborah A Bourgeois, andChristopher M Blais. The role of palliative care at the end of life. OchsnerJ., 11(4):348–352, 2011. → page 11[62] Elham Bidram, Yasaman Esmaeili, Hadi Ranji-Burachaloo, NuhaAl-Zaubai, Ali Zarrabi, Alastair Stewart, and Dave E Dunstan. A concisereview on cancer treatment methods and delivery systems. J. Drug Deliv.Sci. Technol., 54:101350, December 2019. → page 11[63] Muhammad T Amjad, Anusha Chidharla, and Anup Kasi. CancerChemotherapy. StatPearls Publishing, February 2023. → page 11[64] Volker Schirrmacher. From chemotherapy to biological therapy: A reviewof novel concepts to reduce the side effects of systemic cancer treatment(review). Int. J. Oncol., 54(2):407–419, February 2019. → page 11[65] Uttpal Anand, Abhijit Dey, Arvind K Singh Chandel, Rupa Sanyal,Amarnath Mishra, Devendra Kumar Pandey, Valentina De Falco, ArunUpadhyay, Ramesh Kandimalla, Anupama Chaudhary, Jaspreet KaurDhanjal, Saikat Dewanjee, Jayalakshmi Vallamkondu, and Jose´ M Pe´rezde la Lastra. Cancer chemotherapy and beyond: Current status, drugcandidates, associated risks and progress in targeted therapeutics. Genes &Diseases, 10(4):1367–1401, July 2023. → page 11[66] Rajamanickam Baskar, Kuo Ann Lee, Richard Yeo, and Kheng-Wei Yeoh.Cancer and radiation therapy: current advances and future directions. Int. J.Med. Sci., 9(3):193–199, February 2012. → page 1173[67] K S Clifford Chao, Carlos A Perez, and Tony J Wang. Radiation OncologyManagement Decisions. Lippincott Williams & Wilkins, August 2018. →page 11[68] Paula Dobosz and Tomasz Dzieciatkowski. The intriguing history of cancerimmunotherapy. Front. Immunol., 10:2965, December 2019. → page 11[69] A D Waldman, J M Fritz, and M J Lenardo. A guide to cancerimmunotherapy: from T cell basic science to clinical practice. Nat. Rev.Immunol., 2020. → page 12[70] Robert C Sterner and Rosalie M Sterner. CAR-T cell therapy: currentlimitations and potential strategies. Blood Cancer J., 11(4):69, April 2021.→ page 12[71] Jonathan Santos Apolonio, Vinı´cius Lima de Souza Gonc¸alves, Maria Luı´saCordeiro Santos, Marcel Silva Luz, Joa˜o Victor Silva Souza, Samuel LucaRocha Pinheiro, Wedja Rafaela de Souza, Matheus Sande Loureiro, andFabrı´cio Freire de Melo. Oncolytic virus therapy in cancer: A currentreview. World J Virol, 10(5):229–255, September 2021. → page 12[72] Samer Tohme, Richard L Simmons, and Allan Tsung. Surgery for cancer:A trigger for metastases. Cancer Res., 77(7):1548–1552, April 2017. →page 12[73] Lynda Wyld, Riccardo A Audisio, and Graeme J Poston. The evolution ofcancer surgery and future perspectives. Nat. Rev. Clin. Oncol., 12(2):115–124, February 2015. → page 12[74] Nasuh Utku Dogan, Selen Dogan, Giovanni Favero, Christhardt Ko¨hler,and Polat Dursun. The basics of sentinel lymph node biopsy: Anatomicaland pathophysiological considerations and clinical aspects. J. Oncol.,2019:3415630, July 2019. → page 12[75] Simon R Cherry, James A Sorenson, and Michael E Phelps. Physics inNuclear Medicine. Elsevier Health Sciences, April 2012. → pages12, 14, 15[76] Peter Josef Ell and Sanjiv Sam Gambhir. Nuclear Medicine in ClinicalDiagnosis and Treatment. Churchill Livingstone, 2004. → page 12[77] Arman Rahmim and Habib Zaidi. PET versus SPECT: strengths,limitations and challenges. Nucl. Med. Commun., 29(3):193–207, March2008. → page 1274[78] Srikanth Yandrapalli and Yana Puckett. SPECT Imaging. StatPearlsPublishing, October 2022. → page 13[79] Sridhar Goud Nerella, Priti Singh, Tulja Sanam, and Chander SinghDigwal. PET molecular imaging in drug development: The imaging andchemistry perspective. Front. Med., 9:812270, February 2022. → page 13[80] Mustafa Demir, Tu¨rkay Toklu, Mohammad Abuqbeitah, Hu¨seyin C¸etin,H Sezer Sezgin, Nami Yeyin, and Kerim So¨nmezog˘lu. Evaluation of PETscanner performance in PET/MR and PET/CT systems: NEMA tests. Mol.Imaging Radionucl. Ther., 27(1):10–18, February 2018. → page 13[81] Michael G Stabin. Fundamentals of Nuclear Medicine Dosimetry.Springer New York, February 2008. → page 13[82] Serena Gianfaldoni, Roberto Gianfaldoni, Uwe Wollina, Jacopo Lotti,Georgi Tchernev, and Torello Lotti. An overview on radiotherapy: From itshistory to its current applications in dermatology. Open Access Maced JMed Sci, 5(4):521–525, July 2017. → page 14[83] Arne Hessenbruch. A brief history of x-rays. Endeavour, 26(4):137–141,December 2002. → page 14[84] Jerry M Obaldo and Barbara E Hertz. The early years of nuclear medicine:A retelling. Asia Ocean J Nucl Med Biol, 9(2):207–219, 2021. → page 14[85] M Stanley Livingston. Early history of particle Accelerators**Work doneunder the auspices of the U.S. department of energy. In L Marton andC Marton, editors, Advances in Electronics and Electron Physics,volume 50, pages 1–88. Academic Press, January 1980. → page 14[86] Andrew L Farnworth and Sarah L Bugby. Intraoperative gamma cameras:A review of development in the last decade and future outlook. J. ImagingSci. Technol., 9(5), May 2023. → page 14[87] F R Wrenn, Jr, M L Good, and P Handler. The use of positron-emittingradioisotopes for the localization of brain tumors. Science, 113(2940):525–527, May 1951. → page 14[88] P V Harper, K A Lathrop, F Jiminez, R Fink, and A Gottschalk.TECHNETIUM 99M AS a SCANNING AGENT. Radiology, 85:101–109,July 1965. → page 1475[89] Patricia E Edem, Jesper Fonslet, Andreas Kjær, Matthias Herth, andGregory Severin. In vivo radionuclide generators for diagnostics andtherapy. Bioinorg. Chem. Appl., 2016:6148357, December 2016. → page15[90] Shan Tong, Adam M Alessio, and Paul E Kinahan. Image reconstructionfor PET/CT scanners: past achievements and future challenges. ImagingMed., 2(5):529–545, October 2010. → page 15[91] Brian F Hutton. The origins of SPECT and SPECT/CT. Eur. J. Nucl. Med.Mol. Imaging, 41 Suppl 1:S3–16, May 2014. → page 15[92] Terry Jones and David Townsend. History and future technical innovationin positron emission tomography. J Med Imaging (Bellingham), 4(1):011013, January 2017. → page 15[93] Tim Lougheed. Cyclotron production of medical isotopes scales up.CMAJ, 185(11):947, August 2013. → page 15[94] M G Stabin, M Tagesson, S R Thomas, M Ljungberg, and S E Strand.Radiation dosimetry in nuclear medicine. Appl. Radiat. Isot., 50(1):73–87,January 1999. → page 15[95] Jacek Capala, Stephen A Graves, Aaron Scott, George Sgouros, Sara StJames, Pat Zanzonico, and Brian E Zimmerman. Dosimetry forradiopharmaceutical therapy: Current practices and commercial resources.J. Nucl. Med., 62(Suppl 3):3S–11S, December 2021. → pages 15, 93[96] Daphne Merel Valerie Huizing, Berlinda Jantina de Wit-van der Veen,Marcel Verheij, and Marcellus Petrus Maria Stokkel. Dosimetry methodsand clinical applications in peptide receptor radionuclide therapy forneuroendocrine tumours: a literature review. EJNMMI Res., 8(1):89,August 2018. → page 15[97] Søren M Bentzen, Louis S Constine, Joseph O Deasy, Avi Eisbruch,Andrew Jackson, Lawrence B Marks, Randall K Ten Haken, and Ellen DYorke. Quantitative analyses of normal tissue effects in the clinic(QUANTEC): an introduction to the scientific issues. Int. J. Radiat. Oncol.Biol. Phys., 76(3 Suppl):S3–9, March 2010. → page 16[98] W D Bloomer, W H McLaughlin, S J Adelstein, and A P Wolf. Therapeuticapplications of auger and alpha emitting radionuclides. In Nuclearmedicine and biology. inis.iaea.org, 1982. → page 1776[99] A I Kassis, S J Adelstein, and G Mariani. Radiolabeled nucleoside analogsin cancer diagnosis and therapy. Q. J. Nucl. Med., 40(3):301–319,September 1996. → page 17[100] H A Macapinlac, N Kemeny, F Daghighian, R Finn, J Zhang, J Humm,O Squire, and S M Larson. Pilot clinical trial of5-[125i]iodo-2’-deoxyuridine in the treatment of colorectal cancermetastatic to the liver. J. Nucl. Med., 37(4 Suppl):25S–29S, April 1996. →page 17[101] Richard G Zimmermann. Why are investors not interested in myradiotracer? the industrial and regulatory constraints in the development ofradiopharmaceuticals. Nucl. Med. Biol., 40(2):155–166, February 2013. →page 18[102] Nghi C Nguyen, Muhammad Shah, Leonard J Appleman, Rahul Parikh,and James M Mountz. Radium-223 therapy for patients with metastaticCastrate-Resistant prostate cancer: An update on literature with casepresentation. Int. J. Mol. Imaging, 2016:2568031, September 2016. →page 18[103] Roger M Pallares and Rebecca J Abergel. Development ofradiopharmaceuticals for targeted alpha therapy: Where do we stand?Front. Med., 9:1020188, December 2022. → page 18[104] George Sgouros. A persistent belief in radiopharmaceutical therapy. Med.Phys., February 2023. → page 18[105] Mohammad R Alam, Shashi B Singh, Shreeya Thapaliya, ShreeyaShrestha, Sulav Deo, and Kishor Khanal. A review of 177Lutetium-PSMAand 225Actinium-PSMA as emerging theranostic agents in prostate cancer.Cureus, 14(9):e29369, September 2022. → page 18[106] Ravi K Paluri and Robert B Killeen. Neuroendocrine tumorLu-177-Dotatate therapy. In StatPearls. StatPearls Publishing, TreasureIsland (FL), February 2023. → page 18[107] A Otte, E Jermann, M Behe, M Goetze, H C Bucher, H W Roser,A Heppeler, J Mueller-Brand, and H R Maecke. DOTATOC: a powerfulnew tool for receptor-mediated radionuclide therapy. Eur. J. Nucl. Med., 24(7):792–795, July 1997. → page 18[108] George Sgouros and Robert F Hobbs. Dosimetry for radiopharmaceuticaltherapy. Semin. Nucl. Med., 44(3):172–178, May 2014. → page 1977[109] George Sgouros. Radiopharmaceutical therapy. Health Phys., 116(2):175–178, February 2019. → page 20[110] Deepika Deepika and Vikas Kumar. The role of “physiologically basedpharmacokinetic model (PBPK)” new approach methodology (NAM) inpharmaceuticals and environmental chemical risk assessment. Int. J.Environ. Res. Public Health, 20(4), February 2023. → page 23[111] Peter Kletting, Christiane Schuchardt, Harshad R Kulkarni, MostafaShahinfar, Aviral Singh, Gerhard Glatting, Richard P Baum, and Ambros JBeer. Investigating the effect of ligand amount and injected therapeuticactivity: A simulation study for 177Lu-Labeled PSMA-Targeting peptides.PLoS One, 11(9):e0162303, September 2016. → pages 24, 25, 36, 63[112] Luis David Jime´nez-Franco, Gerhard Glatting, Vikas Prasad, Wolfgang AWeber, Ambros J Beer, and Peter Kletting. Effect of tumor perfusion andreceptor density on tumor control probability in 177Lu-DOTATATEtherapy: An in silico analysis for standard and optimized treatment. J.Nucl. Med., 62(1):92–98, January 2021. → page 24[113] Ehsan Samei, Paul Kinahan, Robert M Nishikawa, and Andrew Maidment.Virtual clinical trials: Why and what (special section guest editorial). JMed Imaging (Bellingham), 7(4):042801, July 2020. → page 24[114] Ehsan Abadi, William P Segars, Benjamin M W Tsui, Paul E Kinahan,Nick Bottenus, Alejandro F Frangi, Andrew Maidment, Joseph Lo, andEhsan Samei. Virtual clinical trials in medical imaging: a review. J MedImaging (Bellingham), 7(4):042805, July 2020. → page 24[115] Modeling and simulation.https://www.fda.gov/science-research/about-science-research-fda/how-simulation-can-transform-regulatory-pathways, November 2018.Accessed: 2023-6-22. → page 24[116] Center for Devices and Radiological Health. Reporting of computationalmodeling studies in medical device submissions. https://www.fda.gov/regulatory-information/search-fda-guidance-documents/reporting-computational-modeling-studies-medical-device-submissions.Accessed: 2023-6-22. → page 24[117] Council regulation (EC) no. 440/2008 laying down test methods pursuantto regulation (EC) no. 1907/2006 of the european parliament and of the78council on the registration, evaluation, authorisation and restriction ofchemicals (REACH). https://t.ly/FB9j9. Accessed: 2023-6-22. → page 24[118] Peter Kletting, Donald Bunjes, Sven N Reske, and Gerhard Glatting.Improving anti-CD45 antibody radioimmunotherapy using aphysiologically based pharmacokinetic model. J. Nucl. Med., 50(2):296–302, February 2009. → page 25[119] Peter Kletting, Berthold Muller, Bahar Erentok, Jorn Schmaljohann,Florian F Behrendt, Sven N Reske, Felix M Mottaghy, and GerhardGlatting. Differences in predicted and actually absorbed doses in peptidereceptor radionuclide therapy. Med. Phys., 39(9):5708–5717, September2012. → page 25[120] N D Pfeifer, S L Goss, B Swift, G Ghibellini, M Ivanovic, W D Heizer,L M Gangarosa, and K L R Brouwer. Effect of ritonavir on(99m)Technetium-Mebrofenin disposition in humans: A Semi-PBPKmodeling and in vitro approach to predict Transporter-Mediated DDIs.CPT Pharmacometrics Syst Pharmacol, 2(1):e20, January 2013. → page25[121] Deni Hardiansyah, Christian Maass, Ali Asgar Attarwala, Berthold Mu¨ller,Peter Kletting, Felix M Mottaghy, and Gerhard Glatting. The role ofpatient-based treatment planning in peptide receptor radionuclide therapy.Eur. J. Nucl. Med. Mol. Imaging, 43(5):871–880, May 2016. → page 25[122] Radovan Gospavic, Peter Knoll, Siroos Mirzaei, and Viktor Popov.Physiologically based pharmacokinetic (PBPK) model for biodistributionof radiolabeled peptides in patients with neuroendocrine tumours. AsiaOcean. J. Nucl. Med. Biol., 4(2):90–97, 2016. → page 25[123] Deni Hardiansyah, Nusrat Jihan Begum, Peter Kletting, Felix M Mottaghy,and Gerhard Glatting. Sensitivity analysis of a physiologically basedpharmacokinetic model used for treatment planning in peptide receptorradionuclide therapy. Cancer Biother. Radiopharm., 31(6):217–224,August 2016. → page 25[124] Christian Maaß, Jan Philipp Sachs, Deni Hardiansyah, Felix M Mottaghy,Peter Kletting, and Gerhard Glatting. Dependence of treatment planningaccuracy in peptide receptor radionuclide therapy on the samplingschedule. EJNMMI Res., 6(1):30, December 2016. → page 2579[125] Nusrat J Begum, Anne Thieme, Nina Eberhardt, Robert Tauber, CalogeroD’Alessandria, Ambros J Beer, Gerhard Glatting, Matthias Eiber, and PeterKletting. The effect of total tumor volume on the biologically effectivedose to tumor and kidneys for 177Lu-Labeled PSMA peptides. J. Nucl.Med., 59(6):929–933, June 2018. → page 25[126] Andreas Rinscheid, Jeesoo Lee, Peter Kletting, Ambros J Beer, andGerhard Glatting. A simulation-based method to determine optimalsampling schedules for dosimetry in radioligand therapy. Z. Med. Phys., 29(4):314–325, December 2019. → page 25[127] I H Bartelink, E A van de Stadt, A F Leeuwerik, V L J L Thijssen, J R IHupsel, J F van den Nieuwendijk, I Bahce, M Yaqub, and N H Hendrikse.Physiologically based pharmacokinetic (PBPK) modeling to predict PETimage quality of three generations EGFR TKI in Advanced-Stage NSCLCpatients. Pharmaceuticals, 15(7), June 2022. → page 25[128] Murat Tuncel, Tug˘c¸e Telli, Meltem C¸ag˘lar Tuncalı, and Erdem Karabulut.Predictive factors of tumor sink effect: Insights from177Lu-Prostate-specific membrane antigen therapy. Ann. Nucl. Med., 35(5):529–539, May 2021. → pages 40, 47[129] B Zachariah, S S Jacob, C Gwede, A Cantor, J Patil, L Casey, and A BZachariah. Effect of fractionated regional external beam radiotherapy onperipheral blood cell count. Int. J. Radiat. Oncol. Biol. Phys., 50(2):465–472, June 2001. → page 44[130] SimBiology. https://www.mathworks.com/products/simbiology.html.Accessed: 2023-7-9. → pages 46, 52, 97[131] Yiwei Wang, Daiyuan Chen, Ricardo Dos Santos Augusto, Jixin Liang, ZhiQin, Juntao Liu, and Zhiyi Liu. Production review of Accelerator-Basedmedical isotopes. Molecules, 27(16), August 2022. → page 51[132] Ashutosh Dash, F F (Russ) Knapp, Jr, and M R A Pillai. Industrialradionuclide generators: a potential step towards accelerating radiotracerinvestigations in industry. RSC Adv., 3(35):14890–14909, August 2013. →page 51[133] Maja Thim Larsen, Matthias Kuhlmann, Michael Lykke Hvam, andKenneth A Howard. Albumin-based drug delivery: harnessing nature tocure disease. Mol Cell Ther, 4:3, February 2016. → page 5380[134] Alessandra Spada, Jaber Emami, Jack A Tuszynski, and AfsanehLavasanifar. The uniqueness of albumin as a carrier in nanodrug delivery.Mol. Pharm., 18(5):1862–1894, May 2021. → page 53[135] Philbert Lee and Xiaoyang Wu. Review: modifications of human serumalbumin and their binding effect. Curr. Pharm. Des., 21(14):1862–1865,2015. → page 53[136] Florian Brandt, Martin Ullrich, Markus Laube, Klaus Kopka, MichaelBachmann, Reik Lo¨ser, Jens Pietzsch, Hans-Ju¨rgen Pietzsch, Jo¨rg van denHoff, and Robert Wodtke. “clickable” albumin binders for modulating thetumor uptake of targeted radiopharmaceuticals. J. Med. Chem., 65(1):710–733, January 2022. → pages 53, 60[137] Mengxin Xu, Pu Zhang, Jie Ding, Junyi Chen, Li Huo, and Zhibo Liu.Albumin Binder-Conjugated fibroblast activation protein inhibitorradiopharmaceuticals for cancer therapy. J. Nucl. Med., 63(6):952–958,June 2022. → page 53[138] Aron Roxin, Chengcheng Zhang, Jutta Zeisler, Nadine Colpo, Xinchi Hou,Carlos Uribe, Zhengxing Zhang, Kuo-Shyan Lin, and Francois Benard.Arylhalide albumin Binder-Mediated extended circulation imparts longertumor retention of [177Lu]-LLP2A conjugates in VLA-4 expressingmurine melanoma. J. Nucl. Med., 63(supplement 2):2863–2863, June2022. → page 56[139] Ella N Hoogenboezem and Craig L Duvall. Harnessing albumin as a carrierfor cancer therapies. Adv. Drug Deliv. Rev., 130:73–89, May 2018. → page56[140] Luisa M Deberle, Viviane J Tschan, Francesca Borgna, Fan Sozzi-Guo,Peter Bernhardt, Roger Schibli, and Cristina Mu¨ller. Albumin-BindingPSMA radioligands: Impact of minimal structural changes on the tissuedistribution profile. Molecules, 25(11), May 2020. → page 58[141] Srikanth Boinapally, Suresh Alati, Zirui Jiang, Yu Yan, Alla Lisok, RajanSingh, Gabriela Lofland, Il Minn, Robert F Hobbs, Martin G Pomper, andSangeeta Ray Banerjee. Preclinical evaluation of a new series ofAlbumin-Binding 177Lu-Labeled PSMA-Based Low-Molecular-Weightradiotherapeutics. Molecules, 28(16), August 2023. → page 60[142] Da´niel Szu¨cs, Judit P Szabo´, Vikto´ria Arato´, Barbara Gyuricza, Dezso˝Szikra, Imre To´th, Zita Ke´pes, Gyo¨rgy Trencse´nyi, and Aniko´ Fekete.81Investigation of the effect on the albumin binding moiety for thepharmacokinetic properties of 68ga-, 205/206bi-, and 177Lu-LabeledNAPamide-Based radiopharmaceuticals. Pharmaceuticals, 16(9),September 2023. → page 60[143] Sarah D Busslinger, Anna E Becker, Christian Vaccarin, Luisa M Deberle,Marie-Luise Renz, Viola Groehn, Roger Schibli, and Cristina Mu¨ller.Investigations using albumin binders to modify the tissue distributionprofile of radiopharmaceuticals exemplified with folate radioconjugates.Cancers, 15(17), August 2023. → page 60[144] Suresh Alati, Rajan Singh, Martin G Pomper, Steven P Rowe, andSangeeta Ray Banerjee. Preclinical development in radiopharmaceuticaltherapy for prostate cancer. Semin. Nucl. Med., 53(5):663–686, September2023. → page 60[145] Douglas Hanahan. Hallmarks of cancer: New dimensions. Cancer Discov.,12(1):31–46, January 2022. → page 63[146] Douglas Hanahan and Robert A Weinberg. Hallmarks of cancer: the nextgeneration. Cell, 144(5):646–674, March 2011. → page 63[147] Nicole M Anderson and M Celeste Simon. The tumor microenvironment.Curr. Biol., 30(16):R921–R925, August 2020. → page 63[148] Roghayyeh Baghban, Leila Roshangar, Rana Jahanban-Esfahlan, KhaledSeidi, Abbas Ebrahimi-Kalan, Mehdi Jaymand, Saeed Kolahian, TaherehJavaheri, and Peyman Zare. Tumor microenvironment complexity andtherapeutic implications at a glance. Cell Commun. Signal., 18(1):59, April2020. → page 63[149] Aleksandra Boz˙yk, Kamila Wojas-Krawczyk, Paweł Krawczyk, and JanuszMilanowski. Tumor Microenvironment-A short review of cellular andinteraction diversity. Biology, 11(6), June 2022. → page 63[150] Ming-Zhu Jin and Wei-Lin Jin. The updated landscape of tumormicroenvironment and drug repurposing. Signal Transduct Target Ther, 5(1):166, August 2020. → page 63[151] Aadhya Tiwari, Rakesh Trivedi, and Shiaw-Yih Lin. Tumormicroenvironment: barrier or opportunity towards effective cancer therapy.J. Biomed. Sci., 29(1):83, October 2022. → page 6382[152] Ovidiu Farc and Victor Cristea. An overview of the tumormicroenvironment, from cells to complex networks (review). Exp. Ther.Med., 21(1):96, January 2021. → page 63[153] Jonathan Tranel, Stig Palm, Stephen A Graves, Felix Y Feng, andThomas A Hope. Impact of radiopharmaceutical therapy (177lu, 225ac)microdistribution in a cancer-associated fibroblasts model. EJNMMI Phys,9(1):67, September 2022. → page 63[154] Yi Xiao and Dihua Yu. Tumor microenvironment as a therapeutic target incancer. Pharmacol. Ther., 221:107753, May 2021. → page 63[155] Qingjing Wang, Xueting Shao, Yuxuan Zhang, Miaojin Zhu, Frederick X CWang, Jianjian Mu, Jiaxuan Li, Hangping Yao, and Keda Chen. Role oftumor microenvironment in cancer progression and therapeutic strategy.Cancer Med., 12(10):11149–11165, May 2023. → page 63[156] Sergi Benavente, Almudena Sa´nchez-Garcı´a, Silvia Naches, Matilde EstherLLeonart, and Juan Lorente. Therapy-Induced modulation of the tumormicroenvironment: New opportunities for cancer therapies. Front. Oncol.,10:582884, October 2020. → page 63[157] Krishna Tiwari, Sarubini Kananathan, Matthew G Roberts, Johannes PMeyer, Mohammad Umer Sharif Shohan, Ashley Xavier, Matthieu Maire,Ahmad Zyoud, Jinghao Men, Szeyi Ng, Tung V N Nguyen, Mihai Glont,Henning Hermjakob, and Rahuman S Malik-Sheriff. Reproducibility insystems biology modelling. Mol. Syst. Biol., 17(2):e9982, February 2021.→ page 64[158] Ann E Cowan, Pedro Mendes, and Michael L Blinov.ModelBricks-modules for reproducible modeling improving modelannotation and provenance. NPJ Syst Biol Appl, 5:37, October 2019. →page 64[159] Rahuman S Malik-Sheriff, Mihai Glont, Tung V N Nguyen, KrishnaTiwari, Matthew G Roberts, Ashley Xavier, Manh T Vu, Jinghao Men,Matthieu Maire, Sarubini Kananathan, Emma L Fairbanks, Johannes PMeyer, Chinmay Arankalle, Thawfeek M Varusai, VincentKnight-Schrijver, Lu Li, Corina Duen˜as-Roca, Gaurhari Dass, Sarah MKeating, Young M Park, Nicola Buso, Nicolas Rodriguez, Michael Hucka,and Henning Hermjakob. BioModels-15 years of sharing computationalmodels in life science. Nucleic Acids Res., 48(D1):D407–D415, January2020. → page 6483[160] M Hucka, A Finney, H M Sauro, H Bolouri, J C Doyle, H Kitano, A PArkin, B J Bornstein, D Bray, A Cornish-Bowden, A A Cuellar, S Dronov,E D Gilles, M Ginkel, V Gor, I I Goryanin, W J Hedley, T C Hodgman, J-HHofmeyr, P J Hunter, N S Juty, J L Kasberger, A Kremling, U Kummer,N Le Nove`re, L M Loew, D Lucio, P Mendes, E Minch, E D Mjolsness,Y Nakayama, M R Nelson, P F Nielsen, T Sakurada, J C Schaff, B EShapiro, T S Shimizu, H D Spence, J Stelling, K Takahashi, M Tomita,J Wagner, J Wang, and SBML Forum. The systems biology markuplanguage (SBML): a medium for representation and exchange ofbiochemical network models. Bioinformatics, 19(4):524–531, March 2003.→ page 64[161] A T Turrisi. Considerations on radiotherapy dose intensity for limitedsmall cell lung cancer. Lung Cancer, 10 Suppl 1:S167–73, March 1994. →page 93[162] Joe O’Donoghue, Pat Zanzonico, John Humm, and Adam Kesner.Dosimetry in radiopharmaceutical therapy. J. Nucl. Med., 63(10):1467–1474, October 2022. → page 93[163] Ramesh Chandra and Arman Rahmim. Nuclear medicine physics: thebasics. Wolters Kluwer, Philadelphia, 2017. → page 9584Appendix ASupporting MaterialsA computer without COBOL andFORTRAN is like a piece ofchocolate cake without ketchup ormustard.“Unix fortune program.”This appendix is meant to share the details of the PBRPK model discussed inChapter 2. The information shared here is enough to enable recreating the modelfrom scratch and regenerating the results.A.1 Naming Convention for VariablesIt is often very common in the community of mathematics to show different vari-ables with single letters such as x,α , etc. However, this approach is not reallyscalable and becomes very challenging in assigning names to variables when thereare lots of them in a model. Hence we developed our own naming convention indeveloping our PBRPK model which makes it easily scalable.The naming conventions are quite similar to the strategy when we use object-oriented programming. For instance, suppose that you want to refer to the hot (i.e.labeled) radiopharmaceuticals in the interstitial space of the liver. The name of thatvariable will be like:85liver.int.Hin which “int” reflects the interstitial space, and “H” reflects the hot radiopharma-ceuticals.A.2 Structure of the modelAs we discussed in Chapter 2, the PBRPK model is created by connecting differentorgans to each other using ordinary differential equations. These organs can beorganized as below:Organ TypeBrainLungsHeartAdiposeSkinBoneRed marrowMuscleReceptor NegativeLiverSpleenSalivary glandsProstateGITumorKidneyReceptor PositiveTable A.1: The list of different organs in the PBRPK model. The organs canbe classified into receptor-negative and receptor-positive organs whichare organs that have and do not have radiopharmaceutical uptake respec-tively.Receptor-negative organs are the organs that do not have any radiopharmaceu-tical uptake. On the hand, the receptor-positive organs are those that have radio-pharmaceutical uptakes (whether in the form of specific uptake (bound to actualreceptors), or non-specific uptake (that still can be modeled as binding to someimaginary receptors). The organs in each category have a very similar structure86and are only distinguished due to the different parameters that they have. In thefollowing section, we will explain the internal structure of each category of organs.A.2.1 Internal Structure of the Organs in PBRPKAll receptor-negative organs have a similar structure which is shown in Figure A.1.The only exception is the lung in which the inflow of blood into the organ is fromFigure A.1: Compartmentalized structure of the receptor-negative organs.Note that there are no “bound” and “intern” compartments, which re-flects the fact that the organ is receptor-negative.veins (instead of arteries) and the outflow of blood from the lungs is to the arteries.In contrast, for the receptor-positive organs, we will have slightly differentstructures to take the receptor binding and internalization process into account (seeFigure A.2 ) However, due to the complex nature of the kidney, it has yet anotherstructure to take the kidney functions into account (see Figure A.3)At each compartment (as the inner structure of the organs), there are gener-ally five distinct species called H, C, AH, AC, Alb which stands for hot and cold(labeled and unlabeled) radiopharmaceuticals, hot-albumin and cold-albumin com-plex and albumin itself respectively. These species interact with each other whichcan be summarized in a “reaction graph”.87Figure A.2: Compartmentalized structure of the receptor-positive organs.This reaction graph can be fully described by a system of ODEs as followingdHdt=−λH− kalbon H ∗ [Alb]+ kalbo f fAH (A.1)dCdt= λH− kalbon C ∗ [Alb]+ kalbo f fAC (A.2)dAHdt=−λAH+ kalbon H ∗ [Alb]− kalbo f fAH (A.3)dACdt= λAH+ kalbon C ∗ [Alb]− kalbo f fAC (A.4)Alb= Alb0−AH−AC (A.5)Using the fact that these species are repeated in each compartment, we can nowdescribe the concentration of each of these species in each compartment by writinga differential equation. Because the ODE for all receptor-negative organs (sameas receptor-positive organs) looks similar to each other (except for the numericalvalues of the parameters), we write the ODE system for just one organ from eachcategory.88Figure A.3: Compartmentalized structure of the kidney. The distinct featureof kidney in filtering the blood leads to its different structure than otherreceptor-positive organs.The ODE system for any receptor-negative organ (name it X) will be like this:89Figure A.4: Interactions of the different species with each other. The yellowcircles represent the reactions between species and those circles labeledwith a two-way arrow indicate that the reaction is a two-way reaction.The reactions that are not two-way are the decay process of radiophar-maceuticals.dX .vas.Hdt= Q1−λX .vas.H− kalbon X .vas.H ∗ [X .vas.Alb]+ kalbo f fX .vas.AH (A.6)dX .vas.Cdt= Q2+λX .vas.H− kalbon X .vas.C ∗ [X .vas.Alb]+ kalbo f fX .vas.AC (A.7)dX .vas.AHdt= Q3−λX .vas.AH+ kalbon X .vas.H ∗ [X .vas.Alb]− kalbo f fX .vas.AH (A.8)dX .vas.ACdt= Q4+λX .vas.AH+ kalbon X .vas.C ∗ [X .vas.Alb]− kalbo f fX .vas.AC (A.9)dX .int.Hdt= Q5−λX .int.H (A.10)dX .int.Cdt= Q6+λX .int.H (A.11)X .vas.Alb= X .vas.Alb0−X .vas.AH−X .vas.AC (A.12)90in which we haveQ1 = FX ([art.H]− [X .vas.H])+PSX ([X .int.H]− [X .vas.H]) (A.13)Q2 = FX ([art.C]− [X .vas.C])+PSX ([X .int.C]− [X .vas.C]) (A.14)Q3 = FX ([art.AH]− [X .vas.AH])+PSX ([X .int.AH]− [X .vas.AH]) (A.15)Q4 = FX ([art.AC]− [X .vas.AC])+PSX ([X .int.AC]− [X .vas.AC]) (A.16)Q5 = PSX ([X .vas.H]− [X .int.H]) (A.17)Q6 = PSX ([X .vas.C]− [X .int.C]) (A.18)Note that the variables inside bracket [] represent the concentration of that vari-able. For instance, we have[X .vas.H] =X .vas.HVX,vin which VX,v is the interstitial volume of the organ X.dXvasdt= Ftumor([Xart ]− [Xvas])+PStumor([Xint ]− [Xvas])+RHSX (A.19)dXintdt= PStumor([Xvas]− [Xint ])− konRtumor[Xint ]+ ko f fXbound+RHSX (A.20)dXbounddt= konRtumor[Xint ]− (ko f f +λint)Xbound+RHSX (A.21)dXbounddt= λintXbound−λrelXintern+RHSX (A.22)R= R0−Hbound−Cbound (A.23)Similarly, we can write the ODE system for the receptor-positive systems. TheODE system for the reaction graph for receptor-positive organs will be like the91following:dX .vas.Hdt= T1−λX .vas.H− kalbon X .vas.H ∗ [X .vas.Alb]+ kalbo f fX .vas.AH (A.24)dX .vas.Cdt= T2+λX .vas.H− kalbon X .vas.C ∗ [X .vas.Alb]+ kalbo f fX .vas.AC (A.25)dX .vas.AHdt= T3−λX .vas.AH+ kalbon X .vas.H ∗ [X .vas.Alb]− kalbo f fX .vas.AH (A.26)dX .vas.ACdt= T4+λX .vas.AH+ kalbon X .vas.C ∗ [X .vas.Alb]− kalbo f fX .vas.AC (A.27)dX .int.Hdt= T5−λX .int.H− kalbon X .int.H ∗ [X .int.Alb]+ kalbo f fX .int.AH (A.28)dX .int.Cdt= T6+λX .int.H− kalbon X .int.C ∗ [X .int.Alb]+ kalbo f fX .int.AC (A.29)dX .int.AHdt= T7−λX .int.AH+ kalbon X .int.H ∗ [X .int.Alb]− kalbo f fX .int.AH (A.30)dX .int.ACdt= T8+λX .int.AH+ kalbon X .int.C ∗ [X .int.Alb]− kalbo f fX .int.AC (A.31)dX .bound.Hdt= T9−λX .int.H− kalbon X .int.H ∗ [X .int.Alb]+ kalbo f fX .int.AH (A.32)dX .bound.Cdt= T10+λX .int.H− kalbon X .int.C ∗ [X .int.Alb]+ kalbo f fX .int.AC (A.33)dX .intern.Hdt= T11−λX .int.H− kalbon X .int.H ∗ [X .int.Alb]+ kalbo f fX .int.AH (A.34)dX .intern.Cdt= T12+λX .int.H− kalbon X .int.C ∗ [X .int.Alb]+ kalbo f fX .int.AC (A.35)X .vas.Alb= X .vas.Alb0−X .vas.AH−X .vas.AC (A.36)X .int.Alb= X .int.Alb0−X .int.AH−X .int.AC (A.37)92in which we haveT1 = FX ([art.H]− [X .vas.H])+PSX ([X .int.H]− [X .vas.H]) (A.38)T2 = FX ([art.C]− [X .vas.C])+PSX ([X .int.C]− [X .vas.C]) (A.39)T3 = FX ([art.AH]− [X .vas.AH])+PSX ([X .int.AH]− [X .vas.AH]) (A.40)T4 = FX ([art.AC]− [X .vas.AC])+PSX ([X .int.AC]− [X .vas.AC]) (A.41)T5 = PSX ([X .vas.H]− [X .int.H])− konX .R[X .int.H]+ ko f fX .bound.H (A.42)T6 = PSX ([X .vas.C]− [X .int.C])− konX .R[X .int.C]+ ko f fX .bound.C (A.43)T7 = PSX ([X .vas.AC]− [X .int.AC])− konX .R[X .int.AC]+ ko f fX .bound.AC (A.44)T8 = PSX ([X .vas.AH]− [X .int.AH])− konX .R[X .int.AH]+ ko f fX .bound.AH (A.45)T9 = konX .R[X .int.H]− (ko f f +X .λint)X .bound.H (A.46)T10 = konX .R[X .int.C]− (ko f f +X .λint)X .bound.C (A.47)T11 = X .λintX .bound.H−X .λrelX .intern.H (A.48)T12 = X .λintX .bound.C−X .λrelX .intern.C (A.49)A.3 S-Values and Dose CalculationRadiation’s negative impacts on living systems necessitate a thorough evaluationof the benefits and risks associated with nuclear medicine procedures [95]. Thesignificance of ensuring that the benefits significantly outweigh any potential risksis crucial. The absorbed energy in tissue, known as the radiation dose, plays apivotal role in determining the intensity or likelihood of radiation effects [161].Consequently, assessing the risk is contingent upon knowing the radiation dose apatient will receive from a specific procedure.In nuclear medicine procedures, direct measurement of radiation dose usingdetectors is nearly impossible. Instead, calculations are employed, utilizing vari-ous physical and biological data alongside mathematical equations tailored for thispurpose [162]. However, the accuracy of these calculations is hindered by severalfactors. The physical data concerning radionuclide decay and radiation interactionwith tissues are fairly accurate, but obtaining precise biologic distribution data ischallenging. Often, such data are extrapolated from animal or limited human stud-ies, introducing relatively large errors compared to the physical data. Assumptions93made in these calculations, such as uniform radionuclide distribution or instan-taneous uptake, are rarely true in practice. Radiation dose calculations typicallyemploy standard anatomical models, which may differ significantly from actualpatients, leading to efforts to incorporate population variations. Moreover, the cal-culated dose represents an average over a large volume and cannot estimate thedose at the cellular level. Microdosimetry, studying radiation dose at the cellularlevel, is proposed to enhance understanding of biological effects. These factorscollectively contribute to significant errors in radiation dose calculations, indicat-ing that presented dose values represent average doses from procedures that canvary greatly, even by a factor of 2 or more, in individual cases.Understanding the concept of radiation dose and radiation dose rate, as wellas their units of measurement, is crucial for calculating radiation dose. Radiationdose, specifically radiation absorbed dose (D), quantifies the total energy absorbedby one unit of mass of a substance. In the SI Unit System, the absorbed doseis measured in gray (Gy), where 1 Gy equals 1 joule (J) of energy absorbed perkilogram of substance. Commonly used derived units from gray are centigray (cGy= 10−2 Gy) and milligray (mGy = 10−3 Gy). The older unit of radiation dose is rad,which represents 100 ergs (1 erg = 10−7J) of absorbed energy per gram of tissueor substance. One rad is equivalent to (1/100) Gy or one cGy, and 1 Gy equals 100rad. On the other hand, radiation dose rate (dD/dt) measures the amount of energyabsorbed per unit of time per unit mass of tissue. It can be expressed in units suchas mGy (rad) per minute, cGy (rad) per hour, or Gy (rad) per day.In order to calculate radiation dose, it is necessary to determine the averageenergy absorbed by 1 gram of tissue in a target organ from the total energy re-leased by the decay of a specific amount of radioactivity. Since x-rays or γ-raysare highly penetrating, a small source emitting these types of radiation, localizedanywhere in the body, will irradiate virtually all organs. For instance, if a radionu-clide emitting x-rays or γ-rays is localized solely in the liver (source S), it willdeliver radiation dose not only to the liver but also to all other organs (targets T)in the body. Therefore, when a radiopharmaceutical is localized in multiple organs(sources), the radiation dose from each source to each organ (target) must be calcu-lated. Only then can all the contributions be added together to determine the finalradiation dose for each organ.94Energy (keV)Organ 15 30 50 100 200 500 1000Bladder 0.885 0.464 0.201 0.117 0.116 0.116 0.107Stomach 0.860 0.414 0.176 0.101 0.101 0.101 0.093Kidneys 0.787 0.298 0.112 0.066 0.068 0.073 0.063Liver 0.898 0.543 0.278 0.165 0.158 0.157 0.144Lungs 0.665 0.231 0.089 0.049 0.050 0.051 0.045Pancreas 0.666 0.195 0.068 0.038 0.042 0.044 0.040Skeleton 0.893 0.681 0.400 0.173 0.123 0.118 0.110Spleen 0.817 0.331 0.128 0.071 0.073 0.077 0.070Thyroid 0.592 0.149 0.048 0.028 0.031 0.032 0.029Total Body 0.933 0.774 0.548 0.370 0.338 0.340 0.321Table A.2: Self-absorbed fraction for different gamma-ray energies and vari-ous organs (table from [8]).The process of determining radiation dose involves essential steps [163]. Firstly,calculate the rate of energy emission (erg/h) from the different types of radiationemitted by the radionuclide within the source volume. Next, determining the rateof energy absorption from these radiations by the target volume. Next, from theabove-mentioned, calculating the average dose rate, dD/dt. This dose rate canbe captured via the S-Values (shown in Table A.3 and Table A.4 for Lu-177 self-absorbed doses). Finally, calculating the average dose, D, by multiplying the S-values with the time-integrated activity (TIA). S-values rely on physical data, suchas decay characteristics, and organ shape and size. On the other hand, the TIAnecessitates radiopharmaceutical distribution data.A.4 Parameter ValuesThe following table summarizes the parameter values used for the simulation.95Volume [ml] S-values [Gy∗min−1 ∗MBq−1]0.5 2.77∗10−31 1.40∗10−31.5 9.00∗10−42 7.02∗10−43 4.50∗10−44 3.52∗10−413 1.10∗10−417 8.30∗10−521 6.90∗10−529 4.80∗10−534 4.30∗10−552 2.67∗10−554 2.65∗10−5Table A.3: S-Values for tumor and salivary glandsOrgan S-values [Gy∗min−1 ∗MBq−1]Kidney 4.82∗10−6Table A.4: S-Values used for kidney dose calculation. Table adapted from[9].96Appendix BModel Details in SimbiologyIn this appendix, we will include the details of the PBPK model as exported by theSimbiology software (see [130]). The table will start from the next page.97Model: testModelCompartmentsCompartment Name Scope Value Initial Value Units1 Tumor2Vas Tumor2 1 0.0102 liter2 Tumor2 testModel 1 0.34 liter3 Tumor2Int Tumor2 1 0.1292 liter4 Tumor2Bound Tumor2 1 1 liter5 Tumor2Intern Tumor2 1 1 liter6 Art testModel 1 0.33516 liter7 Vein testModel 1 0.7182 liter8 Tumor1 testModel 1 0.01 liter9 Tumor1Vas Tumor1 1 0.0003 liter10 Tumor1Int Tumor1 1 0.0038 liter11 Tumor1Bound Tumor1 1 1 liter12 Tumor1Intern Tumor1 1 1 liter13 Kidney testModel 1 0.311 liter14 KidneyVas Kidney 1 0.017105 liter15 KidneyInt Kidney 1 0.04665 liter16 KidneyBound Kidney 1 1 liter17 KidneyIntern Kidney 1 1 liter18 Heart testModel 1 0.48028 liter19 HeartVas Heart 1 0.03192 liter20 HeartInt Heart 1 0.1181 liter21 SG testModel 1 0.021 liter22 SGVas SG 1 0.000378 liter23 SGInt SG 1 0.00483 liter24 SGBound SG 1 1 liter25 SGIntern SG 1 1 liter26 Bone testModel 1 12.7676 liter27 BoneVas Bone 1 0.09576 liter28 BoneInt Bone 1 0.80438 liter29 TumorRest testModel 1 0.048872 liter30 TumorRestVas TumorRest 1 0.0014662 liter31 TumorRestInt TumorRest 1 0.018571 liter32 TumorRestBound TumorRest 1 1 liter33 TumorRestIntern TumorRest 1 1 liter34 Spleen testModel 1 0.183 liter35 SpleenVas Spleen 1 0.02196 liter36 SpleenInt Spleen 1 0.0366 liter37 SpleenBound Spleen 1 1 liter38 SpleenIntern Spleen 1 1 liter39 Liver testModel 1 1.91 liter40 LiverVas Liver 1 0.16235 liter41 LiverInt Liver 1 0.382 liter42 LiverBound Liver 1 1 liter43 LiverIntern Liver 1 1 liter44 Prostate testModel 1 0.022535 liter45 ProstateVas Prostate 1 5.4085e-05 liter46 ProstateInt Prostate 1 0.0056338 liter47 ProstateBound Prostate 1 1 liter48 ProstateIntern Prostate 1 1 liter49 GI testModel 1 1.6718 liter50 GIVas GI 1 0.24259 liter51 GIInt GI 1 2.1348 liter52 GIBound GI 1 1 liter53 GIIntern GI 1 1 liter54 Rest testModel 1 11.5046 liter55 RestVas Rest 1 1.4165 liter56 RestInt Rest 1 5.8076 liter57 Skin testModel 1 4.8 liter58 SkinVas Skin 1 0.09576 liter59 SkinInt Skin 1 0.85226 liter60 Muscle testModel 1 42.3634 liter61 MuscleVas Muscle 1 0.44688 liter62 MuscleInt Muscle 1 2.6366 liter63 Brain testModel 1 2.0423 liter64 BrainVas Brain 1 0.038304 liter65 BrainInt Brain 1 1 liter66 RedMarrow testModel 1 1.5493 liter67 RedMarrowVas RedMarrow 1 0.12768 liter68 RedMarrowInt RedMarrow 1 0.47242 liter69 Lungs testModel 1 1.4085 liter70 LungsVas Lungs 1 0.33516 liter71 LungsInt Lungs 1 1.8434 liter72 Adipose testModel 1 18.9648 liter73 AdiposeVas Adipose 1 0.1596 liter74 AdiposeInt Adipose 1 2.4738 liter75 KidneyIntera Kidney 1 0.16483 liter76 Data testModel 1 1 literSpecies in Tumor2VasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in Tumor2Species Name Value Initial Value Units1 R 0 6.46 nanomoleSpecies in Tumor2IntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in Tumor2BoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in Tumor2InternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in ArtSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in VeinSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in Tumor1Species Name Value Initial Value Units1 R 0 0.57 nanomoleSpecies in Tumor1VasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in Tumor1IntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in Tumor1BoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in Tumor1InternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in KidneySpecies Name Value Initial Value Units1 R 0 4.354 nanomoleSpecies in KidneyVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in KidneyIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in KidneyBoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in KidneyInternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in HeartVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in HeartIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in SGSpecies Name Value Initial Value Units1 R 0 0.798 nanomoleSpecies in SGVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in SGIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in SGBoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in SGInternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in BoneVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in BoneIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in TumorRestSpecies Name Value Initial Value Units1 R 0 13 nanomoleSpecies in TumorRestVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in TumorRestIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in TumorRestBoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in TumorRestInternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in SpleenSpecies Name Value Initial Value Units1 R 0 0.097356 nanomoleSpecies in SpleenVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in SpleenIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in SpleenBoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in SpleenInternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in LiverSpecies Name Value Initial Value Units1 R 0 2.5403 nanomoleSpecies in LiverVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in LiverIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in LiverBoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in LiverInternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in ProstateSpecies Name Value Initial Value Units1 R 0 0.59944 nanomoleSpecies in ProstateVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in ProstateIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in ProstateBoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in ProstateInternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in GISpecies Name Value Initial Value Units1 R 0 2.6682 nanomoleSpecies in GIVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in GIIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in GIBoundSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in GIInternSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in RestVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in RestIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in SkinVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in SkinIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in MuscleVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in MuscleIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in BrainVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in BrainIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in RedMarrowVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in RedMarrowIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in LungsVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in LungsIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in AdiposeVasSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomole3 AlbHot 0 0 nanomole4 AlbCold 0 0 nanomole5 Albumin 0 0 nanomoleSpecies in AdiposeIntSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in KidneyInteraSpecies Name Value Initial Value Units1 Hot 0 0 nanomole2 Cold 0 0 nanomoleSpecies in DataSpecies Name Value Initial Value Units1 DataTumor1 0 0 nanomole2 DataTumor2 0 0 nanomole3 DataSG 0 0 nanomole4 DataKidney 0 0 nanomoleModel Scoped and Reaction Scoped ParametersParameter Name Value Initial Value Units1 lambdaPhys 7.15e-05 7.15e-05 1/minute2 k_on_toAlb 1 0 liter/nanomole/minute3 k_off_toAlb 1 0 1/minute4 k_on 0.046 0.046 liter/nanomole/minute5 k_off 0.368 0.368 1/minute6 k_on_AlbPharm 0 0 liter/nanomole/minute7 k_off_AlbPharm 0 0 1/minute8 F_Tumor1 -1 0.005 liter/minute9 PSAlb_Tumor1 -1 0 liter/minute10 PS_Tumor1 -1 0.006 liter/minute11 Rden_Tumor1 -1 57 nanomole/liter12 R0_Tumor1 -1 0.57 nanomole13 lambdaIntern_Tumor1 0.001 0.001 1/minute14 lambdaRel_Tumor1 -1 0.00015 1/minute15 F_Tumor2 -1 0.17 liter/minute16 PSAlb_Tumor2 -1 0 liter/minute17 PS_Tumor2 -1 0.204 liter/minute18 Rden_Tumor2 -1 19 nanomole/liter19 R0_Tumor2 -1 6.46 nanomole20 lambdaIntern_Tumor2 0.001 0.001 1/minute21 lambdaRel_Tumor2 -1 0.00015 1/minute22 F_TumorRest -1 0.024436 liter/minute23 PSAlb_TumorRest -1 0 liter/minute24 PS_TumorRest -1 0.029323 liter/minute25 Rden_TumorRest 266 266 nanomole/liter26 R0_TumorRest -1 13 nanomole27 lambdaIntern_TumorRest 0.001 0.001 1/minute28 lambdaRel_TumorRest -1 0.00015 1/minute29 F_SG -1 0.001554 liter/minute30 PS_SG -1 0.042 liter/minute31 Rden_SG -1 38 nanomole/liter32 R0_SG -1 0.798 nanomole33 lambdaIntern_SG -1 0.001 1/minute34 lambdaRel_SG -1 0.00042 1/minute35 F_Spleen -1 0.11778 liter/minute36 PS_Spleen -1 0.366 liter/minute37 Rden_Spleen -1 0.532 nanomole/liter38 R0_Spleen -1 0.097356 nanomole39 lambdaIntern_Spleen -1 0.001 1/minute40 lambdaRel_Spleen -1 0.00029 1/minute41 F_Prostate -1 0.0024338 liter/minute42 PS_Prostate -1 0.0022535 liter/minute43 Rden_Prostate -1 26.6 nanomole/liter44 R0_Prostate -1 0.59944 nanomole45 lambdaIntern_Prostate -1 0.001 1/minute46 lambdaRel_Prostate -1 0.00029 1/minute47 F_Liver -1 0.2552 liter/minute48 PS_Liver -1 3.82 liter/minute49 Rden_Liver -1 1.33 nanomole/liter50 R0_Liver -1 2.5403 nanomole51 lambdaIntern_Liver -1 0.001 1/minute52 lambdaRel_Liver -1 0.00029 1/minute53 F_GI -1 0.62819 liter/minute54 PS_GI -1 0.033437 liter/minute55 Rden_GI -1 1.596 nanomole/liter56 R0_GI -1 2.6682 nanomole56 R0_GI -1 2.6682 nanomole57 lambdaIntern_GI -1 0.001 1/minute58 lambdaRel_GI -1 0.00029 1/minute59 F_Rest -1 0.17269 liter/minute60 PS_Rest -1 0.23009 liter/minute61 F_Muscle -1 0.66745 liter/minute62 PS_Muscle -1 0.84727 liter/minute63 F_Skin -1 0.19631 liter/minute64 PS_Skin -1 0.096 liter/minute65 F_RedMarrow -1 0.11778 liter/minute66 PS_RedMarrow -1 3.0986 liter/minute67 F_Brain -1 0.47114 liter/minute68 PS_Brain -1 0 liter/minute69 F_Adipose -1 0.19631 liter/minute70 PS_Adipose -1 0.3793 liter/minute71 F_Bone -1 0.19631 liter/minute72 PS_Bone -1 0.25535 liter/minute73 F_Heart -1 0.15705 liter/minute74 PS_Heart -1 0.0096056 liter/minute75 F_Lungs -1 3.9262 liter/minute76 PS_Lungs -1 2.8169 liter/minute77 F_Kidney -1 0.74597 liter/minute78 TER_Kidney -1 0.2 liter/minute79 Rden_Kidney -1 14 nanomole/liter80 R0_Kidney -1 4.354 nanomole81 lambdaIntern_Kidney -1 0.001 1/minute82 lambdaRel_Kidney -1 0.00029 1/minute83 GFR -1 0.088742 liter/minute84 phi 0.66 0.66 dimensionless85 f_exc 0.96 0.96 dimensionless86 lambdaIntern_Normal -1 0.001 1/minute87 lambdaRel_Normal -1 0.00029 1/minute88 density 1 1 kilogram/liter89 bodySurfaceArea -1 1.9 meter^290 hematocrit 0.4 0.4 dimensionless91 bodyHeight -1 160 meter92 bodyWeight -1 100 kilogram93 F -1 3.9262 liter/minute94 V_p -1 3.192 liter95 kPS_Tumor1 0.6 0.6 1/minute96 kPS_Tumor2 0.6 0.6 1/minute97 kPS_TumorRest 0.6 0.6 1/minute98 kPS_SG -1 2 1/minute99 kPS_Spleen -1 2 1/minute100 kPS_Prostate -1 0.1 1/minute101 kPS_Liver -1 2 1/minute102 kPS_Rest -1 0.02 1/minute103 kPS_GI -1 0.02 1/minute104 kPS_Muscle 0.02 0.02 1/minute105 kPS_Skin -1 0.02 1/minute106 kPS_Brain 0 0 1/minute107 kPS_RedMarrow -1 2 1/minute108 kPS_Adipose -1 0.02 1/minute109 kPS_Bone -1 0.02 1/minute110 kPS_Heart -1 0.02 1/minute111 kPS_Lungs -1 2 1/minute112 kPSAlb_Tumor1 -1 0 1/minute113 kPSAlb_Tumor2 -1 0 1/minute114 kPSAlb_TumorRest -1 0 1/minute115 F_Total 1 4.1256 liter/minute116 f_SG 1 0.074 1/minute117 f_Prostate 1 0.108 1/minute118 f_Tumor1 0.5 0.5 1/minute119 f_Tumor2 0.5 0.5 1/minute120 HotTotalAmountOriginal 10 10 nanomole121 ColdTotalAmountOriginal 100 100 nanomole122 RepeatTimeInterval 100 100 minute123 RepeatCount 0 0 dimensionless124 PerInjectionRate 100 100 nanomole/minute125 HotPerInjection 0 20 nanomole126 ColdPerInjection 0 200 nanomole127 dMin 1 1 minute128 dLiter 1 1 liter129 dMeter 1 1 meter130 dLiterKg 1 1 liter/kilogram131 numberPerNanomole 602200000000000 602200000000000 dimensionless132 Tumor1VolumeCoeff 1 1 dimensionless133 Tumor1Volume -1 0.01 liter134 Albumin_0 -1 0 nanomole135 AlbuminDen -1 0 nanomole/liter136 K_D_Alb -1 1 nanomole/liter137 injectionCoeff 2 2 dimensionless138 HotTotalAmount 1 20 nanomole139 ColdTotalAmount 1 200 nanomole140 Rden_Tumor1_Coeff 1 1 dimensionlessInitial AssignmentsInitial Assignments Initial Value1 PS_Tumor1 = kPS_Tumor1 * Tumor1 0.0062 PSAlb_Tumor1 = kPSAlb_Tumor1 * Tumor1 03 PS_Tumor2 = kPS_Tumor2 * Tumor2 0.2044 PSAlb_Tumor2 = kPSAlb_Tumor2 * Tumor2 05 PS_TumorRest = kPS_TumorRest * TumorRest 0.0293236 PSAlb_TumorRest = kPSAlb_TumorRest * TumorRest 07 PS_SG = kPS_SG * SG 0.0428 PS_Liver = kPS_Liver * Liver 3.829 PS_Spleen = kPS_Spleen * Spleen 0.36610 PS_Prostate = kPS_Prostate * Prostate 0.002253511 PS_GI = kPS_GI * GI 0.03343712 PS_Rest = kPS_Rest * Rest 0.2300913 PS_Muscle = kPS_Muscle * Muscle 0.8472714 PS_RedMarrow = kPS_RedMarrow*RedMarrow 3.098615 PS_Adipose = kPS_Adipose * Adipose 0.379316 PS_Bone = kPS_Bone * Bone 0.2553517 PS_Heart = kPS_Heart * Heart 0.009605618 PS_Lungs = kPS_Lungs * Lungs 2.816919 PS_Brain = kPS_Brain * Brain 020 PS_Skin = kPS_Skin * Skin 0.09621 F_Muscle = 0.17 * F 0.6674522 F_GI = 0.16 * F 0.6281923 F_Skin = 0.05 * F 0.1963124 F_Adipose = 0.05 * F 0.1963125 F_RedMarrow = 0.03 * F 0.1177826 F_Bone = 0.05 * F 0.1963127 F_Heart = 0.04 * F 0.1570528 F_Brain = 0.12 * F 0.4711429F_Rest = F -(F_Brain+F_Heart+F_Bone+F_RedMarrow+F_Adipose+F_Skin+F_GI+F_Muscle + F_Liver + F_Kidney + F_Spleen + F_Prostate +F_SG)0.1726930 F_Total = F + F_Tumor1 + F_Tumor2 + F_TumorRest 4.125631 F_Prostate = f_Prostate * Prostate 0.002433832 F_SG = f_SG * SG 0.00155433 F_Liver = 0.065 * F 0.255234 F_Spleen = 0.03 * F 0.1177835 F_Kidney = 0.19 * F 0.7459736 F_Tumor1 = f_Tumor1 * Tumor1 0.00537 F_Tumor2 = f_Tumor2 * Tumor2 0.1738 F_TumorRest = f_Tumor1 * R0_TumorRest / Rden_TumorRest 0.02443639 Tumor1Vas = 0.05 * (1-hematocrit) * Tumor1 0.000340 Tumor1Int = 0.38 * Tumor1 0.003841 Tumor2Vas = 0.05 * (1-hematocrit) * Tumor2 0.010242 Tumor2Int = 0.38 * Tumor2 0.129243 TumorRest = R0_TumorRest / Rden_TumorRest 0.04887244 TumorRestVas = 0.05 * (1-hematocrit) * TumorRest 0.001466245 TumorRestInt = 0.38 * TumorRest 0.01857146 Spleen = 0.183 0.18347 SpleenVas = 0.12 * Spleen 0.0219648 SpleenInt = 0.2 * Spleen 0.036649 SGVas = 0.03* (1-hematocrit) * SG 0.00037850 SGInt = 0.23 * SG 0.0048351 Liver = 1.91 1.9152 LiverVas = 0.085 * Liver 0.1623553 LiverInt = 0.2 * Liver 0.38254 Prostate = 0.016 * bodyWeight / 71 * dLiterKg 0.02253555 ProstateVas = 0.004 * (1-hematocrit) * Prostate 5.4085e-0556 ProstateInt = 0.25 * Prostate 0.005633857 GI = (0.385 + 0.548 + 0.104 + 0.15)*bodyWeight/71 * dLiterKg 1.671858 GIInt = 8.8 * GIVas 2.134859 GIVas = 0.076 * V_p 0.2425960Rest = bodyWeight *dLiterKg -(Lungs +Brain+Heart+Bone+RedMarrow+Adipose+Skin+GI+Muscle +Liver + Kidney + Spleen + Prostate + SG)11.504661 RestInt = 4.1 * RestVas 5.807662RestVas = V_p -(LungsVas +BrainVas+HeartVas+BoneVas+RedMarrowVas+AdiposeVas+SkinVas+GIVas+MuscleVas + LiverVas + KidneyVas + SpleenVas +ProstateVas + SGVas)1.416563 Muscle = 30.078 * bodyWeight/71 * dLiterKg 42.363464 MuscleVas = 0.14 * V_p 0.4468865 MuscleInt = 5.9 * MuscleVas 2.636666 Skin = 3.408 * bodyWeight / 71 * dLiterKg 4.867 SkinVas = 0.03 * V_p 0.0957668 SkinInt = 8.9 * SkinVas 0.8522669 Brain = 1.45 * bodyWeight / 71 * dLiterKg 2.042370 BrainVas = 0.012 * V_p 0.03830471 BrainInt = 1 * dLiter 172 Lungs = 1 * bodyWeight / 71 * dLiterKg 1.408573 LungsVas = 0.105 * V_p 0.3351674 LungsInt = 5.5 * LungsVas 1.843475 Heart = 0.341 * bodyWeight / 71 * dLiterKg 0.4802876 HeartVas = 0.01 * V_p 0.0319277 HeartInt = 3.7 * HeartVas 0.118178 Bone = 10.165 * bodyWeight /71 * dLiterKg - RedMarrow 12.767679 BoneVas = 0.07*V_p - RedMarrowVas 0.0957680 BoneInt = 8.4 * BoneVas 0.8043881 Adipose = 13.465 * bodyWeight / 71 * dLiterKg 18.964882 AdiposeVas = 0.05 * V_p 0.159683 AdiposeInt = 15.5 * AdiposeVas 2.473884 RedMarrow = 1.1 * bodyWeight/71 * dLiterKg 1.549385 RedMarrowVas = 0.04 * V_p 0.1276886 RedMarrowInt = 3.7 * RedMarrowVas 0.4724287 KidneyIntera = (Kidney - KidneyInt - KidneyVas) * 2/3 0.1648388 KidneyVas = 0.055 * Kidney 0.01710589 KidneyInt = 0.15 * Kidney 0.0466590 R0_Tumor1 = Rden_Tumor1 * Tumor1 0.5791 R0_Tumor2 = Rden_Tumor2 * Tumor2 6.4692 R0_Kidney = Rden_Kidney*Kidney 4.35493 R0_Spleen = Rden_Spleen * Spleen 0.09735694 R0_Prostate = Rden_Prostate * Prostate 0.5994495 R0_GI = Rden_GI * GI 2.668296 R0_SG = Rden_SG * SG 0.79897 R0_Liver = Rden_Liver * Liver 2.540398 lambdaRel_TumorRest = (lambdaRel_Tumor1 +lambdaRel_Tumor2 )/2 0.0001599 lambdaIntern_SG = lambdaIntern_Normal 0.001100 lambdaIntern_Liver = lambdaIntern_Tumor1 0.001101 lambdaIntern_Spleen = lambdaIntern_Tumor1 0.001102 lambdaRel_Liver = lambdaRel_Kidney 0.00029103 lambdaRel_Spleen = lambdaRel_Kidney 0.00029104 lambdaIntern_Prostate = lambdaIntern_Normal 0.001105 lambdaIntern_GI = lambdaIntern_Normal 0.001106 lambdaRel_Prostate = lambdaRel_Normal 0.00029107 lambdaRel_GI = lambdaRel_Normal 0.00029108 lambdaRel_Normal = lambdaRel_Kidney 0.00029109 lambdaIntern_Normal = lambdaIntern_Tumor1 0.001110 Rden_Spleen = 0.02 * Rden_Prostate 0.532111 Rden_Liver = 0.05 * Rden_Prostate 1.33112 Rden_Prostate = 0.1 * Rden_TumorRest 26.6113 Rden_GI = 0.06 * Rden_Prostate 1.596114 F_Lungs = F 3.9262115 GFR = TER_Kidney /3 * 201/151 0.088742116 F = V_p*1.23/dMin 3.9262117 V_p = 2.8 * (1-hematocrit) * bodySurfaceArea * dLiter / dMeter^2 3.192118 kPS_Liver = kPS_Muscle * 100 2119 kPS_Spleen = kPS_Liver 2120 kPS_Lungs = kPS_Muscle * 100 2121 kPS_SG = kPS_Muscle * 100 2122 kPS_GI = kPS_Muscle 0.02123 kPS_Skin = kPS_Muscle 0.02124 kPS_Adipose = kPS_Muscle 0.02125 kPS_RedMarrow = kPS_Liver 2126 kPS_Heart = kPS_Muscle 0.02127 kPS_Bone = kPS_Muscle 0.02128 kPS_Rest = kPS_Muscle 0.02129 f_Prostate = 0.18 * (1-hematocrit) / dMin 0.108130 HotPerInjection = HotTotalAmount/(RepeatCount+1) 20131 ColdPerInjection = ColdTotalAmount/(RepeatCount+1) 200132 lambdaIntern_Kidney = lambdaIntern_Tumor1 0.001133 kPS_Prostate = 0.1 0.1134 Tumor1 = Tumor1Volume * Tumor1VolumeCoeff 0.01135 Albumin_0 = AlbuminDen*V_p 0136 Art = 0.06*V_p + 0.045*V_p 0.33516137 Vein = 0.18*V_p + 0.045*V_p 0.7182138 Vein.Albumin = AlbuminDen * Vein 0139 Art.Albumin = AlbuminDen * Art 0140 Tumor1Vas.Albumin = AlbuminDen* Tumor1Vas 0141 Tumor1Int.Albumin = AlbuminDen * Tumor1Int 0142 Tumor2Vas.Albumin = AlbuminDen * Tumor2Vas 0143 Tumor2Int.Albumin = AlbuminDen * Tumor2Int 0144 TumorRestVas.Albumin = AlbuminDen * TumorRestVas 0145 TumorRestInt.Albumin = AlbuminDen * TumorRestInt 0146 KidneyVas.Albumin = AlbuminDen * KidneyVas 0147 SpleenVas.Albumin = AlbuminDen * SpleenVas 0148 ProstateVas.Albumin = AlbuminDen * ProstateVas 0149 GIVas.Albumin = AlbuminDen * GIVas 0150 SkinVas.Albumin = AlbuminDen * SkinVas 0151 BrainVas.Albumin = AlbuminDen * BrainVas 0152 LungsVas.Albumin = AlbuminDen * LungsVas 0153 HeartVas.Albumin = AlbuminDen * HeartVas 0154 BoneVas.Albumin = AlbuminDen * BoneVas 0155 AdiposeVas.Albumin = AlbuminDen * AdiposeVas 0156 RedMarrowVas.Albumin = AlbuminDen * RedMarrowVas 0157 MuscleVas.Albumin = AlbuminDen * MuscleVas 0158 RestVas.Albumin = AlbuminDen * RestVas 0159 LiverVas.Albumin = AlbuminDen * LiverVas 0160 SGVas.Albumin = AlbuminDen * SGVas 0161 k_on_toAlb = k_off_toAlb / K_D_Alb 0162 K_D_Alb = k_off_toAlb / k_on_toAlb 1163 HotTotalAmount = injectionCoeff * HotTotalAmountOriginal 20164 ColdTotalAmount = injectionCoeff * ColdTotalAmountOriginal 200Repeated AssignmentsRepeated Assignments Initial Value1 Tumor2.R = R0_Tumor2 - Tumor2Bound.Hot - Tumor2Bound.Cold 6.462 Tumor1.R = R0_Tumor1 - Tumor1Bound.Hot - Tumor1Bound.Cold 0.573 Kidney.R = R0_Kidney-KidneyBound.Hot-KidneyBound.Cold 4.3544 SG.R = R0_SG - SGBound.Hot - SGBound.Cold 0.7985 TumorRest.R = R0_TumorRest - TumorRestBound.Hot -TumorRestBound.Cold 136 Spleen.R = R0_Spleen - SpleenBound.Hot - SpleenBound.Cold 0.0973567 Liver.R = R0_Liver - LiverBound.Hot - LiverBound.Cold 2.54038 Prostate.R = R0_Prostate - ProstateBound.Hot -ProstateBound.Cold 0.599449 GI.R = R0_GI - GIBound.Hot - GIBound.Cold 2.668210 Data.DataKidney = KidneyVas.Hot + KidneyInt.Hot +KidneyBound.Hot + KidneyIntern.Hot 0ReactionsReactions1 Tumor2Vas.Hot -> Tumor2Vas.ColdlambdaPhys*Tumor2Vas.Hot2 Tumor2Vas.Hot + Tumor2Vas.Albumin <-> Tumor2Vas.AlbHotk_on_toAlb*Tumor2Vas.Hot*Tumor2Vas.Albumin/Tumor2Vas-k_off_toAlb*Tumor2Vas.AlbHot3 Tumor2Vas.AlbHot -> Tumor2Vas.AlbColdlambdaPhys*Tumor2Vas.AlbHot4 Tumor2Vas.Cold + Tumor2Vas.Albumin <-> Tumor2Vas.AlbColdk_on_toAlb*Tumor2Vas.Cold*Tumor2Vas.Albumin/Tumor2Vas-k_off_toAlb*Tumor2Vas.AlbCold5 Tumor2Vas.Hot <-> Tumor2Int.HotPS_Tumor2/Tumor2Vas*Tumor2Vas.Hot - PS_Tumor2/Tumor2Int*Tumor2Int.Hot6 Tumor2Vas.AlbHot -> Tumor2Int.AlbHotPSAlb_Tumor2/Tumor2Vas*Tumor2Vas.AlbHot7 Tumor2Vas.AlbCold -> Tumor2Int.AlbColdPSAlb_Tumor2/Tumor2Vas*Tumor2Vas.AlbCold8 Tumor2Vas.Cold -> Tumor2Int.ColdPS_Tumor2/Tumor2Vas*Tumor2Vas.Cold - PS_Tumor2/Tumor2Int*Tumor2Int.Cold9 Tumor2Int.Hot <-> Tumor2Bound.Hotk_on/Tumor2Int*Tumor2Int.Hot*Tumor2.R - k_off*Tumor2Bound.Hot10 Tumor2Int.Cold <-> Tumor2Bound.Coldk_on/Tumor2Int*Tumor2Int.Cold*Tumor2.R - k_off*Tumor2Bound.Cold11 Tumor2Bound.Hot -> Tumor2Intern.HotlambdaIntern_Tumor2*Tumor2Bound.Hot12 Tumor2Bound.Cold -> Tumor2Intern.ColdlambdaIntern_Tumor2*Tumor2Bound.Cold13 Art.Hot -> Tumor2Vas.HotF_Tumor2/Art*Art.Hot14 Art.AlbHot -> Tumor2Vas.AlbHotF_Tumor2/Art*Art.AlbHot15 Art.AlbCold -> Tumor2Vas.AlbColdF_Tumor2/Art*Art.AlbCold16 Art.Cold -> Tumor2Vas.ColdF_Tumor2/Art*Art.Cold17 Tumor2Vas.Hot -> Vein.HotF_Tumor2/Tumor2Vas*Tumor2Vas.Hot18 Tumor2Vas.AlbHot -> Vein.AlbHotF_Tumor2/Tumor2Vas*Tumor2Vas.AlbHot19 Tumor2Vas.AlbCold -> Vein.AlbColdF_Tumor2/Tumor2Vas*Tumor2Vas.AlbCold20 Tumor2Vas.Cold -> Vein.ColdF_Tumor2/Tumor2Vas*Tumor2Vas.Cold21 Tumor2Int.Hot -> Tumor2Int.ColdlambdaPhys*Tumor2Int.Hot22 Tumor2Int.Hot + Tumor2Int.Albumin <-> Tumor2Int.AlbHotk_on_toAlb*Tumor2Int.Hot*Tumor2Int.Albumin/Tumor2Int-k_off_toAlb*Tumor2Int.AlbHot23 Tumor2Int.AlbHot -> Tumor2Int.AlbColdlambdaPhys*Tumor2Int.AlbHot24 Tumor2Int.Cold + Tumor2Int.Albumin <-> Tumor2Int.AlbColdk_on_toAlb*Tumor2Int.Cold*Tumor2Int.Albumin/Tumor2Int-k_off_toAlb*Tumor2Int.AlbCold25 Tumor2Bound.Hot -> Tumor2Bound.ColdlambdaPhys*Tumor2Bound.Hot26 Tumor2Intern.Hot -> Tumor2Intern.ColdlambdaPhys*Tumor2Intern.Hot27 Tumor2Intern.Hot -> nulllambdaRel_Tumor2*Tumor2Intern.Hot28 Tumor2Intern.Cold -> nulllambdaRel_Tumor2*Tumor2Intern.Cold29 Art.Hot -> Art.ColdlambdaPhys*Art.Hot30 Art.Hot + Art.Albumin <-> Art.AlbHotk_on_toAlb*Art.Hot*Art.Albumin/Art-k_off_toAlb*Art.AlbHot31 Art.AlbHot -> Art.AlbColdlambdaPhys*Art.AlbHot32 Art.Cold + Art.Albumin <-> Art.AlbColdk_on_toAlb*Art.Cold*Art.Albumin/Art-k_off_toAlb*Art.AlbCold33 Vein.Hot -> Vein.ColdlambdaPhys*Vein.Hot34 Vein.Hot + Vein.Albumin <-> Vein.AlbHotk_on_toAlb*Vein.Hot*Vein.Albumin/Vein-k_off_toAlb*Vein.AlbHot35 Vein.AlbHot -> Vein.AlbColdlambdaPhys*Vein.AlbHot36 Vein.Cold + Vein.Albumin <-> Vein.AlbColdk_on_toAlb*Vein.Cold*Vein.Albumin/Vein-k_off_toAlb*Vein.AlbCold37 Tumor1Vas.Hot -> Tumor1Vas.ColdlambdaPhys*Tumor1Vas.Hot38 Tumor1Vas.Hot + Tumor1Vas.Albumin <-> Tumor1Vas.AlbHotk_on_toAlb*Tumor1Vas.Hot*Tumor1Vas.Albumin/Tumor1Vas-k_off_toAlb*Tumor1Vas.AlbHot39 Tumor1Vas.AlbHot -> Tumor1Vas.AlbColdlambdaPhys*Tumor1Vas.AlbHot40 Tumor1Vas.Cold + Tumor1Vas.Albumin <-> Tumor1Vas.AlbColdk_on_toAlb*Tumor1Vas.Cold*Tumor1Vas.Albumin/Tumor1Vas-k_off_toAlb*Tumor1Vas.AlbCold41 Tumor1Vas.Hot <-> Tumor1Int.HotPS_Tumor1/Tumor1Vas*Tumor1Vas.Hot - PS_Tumor1/Tumor1Int*Tumor1Int.Hot42 Tumor1Vas.AlbHot <-> Tumor1Int.AlbHotPSAlb_Tumor1/Tumor1Vas*Tumor1Vas.AlbHot - PSAlb_Tumor1/Tumor1Int*Tumor1Int.AlbHot43 Tumor1Vas.AlbCold -> Tumor1Int.AlbColdPSAlb_Tumor1/Tumor1Vas*Tumor1Vas.AlbCold - PSAlb_Tumor1/Tumor1Int * Tumor1Int.AlbCold44 Tumor1Vas.Cold <-> Tumor1Int.ColdPS_Tumor1/Tumor1Vas*Tumor1Vas.Cold - PS_Tumor1/Tumor1Int*Tumor1Int.Cold45 Tumor1Int.Hot <-> Tumor1Bound.Hotk_on/Tumor1Int*Tumor1Int.Hot*Tumor1.R - k_off*Tumor1Bound.Hot46 Tumor1Int.Cold <-> Tumor1Bound.Coldk_on/Tumor1Int*Tumor1.R*Tumor1Int.Cold - k_off*Tumor1Bound.Cold47 Tumor1Bound.Hot -> Tumor1Intern.HotlambdaIntern_Tumor1*Tumor1Bound.Hot48 Tumor1Bound.Cold -> Tumor1Intern.ColdlambdaIntern_Tumor1*Tumor1Bound.Cold49 Art.Hot -> Tumor1Vas.HotF_Tumor1/Art*Art.Hot50 Art.AlbHot -> Tumor1Vas.AlbHotF_Tumor1/Art*Art.AlbHot51 Art.AlbCold -> Tumor1Vas.AlbColdF_Tumor1/Art*Art.AlbCold52 Art.Cold -> Tumor1Vas.ColdF_Tumor1/Art*Art.Cold53 Tumor1Vas.Hot -> Vein.HotF_Tumor1/Tumor1Vas*Tumor1Vas.Hot54 Tumor1Vas.AlbHot -> Vein.AlbHotF_Tumor1/Tumor1Vas*Tumor1Vas.AlbHot55 Tumor1Vas.AlbCold -> Vein.AlbColdF_Tumor1/Tumor1Vas*Tumor1Vas.AlbCold56 Tumor1Vas.Cold -> Vein.ColdF_Tumor1/Tumor1Vas*Tumor1Vas.Cold57 Tumor1Int.Hot -> Tumor1Int.ColdlambdaPhys*Tumor1Int.Hot58 Tumor1Int.Hot + Tumor1Int.Albumin -> Tumor1Int.AlbHotk_on_toAlb*Tumor1Int.Hot*Tumor1Int.Albumin/Tumor1Int-k_off_toAlb*Tumor1Int.AlbHot59 Tumor1Int.AlbHot -> Tumor1Int.AlbColdlambdaPhys*Tumor1Int.AlbHot60 Tumor1Int.Cold + Tumor1Int.Albumin <-> Tumor1Int.AlbColdk_on_toAlb*Tumor1Int.Cold*Tumor1Int.Albumin/Tumor1Int-k_off_toAlb*Tumor1Int.AlbCold61 Tumor1Bound.Hot -> Tumor1Bound.ColdlambdaPhys*Tumor1Bound.Hot62 Tumor1Intern.Hot -> Tumor1Intern.ColdlambdaPhys*Tumor1Intern.Hot63 Tumor1Intern.Hot -> nulllambdaRel_Tumor1*Tumor1Intern.Hot64 Tumor1Intern.Cold -> nulllambdaRel_Tumor1*Tumor1Intern.Cold65 KidneyVas.Hot -> KidneyVas.ColdlambdaPhys*KidneyVas.Hot66 KidneyVas.Hot + KidneyVas.Albumin <-> KidneyVas.AlbHotk_on_toAlb*KidneyVas.Hot*KidneyVas.Albumin/KidneyVas-k_off_toAlb*KidneyVas.AlbHot67 KidneyVas.AlbHot -> KidneyVas.AlbColdlambdaPhys*KidneyVas.AlbHot68 KidneyVas.Cold + KidneyVas.Albumin <-> KidneyVas.AlbColdk_on_toAlb*KidneyVas.Cold*KidneyVas.Albumin/KidneyVas-k_off_toAlb*KidneyVas.AlbCold69 KidneyInt.Hot <-> KidneyBound.Hotk_on/KidneyInt*KidneyInt.Hot*Kidney.R - k_off*KidneyBound.Hot70 KidneyInt.Cold <-> KidneyBound.Coldk_on/KidneyInt*KidneyInt.Cold*Kidney.R - k_off*KidneyBound.Cold71 KidneyBound.Hot -> KidneyIntern.HotlambdaIntern_Kidney*KidneyBound.Hot72 KidneyBound.Cold -> KidneyIntern.ColdlambdaIntern_Kidney*KidneyBound.Cold73 Art.Hot -> KidneyVas.HotF_Kidney/Art*Art.Hot74 Art.AlbHot -> KidneyVas.AlbHotF_Kidney/Art*Art.AlbHot75 Art.AlbCold -> KidneyVas.AlbColdF_Kidney/Art*Art.AlbCold76 Art.Cold -> KidneyVas.ColdF_Kidney/Art*Art.Cold77 KidneyVas.Hot -> Vein.HotF_Kidney/KidneyVas*KidneyVas.Hot78 KidneyVas.AlbHot -> Vein.AlbHotF_Kidney/KidneyVas*KidneyVas.AlbHot79 KidneyVas.AlbCold -> Vein.AlbColdF_Kidney/KidneyVas*KidneyVas.AlbCold80 KidneyVas.Cold -> Vein.ColdF_Kidney/KidneyVas*KidneyVas.Cold81 KidneyInt.Hot -> KidneyInt.ColdlambdaPhys*KidneyInt.Hot82 KidneyBound.Hot -> KidneyBound.ColdlambdaPhys*KidneyBound.Hot83 KidneyIntern.Hot -> KidneyIntern.ColdlambdaPhys*KidneyIntern.Hot84 KidneyIntern.Hot -> nulllambdaRel_Kidney*KidneyIntern.Hot85 KidneyIntern.Cold -> nulllambdaRel_Kidney*KidneyIntern.Cold86 HeartVas.Hot -> HeartVas.ColdlambdaPhys*HeartVas.Hot87 HeartVas.Hot + HeartVas.Albumin <-> HeartVas.AlbHotk_on_toAlb*HeartVas.Hot*HeartVas.Albumin/HeartVas-k_off_toAlb*HeartVas.AlbHot88 HeartVas.AlbHot -> HeartVas.AlbColdlambdaPhys*HeartVas.AlbHot89 HeartVas.Cold + HeartVas.Albumin <-> HeartVas.AlbColdk_on_toAlb*HeartVas.Cold*HeartVas.Albumin/HeartVas-k_off_toAlb*HeartVas.AlbCold90 HeartVas.Hot <-> HeartInt.HotPS_Heart/HeartVas*HeartVas.Hot - PS_Heart/HeartInt*HeartInt.Hot91 HeartVas.Cold <-> HeartInt.ColdPS_Heart/HeartVas*HeartVas.Cold - PS_Heart/HeartInt*HeartInt.Cold92 Art.Hot -> HeartVas.HotF_Heart/Art*Art.Hot93 Art.AlbHot -> HeartVas.AlbHotF_Heart/Art*Art.AlbHot94 Art.AlbCold -> HeartVas.AlbColdF_Heart/Art*Art.AlbCold95 Art.Cold -> HeartVas.ColdF_Heart/Art*Art.Cold96 HeartVas.Hot -> Vein.HotF_Heart/HeartVas*HeartVas.Hot97 HeartVas.AlbHot -> Vein.AlbHotF_Heart/HeartVas*HeartVas.AlbHot98 HeartVas.AlbCold -> Vein.AlbColdF_Heart/HeartVas*HeartVas.AlbCold99 HeartVas.Cold -> Vein.ColdF_Heart/HeartVas*HeartVas.Cold100 HeartInt.Hot -> HeartInt.ColdlambdaPhys*HeartInt.Hot101 SGVas.Hot -> SGVas.ColdlambdaPhys*SGVas.Hot102 SGVas.Hot + SGVas.Albumin <-> SGVas.AlbHotk_on_toAlb*SGVas.Hot*SGVas.Albumin/SGVas-k_off_toAlb*SGVas.AlbHot103 SGVas.AlbHot -> SGVas.AlbColdlambdaPhys*SGVas.AlbHot104 SGVas.Cold + SGVas.Albumin <-> SGVas.AlbColdk_on_toAlb*SGVas.Cold*SGVas.Albumin/SGVas-k_off_toAlb*SGVas.AlbCold105 SGVas.Hot <-> SGInt.HotPS_SG/SGVas*SGVas.Hot - PS_SG/SGInt*SGInt.Hot106 SGVas.Cold <-> SGInt.ColdPS_SG/SGVas*SGVas.Cold - PS_SG/SGInt*SGInt.Cold107 SGInt.Hot <-> SGBound.Hotk_on/SGInt*SGInt.Hot*SG.R - k_off*SGBound.Hot108 SGInt.Cold <-> SGBound.Coldk_on/SGInt*SGInt.Cold*SG.R - k_off*SGBound.Cold109 SGBound.Hot -> SGIntern.HotlambdaIntern_SG*SGBound.Hot110 SGBound.Cold -> SGIntern.ColdlambdaIntern_SG*SGBound.Cold111 Art.Hot -> SGVas.HotF_SG/Art*Art.Hot112 Art.AlbHot -> SGVas.AlbHotF_SG/Art*Art.AlbHot113 Art.AlbCold -> SGVas.AlbColdF_SG/Art*Art.AlbCold114 Art.Cold -> SGVas.ColdF_SG/Art*Art.Cold115 SGVas.Hot -> Vein.HotF_SG/SGVas*SGVas.Hot116 SGVas.AlbHot -> Vein.AlbHotF_SG/SGVas*SGVas.AlbHot117 SGVas.AlbCold -> Vein.AlbColdF_SG/SGVas*SGVas.AlbCold118 SGVas.Cold -> Vein.ColdF_SG/SGVas*SGVas.Cold119 SGInt.Hot -> SGInt.ColdlambdaPhys*SGInt.Hot120 SGBound.Hot -> SGBound.ColdlambdaPhys*SGBound.Hot121 SGIntern.Hot -> SGIntern.ColdlambdaPhys*SGIntern.Hot122 SGIntern.Hot -> nulllambdaRel_SG*SGIntern.Hot123 SGIntern.Cold -> nulllambdaRel_SG*SGIntern.Cold124 BoneVas.Hot -> BoneVas.ColdlambdaPhys*BoneVas.Hot125 BoneVas.Hot + BoneVas.Albumin <-> BoneVas.AlbHotk_on_toAlb*BoneVas.Hot*BoneVas.Albumin/BoneVas-k_off_toAlb*BoneVas.AlbHot126 BoneVas.AlbHot -> BoneVas.AlbColdlambdaPhys*BoneVas.AlbHot127 BoneVas.Cold + BoneVas.Albumin <-> BoneVas.AlbColdk_on_toAlb*BoneVas.Cold*BoneVas.Albumin/BoneVas-k_off_toAlb*BoneVas.AlbCold128 BoneVas.Hot <-> BoneInt.HotPS_Bone/BoneVas*BoneVas.Hot-PS_Bone/BoneInt*BoneInt.Hot129 BoneVas.Cold <-> BoneInt.ColdPS_Bone/BoneVas*BoneVas.Cold - PS_Bone/BoneInt*BoneInt.Cold130 Art.Hot -> BoneVas.HotF_Bone/Art*Art.Hot131 Art.AlbHot -> BoneVas.AlbHotF_Bone/Art*Art.AlbHot132 Art.AlbCold -> BoneVas.AlbColdF_Bone/Art*Art.AlbCold133 Art.Cold -> BoneVas.ColdF_Bone/Art*Art.Cold134 BoneVas.Hot -> Vein.HotF_Bone/BoneVas*BoneVas.Hot135 BoneVas.AlbHot -> Vein.AlbHotF_Bone/BoneVas*BoneVas.AlbHot136 BoneVas.AlbCold -> Vein.AlbColdF_Bone/BoneVas*BoneVas.AlbCold137 BoneVas.Cold -> Vein.ColdF_Bone/BoneVas*BoneVas.Cold138 BoneInt.Hot -> BoneInt.ColdlambdaPhys*BoneInt.Hot139 TumorRestVas.Hot -> TumorRestVas.ColdlambdaPhys*TumorRestVas.Hot140 TumorRestVas.Hot + TumorRestVas.Albumin <-> TumorRestVas.AlbHotk_on_toAlb*TumorRestVas.Hot*TumorRestVas.Albumin/TumorRestVas-k_off_toAlb*TumorRestVas.AlbHot141 TumorRestVas.AlbHot -> TumorRestVas.AlbColdlambdaPhys*TumorRestVas.AlbHot142 TumorRestVas.Cold + TumorRestVas.Albumin <-> TumorRestVas.AlbColdk_on_toAlb*TumorRestVas.Cold*TumorRestVas.Albumin/TumorRestVas-k_off_toAlb*TumorRestVas.AlbCold143 TumorRestVas.Hot <-> TumorRestInt.HotPS_TumorRest/TumorRestVas*TumorRestVas.Hot - PS_TumorRest/TumorRestInt*TumorRestInt.Hot144 TumorRestVas.AlbHot <-> TumorRestInt.AlbHotPSAlb_TumorRest/TumorRestVas*TumorRestVas.AlbHot - PSAlb_TumorRest/TumorRestInt*TumorRestInt.AlbHot145 TumorRestVas.AlbCold <-> TumorRestInt.AlbColdPSAlb_TumorRest/TumorRestVas*TumorRestVas.AlbCold - PSAlb_TumorRest/TumorRestInt*TumorRestInt.AlbCold146 TumorRestVas.Cold <-> TumorRestInt.ColdPS_TumorRest/TumorRestVas * TumorRestVas.Cold - PS_TumorRest/TumorRestInt*TumorRestInt.Cold147 TumorRestInt.Hot <-> TumorRestBound.Hotk_on/TumorRestInt*TumorRestInt.Hot*TumorRest.R - k_off*TumorRestBound.Hot148 TumorRestInt.Cold <-> TumorRestBound.Coldk_on/TumorRestInt*TumorRestInt.Cold*TumorRest.R - k_off*TumorRestBound.Cold149 TumorRestBound.Hot -> TumorRestIntern.HotlambdaIntern_TumorRest*TumorRestBound.Hot150 TumorRestBound.Cold -> TumorRestIntern.ColdlambdaIntern_TumorRest*TumorRestBound.Cold151 Art.Hot -> TumorRestVas.HotF_TumorRest/Art*Art.Hot152 Art.AlbHot -> TumorRestVas.AlbHotF_TumorRest/Art*Art.AlbHot153 Art.AlbCold <-> TumorRestVas.AlbColdF_TumorRest/Art*Art.AlbCold154 Art.Cold <-> TumorRestVas.ColdF_TumorRest/Art*Art.Cold155 TumorRestVas.Hot -> Vein.HotF_TumorRest/TumorRestVas*TumorRestVas.Hot156 TumorRestVas.AlbHot -> Vein.AlbHotF_TumorRest/TumorRestVas*TumorRestVas.AlbHot157 TumorRestVas.AlbCold -> Vein.AlbColdF_TumorRest/TumorRestVas*TumorRestVas.AlbCold158 TumorRestVas.Cold -> Vein.ColdF_TumorRest/TumorRestVas*TumorRestVas.Cold159 TumorRestInt.Hot -> TumorRestInt.ColdlambdaPhys*TumorRestInt.Hot160 TumorRestInt.Hot + TumorRestInt.Albumin -> TumorRestInt.AlbHotk_on_toAlb*TumorRestInt.Hot*TumorRestInt.Albumin/TumorRestInt-k_off_toAlb*TumorRestInt.AlbHot161 TumorRestInt.AlbHot -> TumorRestInt.AlbColdlambdaPhys*TumorRestInt.AlbHot162 TumorRestInt.Cold + TumorRestInt.Albumin <-> TumorRestInt.AlbColdk_on_toAlb*TumorRestInt.Cold*TumorRestInt.Albumin/TumorRestInt-k_off_toAlb*TumorRestInt.AlbCold163 TumorRestBound.Hot -> TumorRestBound.ColdlambdaPhys*TumorRestBound.Hot164 TumorRestIntern.Hot -> TumorRestIntern.ColdlambdaPhys*TumorRestIntern.Hot165 TumorRestIntern.Hot -> nulllambdaRel_TumorRest*TumorRestIntern.Hot166 TumorRestIntern.Cold -> nulllambdaRel_TumorRest*TumorRestIntern.Cold167 SpleenVas.Hot -> SpleenVas.ColdlambdaPhys*SpleenVas.Hot168 SpleenVas.Hot + SpleenVas.Albumin <-> SpleenVas.AlbHotk_on_toAlb*SpleenVas.Hot*SpleenVas.Albumin/SpleenVas-k_off_toAlb*SpleenVas.AlbHot169 SpleenVas.AlbHot -> SpleenVas.AlbColdlambdaPhys*SpleenVas.AlbHot170 SpleenVas.Cold + SpleenVas.Albumin <-> SpleenVas.AlbColdk_on_toAlb*SpleenVas.Cold*SpleenVas.Albumin/SpleenVas-k_off_toAlb*SpleenVas.AlbCold171 SpleenVas.Hot <-> SpleenInt.HotPS_Spleen/SpleenVas*SpleenVas.Hot - PS_Spleen/SpleenInt*SpleenInt.Hot172 SpleenVas.Cold <-> SpleenInt.ColdPS_Spleen/SpleenVas*SpleenVas.Cold - PS_Spleen/SpleenInt*SpleenInt.Cold173 SpleenInt.Hot <-> SpleenBound.Hotk_on/SpleenInt*SpleenInt.Hot*Spleen.R - k_off*SpleenBound.Hot174 SpleenInt.Cold <-> SpleenBound.Coldk_on/SpleenInt*SpleenInt.Cold*Spleen.R - k_off*SpleenBound.Cold175 SpleenBound.Hot -> SpleenIntern.HotlambdaIntern_Spleen*SpleenBound.Hot176 SpleenBound.Cold -> SpleenIntern.ColdlambdaIntern_Spleen*SpleenBound.Cold177 Art.Hot -> SpleenVas.HotF_Spleen/Art*Art.Hot178 Art.AlbHot -> SpleenVas.AlbHotF_Spleen/Art*Art.AlbHot179 Art.AlbCold -> SpleenVas.AlbColdF_Spleen/Art*Art.AlbCold180 Art.Cold -> SpleenVas.ColdF_Spleen/Art*Art.Cold181 SpleenInt.Hot -> SpleenInt.ColdlambdaPhys*SpleenInt.Hot182 SpleenBound.Hot -> SpleenBound.ColdlambdaPhys*SpleenBound.Hot183 SpleenIntern.Hot -> SpleenIntern.ColdlambdaPhys*SpleenIntern.Hot184 SpleenIntern.Hot -> nulllambdaRel_Spleen*SpleenIntern.Hot185 SpleenIntern.Cold -> nulllambdaRel_Spleen*SpleenIntern.Cold186 LiverVas.Hot -> LiverVas.ColdlambdaPhys*LiverVas.Hot187 LiverVas.Hot + LiverVas.Albumin <-> LiverVas.AlbHotk_on_toAlb*LiverVas.Hot*LiverVas.Albumin/LiverVas-k_off_toAlb*LiverVas.AlbHot188 LiverVas.AlbHot -> LiverVas.AlbColdlambdaPhys*LiverVas.AlbHot189 LiverVas.Cold + LiverVas.Albumin <-> LiverVas.AlbColdk_on_toAlb*LiverVas.Cold*LiverVas.Albumin/LiverVas-k_off_toAlb*LiverVas.AlbCold190 LiverVas.Hot <-> LiverInt.HotPS_Liver/LiverVas*LiverVas.Hot - PS_Liver/LiverInt*LiverInt.Hot191 LiverVas.Cold <-> LiverInt.ColdPS_Liver/LiverVas*LiverVas.Cold - PS_Liver/LiverInt*LiverInt.Cold192 LiverInt.Hot <-> LiverBound.Hotk_on/LiverInt*LiverInt.Hot*Liver.R - k_off*LiverBound.Hot193 LiverInt.Cold <-> LiverBound.Coldk_on/LiverInt*LiverInt.Cold*Liver.R - k_off*LiverBound.Cold194 LiverBound.Hot -> LiverIntern.HotlambdaIntern_Liver*LiverBound.Hot195 LiverBound.Cold -> LiverIntern.ColdlambdaIntern_Liver*LiverBound.Cold196 Art.Hot -> LiverVas.HotF_Liver/Art*Art.Hot197 Art.AlbHot -> LiverVas.AlbHotF_Liver/Art*Art.AlbHot198 Art.AlbCold -> LiverVas.AlbColdF_Liver/Art*Art.AlbCold199 Art.Cold -> LiverVas.ColdF_Liver/Art*Art.Cold200 LiverVas.Hot -> Vein.HotF_Liver/LiverVas*LiverVas.Hot201 LiverVas.AlbHot -> Vein.AlbHotF_Liver/LiverVas*LiverVas.AlbHot202 LiverVas.AlbCold -> Vein.AlbColdF_Liver/LiverVas*LiverVas.AlbCold203 LiverVas.Cold -> Vein.ColdF_Liver/LiverVas*LiverVas.Cold204 LiverInt.Hot -> LiverInt.ColdlambdaPhys*LiverInt.Hot205 LiverBound.Hot -> LiverBound.ColdlambdaPhys*LiverBound.Hot206 LiverIntern.Hot -> LiverIntern.ColdlambdaPhys*LiverIntern.Hot207 LiverIntern.Hot -> nulllambdaRel_Liver*LiverIntern.Hot208 LiverIntern.Cold -> nulllambdaRel_Liver*LiverIntern.Cold209 ProstateVas.Hot -> ProstateVas.ColdlambdaPhys*ProstateVas.Hot210 ProstateVas.Hot + ProstateVas.Albumin <-> ProstateVas.AlbHotk_on_toAlb*ProstateVas.Hot*ProstateVas.Albumin/ProstateVas-k_off_toAlb*ProstateVas.AlbHot211 ProstateVas.AlbHot -> ProstateVas.AlbColdlambdaPhys*ProstateVas.AlbHot212 ProstateVas.Cold + ProstateVas.Albumin <-> ProstateVas.AlbColdk_on_toAlb*ProstateVas.Cold*ProstateVas.Albumin/ProstateVas-k_off_toAlb*ProstateVas.AlbCold213 ProstateVas.Hot <-> ProstateInt.HotPS_Prostate/ProstateVas*ProstateVas.Hot - PS_Prostate/ProstateInt*ProstateInt.Hot214 ProstateVas.Cold <-> ProstateInt.ColdPS_Prostate/ProstateVas*ProstateVas.Cold - PS_Prostate/ProstateInt*ProstateInt.Cold215 ProstateInt.Hot <-> ProstateBound.Hotk_on/ProstateInt*ProstateInt.Hot*Prostate.R-k_off*ProstateBound.Hot216 ProstateInt.Cold <-> ProstateBound.Coldk_on/ProstateInt*ProstateInt.Cold*Prostate.R-k_off*ProstateBound.Cold217 ProstateBound.Hot -> ProstateIntern.HotlambdaIntern_Prostate*ProstateBound.Hot218 ProstateBound.Cold -> ProstateIntern.ColdlambdaIntern_Prostate*ProstateBound.Cold219 Art.Hot -> ProstateVas.HotF_Prostate/Art*Art.Hot220 Art.AlbHot -> ProstateVas.AlbHotF_Prostate/Art*Art.AlbHot221 Art.AlbCold -> ProstateVas.AlbColdF_Prostate/Art*Art.AlbCold222 Art.Cold -> ProstateVas.ColdF_Prostate/Art*Art.Cold223 ProstateVas.Hot -> Vein.HotF_Prostate/ProstateVas*ProstateVas.Hot224 ProstateVas.AlbHot -> Vein.AlbHotF_Prostate/ProstateVas*ProstateVas.AlbHot225 ProstateVas.AlbCold -> Vein.AlbColdF_Prostate/ProstateVas*ProstateVas.AlbCold226 ProstateVas.Cold -> Vein.ColdF_Prostate/ProstateVas*ProstateVas.Cold227 ProstateInt.Hot -> ProstateInt.ColdlambdaPhys*ProstateInt.Hot228 ProstateBound.Hot -> ProstateBound.ColdlambdaPhys*ProstateBound.Hot229 ProstateIntern.Hot -> ProstateIntern.ColdlambdaPhys*ProstateIntern.Hot230 ProstateIntern.Hot -> nulllambdaRel_Prostate*ProstateIntern.Hot231 ProstateIntern.Cold -> nulllambdaRel_Prostate*ProstateIntern.Cold232 GIVas.Hot -> GIVas.ColdlambdaPhys*GIVas.Hot233 GIVas.Hot + GIVas.Albumin <-> GIVas.AlbHotk_on_toAlb*GIVas.Hot*GIVas.Albumin/GIVas-k_off_toAlb*GIVas.AlbHot234 GIVas.AlbHot -> GIVas.AlbColdlambdaPhys*GIVas.AlbHot235 GIVas.Cold + GIVas.Albumin <-> GIVas.AlbColdk_on_toAlb*GIVas.Cold*GIVas.Albumin/GIVas-k_off_toAlb*GIVas.AlbCold236 GIVas.Hot <-> GIInt.HotPS_GI/GIVas*GIVas.Hot - PS_GI/GIInt*GIInt.Hot237 GIVas.Cold <-> GIInt.ColdPS_GI/GIVas*GIVas.Cold - PS_GI/GIInt*GIInt.Cold238 GIInt.Hot <-> GIBound.Hotk_on/GIInt*GIInt.Hot*GI.R - k_off*GIBound.Hot239 GIInt.Cold <-> GIBound.Coldk_on/GIInt*GIInt.Cold*GI.R - k_off*GIBound.Cold240 GIBound.Hot -> GIIntern.HotlambdaIntern_GI*GIBound.Hot241 GIBound.Cold -> GIIntern.ColdlambdaIntern_GI*GIBound.Cold242 Art.Hot -> GIVas.HotF_GI/Art*Art.Hot243 Art.AlbHot -> GIVas.AlbHotF_GI/Art*Art.AlbHot244 Art.AlbCold -> GIVas.AlbColdF_GI/Art*Art.AlbCold245 Art.Cold -> GIVas.ColdF_GI/Art*Art.Cold246 GIInt.Hot -> GIInt.ColdlambdaPhys*GIInt.Hot247 GIBound.Hot -> GIBound.ColdlambdaPhys*GIBound.Hot248 GIIntern.Hot -> GIIntern.ColdlambdaPhys*GIIntern.Hot249 GIIntern.Hot -> nulllambdaRel_GI*GIIntern.Hot250 GIIntern.Cold -> nulllambdaRel_GI*GIIntern.Cold251 RestVas.Hot -> RestVas.ColdlambdaPhys*RestVas.Hot252 RestVas.Hot + RestVas.Albumin <-> RestVas.AlbHotk_on_toAlb*RestVas.Hot*RestVas.Albumin/RestVas-k_off_toAlb*RestVas.AlbHot253 RestVas.AlbHot -> RestVas.AlbColdlambdaPhys*RestVas.AlbHot254 RestVas.Cold + RestVas.Albumin <-> RestVas.AlbColdk_on_toAlb*RestVas.Cold*RestVas.Albumin/RestVas-k_off_toAlb*RestVas.AlbCold255 RestVas.Hot <-> RestInt.HotPS_Rest/RestVas*RestVas.Hot - PS_Rest/RestInt*RestInt.Hot256 RestVas.Cold <-> RestInt.ColdPS_Rest/RestVas*RestVas.Cold - PS_Rest/RestInt*RestInt.Cold257 Art.Hot -> RestVas.HotF_Rest/Art*Art.Hot258 Art.AlbHot -> RestVas.AlbHotF_Rest/Art*Art.AlbHot259 Art.AlbCold -> RestVas.AlbColdF_Rest/Art*Art.AlbCold260 Art.Cold -> RestVas.ColdF_Rest/Art*Art.Cold261 RestVas.Hot -> Vein.HotF_Rest/RestVas*RestVas.Hot262 RestVas.AlbHot -> Vein.AlbHotF_Rest/RestVas*RestVas.AlbHot263 RestVas.AlbCold -> Vein.AlbColdF_Rest/RestVas*RestVas.AlbCold264 RestVas.Cold -> Vein.ColdF_Rest/RestVas*RestVas.Cold265 RestInt.Hot -> RestInt.ColdlambdaPhys*RestInt.Hot266 SkinVas.Hot -> SkinVas.ColdlambdaPhys*SkinVas.Hot267 SkinVas.Hot + SkinVas.Albumin <-> SkinVas.AlbHotk_on_toAlb*SkinVas.Hot*SkinVas.Albumin/SkinVas-k_off_toAlb*SkinVas.AlbHot268 SkinVas.AlbHot -> SkinVas.AlbColdlambdaPhys*SkinVas.AlbHot269 SkinVas.Cold + SkinVas.Albumin <-> SkinVas.AlbColdk_on_toAlb*SkinVas.Cold*SkinVas.Albumin/SkinVas-k_off_toAlb*SkinVas.AlbCold270 SkinVas.Hot <-> SkinInt.HotPS_Skin/SkinVas*SkinVas.Hot - PS_Skin/SkinVas*SkinInt.Hot271 SkinVas.Cold <-> SkinInt.ColdPS_Skin/SkinVas*SkinVas.Cold - PS_Skin/SkinInt*SkinInt.Cold272 Art.Hot -> SkinVas.HotF_Skin/Art*Art.Hot273 Art.AlbHot -> SkinVas.AlbHotF_Skin/Art*Art.AlbHot274 Art.AlbCold -> SkinVas.AlbColdF_Skin/Art*Art.AlbCold275 Art.Cold -> SkinVas.ColdF_Skin/Art*Art.Cold276 SkinVas.Hot -> Vein.HotF_Skin/SkinVas*SkinVas.Hot277 SkinVas.AlbHot -> Vein.AlbHotF_Skin/SkinVas*SkinVas.AlbHot278 SkinVas.AlbCold -> Vein.AlbColdF_Skin/SkinVas*SkinVas.AlbCold279 SkinVas.Cold -> Vein.ColdF_Skin/SkinVas*SkinVas.Cold280 SkinInt.Hot -> SkinInt.ColdlambdaPhys*SkinInt.Hot281 MuscleVas.Hot -> MuscleVas.ColdlambdaPhys*MuscleVas.Hot282 MuscleVas.Hot + MuscleVas.Albumin <-> MuscleVas.AlbHotk_on_toAlb*MuscleVas.Hot*MuscleVas.Albumin/MuscleVas-k_off_toAlb*MuscleVas.AlbHot283 MuscleVas.AlbHot -> MuscleVas.AlbColdlambdaPhys*MuscleVas.AlbHot284 MuscleVas.Cold + MuscleVas.Albumin <-> MuscleVas.AlbColdk_on_toAlb*MuscleVas.Cold*MuscleVas.Albumin/MuscleVas-k_off_toAlb*MuscleVas.AlbCold285 MuscleVas.Hot <-> MuscleInt.HotPS_Muscle/MuscleVas*MuscleVas.Hot - PS_Muscle/MuscleInt*MuscleInt.Hot286 MuscleVas.Cold <-> MuscleInt.ColdPS_Muscle/MuscleVas*MuscleVas.Cold - PS_Muscle/MuscleInt*MuscleInt.Cold287 Art.Hot -> MuscleVas.HotF_Muscle/Art*Art.Hot288 Art.AlbHot -> MuscleVas.AlbHotF_Muscle/Art*Art.AlbHot289 Art.AlbCold -> MuscleVas.AlbColdF_Muscle/Art*Art.AlbCold290 Art.Cold -> MuscleVas.ColdF_Muscle/Art*Art.Cold291 MuscleVas.Hot -> Vein.HotF_Muscle/MuscleVas*MuscleVas.Hot292 MuscleVas.AlbHot -> Vein.AlbHotF_Muscle/MuscleVas*MuscleVas.AlbHot293 MuscleVas.AlbCold -> Vein.AlbColdF_Muscle/MuscleVas*MuscleVas.AlbCold294 MuscleVas.Cold -> Vein.ColdF_Muscle/MuscleVas*MuscleVas.Cold295 MuscleInt.Hot -> MuscleInt.ColdlambdaPhys*MuscleInt.Hot296 BrainVas.Hot -> BrainVas.ColdlambdaPhys*BrainVas.Hot297 BrainVas.Hot + BrainVas.Albumin <-> BrainVas.AlbHotk_on_toAlb*BrainVas.Hot*BrainVas.Albumin/BrainVas-k_off_toAlb*BrainVas.AlbHot298 BrainVas.AlbHot -> BrainVas.AlbColdlambdaPhys*BrainVas.AlbHot299 BrainVas.Cold + BrainVas.Albumin <-> BrainVas.AlbColdk_on_toAlb*BrainVas.Cold*BrainVas.Albumin/BrainVas-k_off_toAlb*BrainVas.AlbCold300 BrainVas.Hot <-> BrainInt.HotPS_Brain/BrainVas*BrainVas.Hot-PS_Brain/BrainInt*BrainInt.Hot301 BrainVas.Cold <-> BrainInt.ColdPS_Brain/BrainVas*BrainVas.Cold - PS_Brain/BrainInt*BrainInt.Cold302 Art.Hot -> BrainVas.HotF_Brain/Art*Art.Hot303 Art.AlbHot -> BrainVas.AlbHotF_Brain/Art*Art.AlbHot304 Art.AlbCold -> BrainVas.AlbColdF_Brain/Art*Art.AlbCold305 Art.Cold -> BrainVas.ColdF_Brain/Art*Art.Cold306 BrainVas.Hot -> Vein.HotF_Brain/BrainVas*BrainVas.Hot307 BrainVas.AlbHot -> Vein.AlbHotF_Brain/BrainVas*BrainVas.AlbHot308 BrainVas.AlbCold -> Vein.AlbColdF_Brain/BrainVas*BrainVas.AlbCold309 BrainVas.Cold -> Vein.ColdF_Brain/BrainVas*BrainVas.Cold310 BrainInt.Hot -> BrainInt.ColdlambdaPhys*BrainInt.Hot311 RedMarrowVas.Hot -> RedMarrowVas.ColdlambdaPhys*RedMarrowVas.Hot312 RedMarrowVas.Hot + RedMarrowVas.Albumin <-> RedMarrowVas.AlbHotk_on_toAlb*RedMarrowVas.Hot*RedMarrowVas.Albumin/RedMarrowVas-k_off_toAlb*RedMarrowVas.AlbHot313 RedMarrowVas.AlbHot -> RedMarrowVas.AlbColdlambdaPhys*RedMarrowVas.AlbHot314 RedMarrowVas.Cold + RedMarrowVas.Albumin <-> RedMarrowVas.AlbColdk_on_toAlb*RedMarrowVas.Cold*RedMarrowVas.Albumin/RedMarrowVas-k_off_toAlb*RedMarrowVas.AlbCold315 RedMarrowVas.Hot <-> RedMarrowInt.HotPS_RedMarrow/RedMarrowVas*RedMarrowVas.Hot - PS_RedMarrow/RedMarrowInt*RedMarrowInt.Hot316 RedMarrowVas.Cold <-> RedMarrowInt.ColdPS_RedMarrow/RedMarrowVas*RedMarrowVas.Cold - PS_RedMarrow/RedMarrowInt*RedMarrowInt.Cold317 Art.Hot -> RedMarrowVas.HotF_RedMarrow/Art*Art.Hot318 Art.AlbHot -> RedMarrowVas.AlbHotF_RedMarrow/Art*Art.AlbHot319 Art.AlbCold -> RedMarrowVas.AlbColdF_RedMarrow/Art*Art.AlbCold320 Art.Cold -> RedMarrowVas.ColdF_RedMarrow/Art*Art.Cold321 RedMarrowVas.Hot -> Vein.HotF_RedMarrow/RedMarrowVas*RedMarrowVas.Hot322 RedMarrowVas.AlbHot -> Vein.AlbHotF_RedMarrow/RedMarrowVas*RedMarrowVas.AlbHot323 RedMarrowVas.AlbCold -> Vein.AlbColdF_RedMarrow/RedMarrowVas*RedMarrowVas.AlbCold324 RedMarrowVas.Cold -> Vein.ColdF_RedMarrow/RedMarrowVas*RedMarrowVas.Cold325 RedMarrowInt.Hot -> RedMarrowInt.ColdlambdaPhys*RedMarrowInt.Hot326 LungsVas.Hot -> LungsVas.ColdlambdaPhys*LungsVas.Hot327 LungsVas.Hot + LungsVas.Albumin <-> LungsVas.AlbHotk_on_toAlb*LungsVas.Hot*LungsVas.Albumin/LungsVas-k_off_toAlb*LungsVas.AlbHot328 LungsVas.AlbHot -> LungsVas.AlbColdlambdaPhys*LungsVas.AlbHot329 LungsVas.Cold + LungsVas.Albumin <-> LungsVas.AlbColdk_on_toAlb*LungsVas.Cold*LungsVas.Albumin/LungsVas-k_off_toAlb*LungsVas.AlbCold330 LungsVas.Hot <-> LungsInt.HotPS_Lungs/LungsVas*LungsVas.Hot- PS_Lungs/LungsInt*LungsInt.Hot331 LungsVas.Cold <-> LungsInt.ColdPS_Lungs/LungsVas*LungsVas.Cold - PS_Lungs/LungsInt*LungsInt.Cold332 LungsVas.Hot -> Art.HotF_Lungs/LungsVas*LungsVas.Hot333 LungsVas.AlbHot -> Art.AlbHotF_Lungs/LungsVas*LungsVas.AlbHot334 LungsVas.AlbCold -> Art.AlbColdF_Lungs/LungsVas*LungsVas.AlbCold335 LungsVas.Cold -> Art.ColdF_Lungs/LungsVas*LungsVas.Cold336 Vein.Hot -> LungsVas.HotF_Lungs/Vein*Vein.Hot337 Vein.AlbHot -> LungsVas.AlbHotF_Lungs/Vein*Vein.AlbHot338 Vein.AlbCold -> LungsVas.AlbColdF_Lungs/Vein*Vein.AlbCold339 Vein.Cold -> LungsVas.ColdF_Lungs/Vein*Vein.Cold340 LungsInt.Hot -> LungsInt.ColdlambdaPhys*LungsInt.Hot341 AdiposeVas.Hot -> AdiposeVas.ColdlambdaPhys*AdiposeVas.Hot342 AdiposeVas.Hot + AdiposeVas.Albumin <-> AdiposeVas.AlbHotk_on_toAlb*AdiposeVas.Hot*AdiposeVas.Albumin/AdiposeVas-k_off_toAlb*AdiposeVas.AlbHot343 AdiposeVas.AlbHot -> AdiposeVas.AlbColdlambdaPhys*AdiposeVas.AlbHot344 AdiposeVas.Cold + AdiposeVas.Albumin <-> AdiposeVas.AlbColdk_on_toAlb*AdiposeVas.Cold*AdiposeVas.Albumin/AdiposeVas-k_off_toAlb*AdiposeVas.AlbCold345 AdiposeVas.Hot <-> AdiposeInt.HotPS_Adipose/AdiposeVas*AdiposeVas.Hot - PS_Adipose/AdiposeInt*AdiposeInt.Hot346 AdiposeVas.Cold <-> AdiposeInt.ColdPS_Adipose/AdiposeVas*AdiposeVas.Cold - PS_Adipose/AdiposeInt*AdiposeInt.Cold347 Art.Hot -> AdiposeVas.HotF_Adipose/Art*Art.Hot348 Art.AlbHot -> AdiposeVas.AlbHotF_Adipose/Art*Art.AlbHot349 Art.AlbCold -> AdiposeVas.AlbColdF_Adipose/Art*Art.AlbCold350 Art.Cold -> AdiposeVas.ColdF_Adipose/Art*Art.Cold351 AdiposeVas.Hot -> Vein.HotF_Adipose/AdiposeVas*AdiposeVas.Hot352 AdiposeVas.AlbHot -> Vein.AlbHotF_Adipose/AdiposeVas*AdiposeVas.AlbHot353 AdiposeVas.AlbCold -> Vein.AlbColdF_Adipose/AdiposeVas*AdiposeVas.AlbCold354 AdiposeVas.Cold -> Vein.ColdF_Adipose/AdiposeVas*AdiposeVas.Cold355 AdiposeInt.Hot -> AdiposeInt.ColdlambdaPhys*AdiposeInt.Hot356 KidneyVas.Hot -> KidneyInt.HotGFR*phi/KidneyVas*KidneyVas.Hot357 KidneyVas.Cold -> KidneyInt.ColdGFR*phi/KidneyVas*KidneyVas.Cold358 KidneyInt.Hot -> KidneyIntera.HotGFR*phi*(1-f_exc)/KidneyInt*KidneyInt.Hot359 KidneyInt.Cold -> KidneyIntera.ColdGFR*phi*(1-f_exc)/KidneyInt*KidneyInt.Cold360 KidneyIntera.Hot -> KidneyVas.HotGFR*phi*(1-f_exc)/KidneyIntern*KidneyIntera.Hot361 KidneyIntera.Cold -> KidneyVas.ColdGFR*phi*(1-f_exc)/KidneyIntern*KidneyIntera.Cold362 KidneyInt.Cold -> nullGFR*phi*f_exc/KidneyInt*KidneyInt.Cold363 KidneyInt.Hot -> nullGFR*phi*f_exc/KidneyInt*KidneyInt.Hot364 SpleenVas.Hot -> LiverVas.HotF_Spleen/SpleenVas*SpleenVas.Hot365 GIVas.Hot -> LiverVas.HotF_GI/GIVas*GIVas.Hot366 SpleenVas.AlbHot -> LiverVas.AlbHotF_Spleen/SpleenVas*SpleenVas.AlbHot367 SpleenVas.AlbCold -> LiverVas.AlbColdF_Spleen/SpleenVas*SpleenVas.AlbCold368 SpleenVas.Cold -> LiverVas.ColdF_Spleen/SpleenVas * SpleenVas.Cold369 GIVas.AlbHot -> LiverVas.AlbHotF_GI/GIVas*GIVas.AlbHot370 GIVas.AlbCold -> LiverVas.AlbColdF_GI/GIVas*GIVas.AlbCold371 GIVas.Cold -> LiverVas.ColdF_GI/GIVas*GIVas.Cold372 Art.Albumin -> Tumor2Vas.AlbuminF_Tumor2/Art*Art.Albumin373 Art.Albumin -> Tumor1Vas.AlbuminF_Tumor1/Art*Art.Albumin374 Tumor1Vas.Albumin -> Vein.AlbuminF_Tumor1/Tumor1Vas*Tumor1Vas.Albumin375 Tumor2Vas.Albumin -> Vein.AlbuminF_Tumor2/Tumor2Vas*Tumor2Vas.Albumin376 Art.Albumin -> KidneyVas.AlbuminF_Kidney/Art*Art.Albumin377 KidneyVas.Albumin -> Vein.AlbuminF_Kidney/KidneyVas*KidneyVas.Albumin378 Art.Albumin -> SpleenVas.AlbuminF_Spleen/Art*Art.Albumin379 SpleenVas.Albumin -> Vein.AlbuminF_Spleen/SpleenVas*SpleenVas.Albumin380 Art.Albumin -> ProstateVas.AlbuminF_Prostate/Art*Art.Albumin381 ProstateVas.Albumin -> Vein.AlbuminF_Prostate/ProstateVas*ProstateVas.Albumin382 Art.Albumin -> GIVas.AlbuminF_GI/Art*Art.Albumin383 GIVas.Albumin -> Vein.AlbuminF_GI/GIVas*GIVas.Albumin384 Art.Albumin -> SkinVas.AlbuminF_Skin/Art*Art.Albumin385 SkinVas.Albumin -> Vein.AlbuminF_Skin/SkinVas*SkinVas.Albumin386 Art.Albumin -> BrainVas.AlbuminF_Brain/Art*Art.Albumin387 BrainVas.Albumin -> Vein.AlbuminF_Brain/BrainVas*BrainVas.Albumin388 Vein.Albumin -> LungsVas.AlbuminF_Lungs/Vein*Vein.Albumin389 LungsVas.Albumin -> Art.AlbuminF_Lungs/LungsVas*LungsVas.Albumin390 Art.Albumin -> HeartVas.AlbuminF_Heart/Art*Art.Albumin391 HeartVas.Albumin -> Vein.AlbuminF_Heart/HeartVas*HeartVas.Albumin392 Art.Albumin -> BoneVas.AlbuminF_Bone/Art*Art.Albumin393 BoneVas.Albumin -> Vein.AlbuminF_Bone/BoneVas*BoneVas.Albumin394 Art.Albumin -> AdiposeVas.AlbuminF_Adipose/Art*Art.Albumin395 AdiposeVas.Albumin -> Vein.AlbuminF_Adipose/AdiposeVas*AdiposeVas.Albumin396 Art.Albumin -> RedMarrowVas.AlbuminF_RedMarrow/Art*Art.Albumin397 RedMarrowVas.Albumin -> Vein.AlbuminF_RedMarrow/RedMarrowVas*RedMarrowVas.Albumin398 Art.Albumin -> MuscleVas.AlbuminF_Muscle/Art*Art.Albumin399 MuscleVas.Albumin -> Vein.AlbuminF_Muscle/MuscleVas*MuscleVas.Albumin400 Art.Albumin -> RestVas.AlbuminF_Rest/Art*Art.Albumin401 RestVas.Albumin -> Vein.AlbuminF_Rest/RestVas*RestVas.Albumin402 Art.Albumin -> LiverVas.AlbuminF_Liver/Art*Art.Albumin403 LiverVas.Albumin -> Vein.AlbuminF_Liver/LiverVas*LiverVas.Albumin404 Art.Albumin -> SGVas.AlbuminF_SG/Art*Art.Albumin405 SGVas.Albumin -> Vein.AlbuminF_SG/SGVas*SGVas.Albumin406 Art.Albumin -> TumorRestVas.AlbuminF_TumorRest/Art*Art.Albumin407 TumorRestVas.Albumin -> Vein.AlbuminF_TumorRest/TumorRestVas*TumorRestVas.Albumin408 Tumor2Vas.Albumin <-> Tumor2Int.AlbuminPSAlb_Tumor2/Tumor2Vas*Tumor2Vas.Albumin - PSAlb_Tumor2/Tumor2Int*Tumor2Int.Albumin409 Tumor1Vas.Albumin <-> Tumor1Int.AlbuminPSAlb_Tumor1/Tumor1Vas*Tumor1Vas.Albumin - PSAlb_Tumor1/Tumor1Int*Tumor1Int.Albumin410 TumorRestVas.Albumin <-> TumorRestInt.AlbuminPSAlb_TumorRest/TumorRestVas*TumorRestVas.Albumin - PSAlb_TumorRest/TumorRestInt*TumorRestInt.AlbuminObservablesObservables1 Tumor1_TotalHot = Tumor1Vas.Hot + Tumor1Int.Hot + Tumor1Bound.Hot + Tumor1Intern.Hot + Tumor1Vas.AlbHot +Tumor1Int.AlbHot2 Tumor2_TotalHot = Tumor2Vas.Hot + Tumor2Int.Hot + Tumor2Bound.Hot + Tumor2Intern.Hot + Tumor2Vas.AlbHot +Tumor2Int.AlbHot3 TumorTotalHot = Tumor1_TotalHot4 KidneyTotalHot = KidneyVas.Hot + KidneyInt.Hot + KidneyBound.Hot + KidneyIntern.Hot5 SGTotalHot = SGVas.Hot + SGInt.Hot + SGBound.Hot + SGIntern.Hot6 LiverTotalHot = LiverVas.Hot + LiverInt.Hot + LiverBound.Hot + LiverIntern.Hot7 ProstateTotalHot = ProstateVas.Hot + ProstateInt.Hot + ProstateBound.Hot + ProstateIntern.Hot8 SpleenTotalHot = SpleenVas.Hot + SpleenInt.Hot + SpleenBound.Hot + SpleenIntern.Hot9 RedMarrowTotalHot = RedMarrowVas.Hot + RedMarrowInt.Hot10 BoneTotalHot = BoneVas.Hot + BoneInt.Hot11 TIA_TumorTotal = trapz(time, TumorTotalHot .* lambdaPhys ./ 60 .* numberPerNanomole)12 TIA_Kidney = trapz(time, KidneyTotalHot .* lambdaPhys ./ 60 .* numberPerNanomole)13 TIA_SG = trapz(time, SGTotalHot .* lambdaPhys ./ 60 .* numberPerNanomole)14 TIA_Liver = trapz(time, LiverTotalHot .* lambdaPhys ./ 60 .* numberPerNanomole)15 TIA_Spleen = trapz(time, SpleenTotalHot .* lambdaPhys ./ 60 .* numberPerNanomole)16 TIA_RedMarrow = trapz(time, RedMarrowTotalHot .* lambdaPhys ./ 60 .* numberPerNanomole)17 HotStuffBlood = Vein.Hot + Vein.AlbHot18 BloodTIA = trapz(time, HotStuffBlood .* lambdaPhys ./ 60 .* numberPerNanomole)Repeat DosesTargetName Amount Rate StartTime RepeatCount Interval Name1 Vein.Hot HotPerInjection PerInjectionRate 0 (minute) RepeatCountRepeatTimeInterval HotInjection2 Vein.Cold ColdPerInjectionPerInjectionRate 0 (minute) RepeatCountRepeatTimeInterval ColdInjectionModel EquationsODEsODEs1d(Tumor2Vas.Hot)/dt = -(lambdaPhys*Tumor2Vas.Hot) - (k_on_toAlb*Tumor2Vas.Hot*Tumor2Vas.Albumin/Tumor2Vas-k_off_toAlb*Tumor2Vas.AlbHot) - (PS_Tumor2/Tumor2Vas*Tumor2Vas.Hot-PS_Tumor2/Tumor2Int*Tumor2Int.Hot) +(F_Tumor2/Art*Art.Hot) - (F_Tumor2/Tumor2Vas*Tumor2Vas.Hot)2d(Tumor2Vas.Cold)/dt = (lambdaPhys*Tumor2Vas.Hot) - (k_on_toAlb*Tumor2Vas.Cold*Tumor2Vas.Albumin/Tumor2Vas-k_off_toAlb*Tumor2Vas.AlbCold) - (PS_Tumor2/Tumor2Vas*Tumor2Vas.Cold-PS_Tumor2/Tumor2Int*Tumor2Int.Cold) +(F_Tumor2/Art*Art.Cold) - (F_Tumor2/Tumor2Vas*Tumor2Vas.Cold)3 d(Tumor2Vas.AlbHot)/dt = (k_on_toAlb*Tumor2Vas.Hot*Tumor2Vas.Albumin/Tumor2Vas-k_off_toAlb*Tumor2Vas.AlbHot) -(lambdaPhys*Tumor2Vas.AlbHot) - (PSAlb_Tumor2/Tumor2Vas*Tumor2Vas.AlbHot) + (F_Tumor2/Art*Art.AlbHot) -(F_Tumor2/Tumor2Vas*Tumor2Vas.AlbHot)4d(Tumor2Vas.AlbCold)/dt = (lambdaPhys*Tumor2Vas.AlbHot) + (k_on_toAlb*Tumor2Vas.Cold*Tumor2Vas.Albumin/Tumor2Vas-k_off_toAlb*Tumor2Vas.AlbCold) - (PSAlb_Tumor2/Tumor2Vas*Tumor2Vas.AlbCold) + (F_Tumor2/Art*Art.AlbCold) -(F_Tumor2/Tumor2Vas*Tumor2Vas.AlbCold)5d(Tumor2Vas.Albumin)/dt = -(k_on_toAlb*Tumor2Vas.Hot*Tumor2Vas.Albumin/Tumor2Vas-k_off_toAlb*Tumor2Vas.AlbHot) -(k_on_toAlb*Tumor2Vas.Cold*Tumor2Vas.Albumin/Tumor2Vas-k_off_toAlb*Tumor2Vas.AlbCold) + (F_Tumor2/Art*Art.Albumin) -(F_Tumor2/Tumor2Vas*Tumor2Vas.Albumin) - (PSAlb_Tumor2/Tumor2Vas*Tumor2Vas.Albumin-PSAlb_Tumor2/Tumor2Int*Tumor2Int.Albumin)6d(Tumor2Int.Hot)/dt = (PS_Tumor2/Tumor2Vas*Tumor2Vas.Hot-PS_Tumor2/Tumor2Int*Tumor2Int.Hot) -(k_on/Tumor2Int*Tumor2Int.Hot*Tumor2.R-k_off*Tumor2Bound.Hot) - (lambdaPhys*Tumor2Int.Hot) -(k_on_toAlb*Tumor2Int.Hot*Tumor2Int.Albumin/Tumor2Int-k_off_toAlb*Tumor2Int.AlbHot)7d(Tumor2Int.Cold)/dt = (PS_Tumor2/Tumor2Vas*Tumor2Vas.Cold-PS_Tumor2/Tumor2Int*Tumor2Int.Cold) -(k_on/Tumor2Int*Tumor2Int.Cold*Tumor2.R-k_off*Tumor2Bound.Cold) + (lambdaPhys*Tumor2Int.Hot) -(k_on_toAlb*Tumor2Int.Cold*Tumor2Int.Albumin/Tumor2Int-k_off_toAlb*Tumor2Int.AlbCold)8 d(Tumor2Int.AlbHot)/dt = (PSAlb_Tumor2/Tumor2Vas*Tumor2Vas.AlbHot) + (k_on_toAlb*Tumor2Int.Hot*Tumor2Int.Albumin/Tumor2Int-k_off_toAlb*Tumor2Int.AlbHot) - (lambdaPhys*Tumor2Int.AlbHot)9 d(Tumor2Int.AlbCold)/dt = (PSAlb_Tumor2/Tumor2Vas*Tumor2Vas.AlbCold) + (lambdaPhys*Tumor2Int.AlbHot) +(k_on_toAlb*Tumor2Int.Cold*Tumor2Int.Albumin/Tumor2Int-k_off_toAlb*Tumor2Int.AlbCold)10d(Tumor2Int.Albumin)/dt = -(k_on_toAlb*Tumor2Int.Hot*Tumor2Int.Albumin/Tumor2Int-k_off_toAlb*Tumor2Int.AlbHot) -(k_on_toAlb*Tumor2Int.Cold*Tumor2Int.Albumin/Tumor2Int-k_off_toAlb*Tumor2Int.AlbCold) +(PSAlb_Tumor2/Tumor2Vas*Tumor2Vas.Albumin-PSAlb_Tumor2/Tumor2Int*Tumor2Int.Albumin)11 d(Tumor2Bound.Hot)/dt = (k_on/Tumor2Int*Tumor2Int.Hot*Tumor2.R-k_off*Tumor2Bound.Hot) -(lambdaIntern_Tumor2*Tumor2Bound.Hot) - (lambdaPhys*Tumor2Bound.Hot)12 d(Tumor2Bound.Cold)/dt = (k_on/Tumor2Int*Tumor2Int.Cold*Tumor2.R-k_off*Tumor2Bound.Cold) -(lambdaIntern_Tumor2*Tumor2Bound.Cold) + (lambdaPhys*Tumor2Bound.Hot)13 d(Tumor2Intern.Hot)/dt = (lambdaIntern_Tumor2*Tumor2Bound.Hot) - (lambdaPhys*Tumor2Intern.Hot) -(lambdaRel_Tumor2*Tumor2Intern.Hot)14 d(Tumor2Intern.Cold)/dt = (lambdaIntern_Tumor2*Tumor2Bound.Cold) + (lambdaPhys*Tumor2Intern.Hot) -(lambdaRel_Tumor2*Tumor2Intern.Cold)15d(Art.Hot)/dt = -(F_Tumor2/Art*Art.Hot) - (lambdaPhys*Art.Hot) - (k_on_toAlb*Art.Hot*Art.Albumin/Art-k_off_toAlb*Art.AlbHot) -(F_Tumor1/Art*Art.Hot) - (F_Kidney/Art*Art.Hot) - (F_Heart/Art*Art.Hot) - (F_SG/Art*Art.Hot) - (F_Bone/Art*Art.Hot) -(F_TumorRest/Art*Art.Hot) - (F_Spleen/Art*Art.Hot) - (F_Liver/Art*Art.Hot) - (F_Prostate/Art*Art.Hot) - (F_GI/Art*Art.Hot) -(F_Rest/Art*Art.Hot) - (F_Skin/Art*Art.Hot) - (F_Muscle/Art*Art.Hot) - (F_Brain/Art*Art.Hot) - (F_RedMarrow/Art*Art.Hot) +(F_Lungs/LungsVas*LungsVas.Hot) - (F_Adipose/Art*Art.Hot)16d(Art.Cold)/dt = -(F_Tumor2/Art*Art.Cold) + (lambdaPhys*Art.Hot) - (k_on_toAlb*Art.Cold*Art.Albumin/Art-k_off_toAlb*Art.AlbCold) -(F_Tumor1/Art*Art.Cold) - (F_Kidney/Art*Art.Cold) - (F_Heart/Art*Art.Cold) - (F_SG/Art*Art.Cold) - (F_Bone/Art*Art.Cold) -(F_TumorRest/Art*Art.Cold) - (F_Spleen/Art*Art.Cold) - (F_Liver/Art*Art.Cold) - (F_Prostate/Art*Art.Cold) - (F_GI/Art*Art.Cold) -(F_Rest/Art*Art.Cold) - (F_Skin/Art*Art.Cold) - (F_Muscle/Art*Art.Cold) - (F_Brain/Art*Art.Cold) - (F_RedMarrow/Art*Art.Cold) +(F_Lungs/LungsVas*LungsVas.Cold) - (F_Adipose/Art*Art.Cold)17d(Art.AlbHot)/dt = -(F_Tumor2/Art*Art.AlbHot) + (k_on_toAlb*Art.Hot*Art.Albumin/Art-k_off_toAlb*Art.AlbHot) - (lambdaPhys*Art.AlbHot)- (F_Tumor1/Art*Art.AlbHot) - (F_Kidney/Art*Art.AlbHot) - (F_Heart/Art*Art.AlbHot) - (F_SG/Art*Art.AlbHot) - (F_Bone/Art*Art.AlbHot) -(F_TumorRest/Art*Art.AlbHot) - (F_Spleen/Art*Art.AlbHot) - (F_Liver/Art*Art.AlbHot) - (F_Prostate/Art*Art.AlbHot) - (F_GI/Art*Art.AlbHot) -(F_Rest/Art*Art.AlbHot) - (F_Skin/Art*Art.AlbHot) - (F_Muscle/Art*Art.AlbHot) - (F_Brain/Art*Art.AlbHot) - (F_RedMarrow/Art*Art.AlbHot) +(F_Lungs/LungsVas*LungsVas.AlbHot) - (F_Adipose/Art*Art.AlbHot)18d(Art.AlbCold)/dt = -(F_Tumor2/Art*Art.AlbCold) + (lambdaPhys*Art.AlbHot) + (k_on_toAlb*Art.Cold*Art.Albumin/Art-k_off_toAlb*Art.AlbCold) - (F_Tumor1/Art*Art.AlbCold) - (F_Kidney/Art*Art.AlbCold) - (F_Heart/Art*Art.AlbCold) - (F_SG/Art*Art.AlbCold) -(F_Bone/Art*Art.AlbCold) - (F_TumorRest/Art*Art.AlbCold) - (F_Spleen/Art*Art.AlbCold) - (F_Liver/Art*Art.AlbCold) -(F_Prostate/Art*Art.AlbCold) - (F_GI/Art*Art.AlbCold) - (F_Rest/Art*Art.AlbCold) - (F_Skin/Art*Art.AlbCold) - (F_Muscle/Art*Art.AlbCold) -(F_Brain/Art*Art.AlbCold) - (F_RedMarrow/Art*Art.AlbCold) + (F_Lungs/LungsVas*LungsVas.AlbCold) - (F_Adipose/Art*Art.AlbCold)19d(Art.Albumin)/dt = -(k_on_toAlb*Art.Hot*Art.Albumin/Art-k_off_toAlb*Art.AlbHot) - (k_on_toAlb*Art.Cold*Art.Albumin/Art-k_off_toAlb*Art.AlbCold) - (F_Tumor2/Art*Art.Albumin) - (F_Tumor1/Art*Art.Albumin) - (F_Kidney/Art*Art.Albumin) -(F_Spleen/Art*Art.Albumin) - (F_Prostate/Art*Art.Albumin) - (F_GI/Art*Art.Albumin) - (F_Skin/Art*Art.Albumin) - (F_Brain/Art*Art.Albumin)+ (F_Lungs/LungsVas*LungsVas.Albumin) - (F_Heart/Art*Art.Albumin) - (F_Bone/Art*Art.Albumin) - (F_Adipose/Art*Art.Albumin) -(F_RedMarrow/Art*Art.Albumin) - (F_Muscle/Art*Art.Albumin) - (F_Rest/Art*Art.Albumin) - (F_Liver/Art*Art.Albumin) -(F_SG/Art*Art.Albumin) - (F_TumorRest/Art*Art.Albumin)20d(Vein.Hot)/dt = (F_Tumor2/Tumor2Vas*Tumor2Vas.Hot) - (lambdaPhys*Vein.Hot) - (k_on_toAlb*Vein.Hot*Vein.Albumin/Vein-k_off_toAlb*Vein.AlbHot) + (F_Tumor1/Tumor1Vas*Tumor1Vas.Hot) + (F_Kidney/KidneyVas*KidneyVas.Hot) +(F_Heart/HeartVas*HeartVas.Hot) + (F_SG/SGVas*SGVas.Hot) + (F_Bone/BoneVas*BoneVas.Hot) +(F_TumorRest/TumorRestVas*TumorRestVas.Hot) + (F_Liver/LiverVas*LiverVas.Hot) + (F_Prostate/ProstateVas*ProstateVas.Hot) +(F_Rest/RestVas*RestVas.Hot) + (F_Skin/SkinVas*SkinVas.Hot) + (F_Muscle/MuscleVas*MuscleVas.Hot) +(F_Brain/BrainVas*BrainVas.Hot) + (F_RedMarrow/RedMarrowVas*RedMarrowVas.Hot) - (F_Lungs/Vein*Vein.Hot) +(F_Adipose/AdiposeVas*AdiposeVas.Hot) + HotInjection21d(Vein.Cold)/dt = (F_Tumor2/Tumor2Vas*Tumor2Vas.Cold) + (lambdaPhys*Vein.Hot) - (k_on_toAlb*Vein.Cold*Vein.Albumin/Vein-k_off_toAlb*Vein.AlbCold) + (F_Tumor1/Tumor1Vas*Tumor1Vas.Cold) + (F_Kidney/KidneyVas*KidneyVas.Cold) +(F_Heart/HeartVas*HeartVas.Cold) + (F_SG/SGVas*SGVas.Cold) + (F_Bone/BoneVas*BoneVas.Cold) +(F_TumorRest/TumorRestVas*TumorRestVas.Cold) + (F_Liver/LiverVas*LiverVas.Cold) + (F_Prostate/ProstateVas*ProstateVas.Cold) +(F_Rest/RestVas*RestVas.Cold) + (F_Skin/SkinVas*SkinVas.Cold) + (F_Muscle/MuscleVas*MuscleVas.Cold) +(F_Brain/BrainVas*BrainVas.Cold) + (F_RedMarrow/RedMarrowVas*RedMarrowVas.Cold) - (F_Lungs/Vein*Vein.Cold) +(F_Adipose/AdiposeVas*AdiposeVas.Cold) + ColdInjection22d(Vein.AlbHot)/dt = (F_Tumor2/Tumor2Vas*Tumor2Vas.AlbHot) + (k_on_toAlb*Vein.Hot*Vein.Albumin/Vein-k_off_toAlb*Vein.AlbHot) -(lambdaPhys*Vein.AlbHot) + (F_Tumor1/Tumor1Vas*Tumor1Vas.AlbHot) + (F_Kidney/KidneyVas*KidneyVas.AlbHot) +(F_Heart/HeartVas*HeartVas.AlbHot) + (F_SG/SGVas*SGVas.AlbHot) + (F_Bone/BoneVas*BoneVas.AlbHot) +(F_TumorRest/TumorRestVas*TumorRestVas.AlbHot) + (F_Liver/LiverVas*LiverVas.AlbHot) +(F_Prostate/ProstateVas*ProstateVas.AlbHot) + (F_Rest/RestVas*RestVas.AlbHot) + (F_Skin/SkinVas*SkinVas.AlbHot) +(F_Muscle/MuscleVas*MuscleVas.AlbHot) + (F_Brain/BrainVas*BrainVas.AlbHot) + (F_RedMarrow/RedMarrowVas*RedMarrowVas.AlbHot)- (F_Lungs/Vein*Vein.AlbHot) + (F_Adipose/AdiposeVas*AdiposeVas.AlbHot)23d(Vein.AlbCold)/dt = (F_Tumor2/Tumor2Vas*Tumor2Vas.AlbCold) + (lambdaPhys*Vein.AlbHot) +(k_on_toAlb*Vein.Cold*Vein.Albumin/Vein-k_off_toAlb*Vein.AlbCold) + (F_Tumor1/Tumor1Vas*Tumor1Vas.AlbCold) +(F_Kidney/KidneyVas*KidneyVas.AlbCold) + (F_Heart/HeartVas*HeartVas.AlbCold) + (F_SG/SGVas*SGVas.AlbCold) +(F_Bone/BoneVas*BoneVas.AlbCold) + (F_TumorRest/TumorRestVas*TumorRestVas.AlbCold) + (F_Liver/LiverVas*LiverVas.AlbCold) +(F_Prostate/ProstateVas*ProstateVas.AlbCold) + (F_Rest/RestVas*RestVas.AlbCold) + (F_Skin/SkinVas*SkinVas.AlbCold) +(F_Muscle/MuscleVas*MuscleVas.AlbCold) + (F_Brain/BrainVas*BrainVas.AlbCold) +(F_RedMarrow/RedMarrowVas*RedMarrowVas.AlbCold) - (F_Lungs/Vein*Vein.AlbCold) + (F_Adipose/AdiposeVas*AdiposeVas.AlbCold)24d(Vein.Albumin)/dt = -(k_on_toAlb*Vein.Hot*Vein.Albumin/Vein-k_off_toAlb*Vein.AlbHot) - (k_on_toAlb*Vein.Cold*Vein.Albumin/Vein-k_off_toAlb*Vein.AlbCold) + (F_Tumor1/Tumor1Vas*Tumor1Vas.Albumin) + (F_Tumor2/Tumor2Vas*Tumor2Vas.Albumin) +(F_Kidney/KidneyVas*KidneyVas.Albumin) + (F_Spleen/SpleenVas*SpleenVas.Albumin) + (F_Prostate/ProstateVas*ProstateVas.Albumin)+ (F_GI/GIVas*GIVas.Albumin) + (F_Skin/SkinVas*SkinVas.Albumin) + (F_Brain/BrainVas*BrainVas.Albumin) -(F_Lungs/Vein*Vein.Albumin) + (F_Heart/HeartVas*HeartVas.Albumin) + (F_Bone/BoneVas*BoneVas.Albumin) +(F_Adipose/AdiposeVas*AdiposeVas.Albumin) + (F_RedMarrow/RedMarrowVas*RedMarrowVas.Albumin) +(F_Muscle/MuscleVas*MuscleVas.Albumin) + (F_Rest/RestVas*RestVas.Albumin) + (F_Liver/LiverVas*LiverVas.Albumin) +(F_SG/SGVas*SGVas.Albumin) + (F_TumorRest/TumorRestVas*TumorRestVas.Albumin)25d(Tumor1Vas.Hot)/dt = -(lambdaPhys*Tumor1Vas.Hot) - (k_on_toAlb*Tumor1Vas.Hot*Tumor1Vas.Albumin/Tumor1Vas-k_off_toAlb*Tumor1Vas.AlbHot) - (PS_Tumor1/Tumor1Vas*Tumor1Vas.Hot-PS_Tumor1/Tumor1Int*Tumor1Int.Hot) +(F_Tumor1/Art*Art.Hot) - (F_Tumor1/Tumor1Vas*Tumor1Vas.Hot)26d(Tumor1Vas.Cold)/dt = (lambdaPhys*Tumor1Vas.Hot) - (k_on_toAlb*Tumor1Vas.Cold*Tumor1Vas.Albumin/Tumor1Vas-k_off_toAlb*Tumor1Vas.AlbCold) - (PS_Tumor1/Tumor1Vas*Tumor1Vas.Cold-PS_Tumor1/Tumor1Int*Tumor1Int.Cold) +(F_Tumor1/Art*Art.Cold) - (F_Tumor1/Tumor1Vas*Tumor1Vas.Cold)27d(Tumor1Vas.AlbHot)/dt = (k_on_toAlb*Tumor1Vas.Hot*Tumor1Vas.Albumin/Tumor1Vas-k_off_toAlb*Tumor1Vas.AlbHot) -(lambdaPhys*Tumor1Vas.AlbHot) - (PSAlb_Tumor1/Tumor1Vas*Tumor1Vas.AlbHot-PSAlb_Tumor1/Tumor1Int*Tumor1Int.AlbHot) +(F_Tumor1/Art*Art.AlbHot) - (F_Tumor1/Tumor1Vas*Tumor1Vas.AlbHot)28d(Tumor1Vas.AlbCold)/dt = (lambdaPhys*Tumor1Vas.AlbHot) + (k_on_toAlb*Tumor1Vas.Cold*Tumor1Vas.Albumin/Tumor1Vas-k_off_toAlb*Tumor1Vas.AlbCold) - (PSAlb_Tumor1/Tumor1Vas*Tumor1Vas.AlbCold-PSAlb_Tumor1/Tumor1Int*Tumor1Int.AlbCold) +(F_Tumor1/Art*Art.AlbCold) - (F_Tumor1/Tumor1Vas*Tumor1Vas.AlbCold)29d(Tumor1Vas.Albumin)/dt = -(k_on_toAlb*Tumor1Vas.Hot*Tumor1Vas.Albumin/Tumor1Vas-k_off_toAlb*Tumor1Vas.AlbHot) -(k_on_toAlb*Tumor1Vas.Cold*Tumor1Vas.Albumin/Tumor1Vas-k_off_toAlb*Tumor1Vas.AlbCold) + (F_Tumor1/Art*Art.Albumin) -(F_Tumor1/Tumor1Vas*Tumor1Vas.Albumin) - (PSAlb_Tumor1/Tumor1Vas*Tumor1Vas.Albumin-PSAlb_Tumor1/Tumor1Int*Tumor1Int.Albumin)30d(Tumor1Int.Hot)/dt = (PS_Tumor1/Tumor1Vas*Tumor1Vas.Hot-PS_Tumor1/Tumor1Int*Tumor1Int.Hot) -(k_on/Tumor1Int*Tumor1Int.Hot*Tumor1.R-k_off*Tumor1Bound.Hot) - (lambdaPhys*Tumor1Int.Hot) -(k_on_toAlb*Tumor1Int.Hot*Tumor1Int.Albumin/Tumor1Int-k_off_toAlb*Tumor1Int.AlbHot)31d(Tumor1Int.Cold)/dt = (PS_Tumor1/Tumor1Vas*Tumor1Vas.Cold-PS_Tumor1/Tumor1Int*Tumor1Int.Cold) -(k_on/Tumor1Int*Tumor1.R*Tumor1Int.Cold-k_off*Tumor1Bound.Cold) + (lambdaPhys*Tumor1Int.Hot) -(k_on_toAlb*Tumor1Int.Cold*Tumor1Int.Albumin/Tumor1Int-k_off_toAlb*Tumor1Int.AlbCold)32 d(Tumor1Int.AlbHot)/dt = (PSAlb_Tumor1/Tumor1Vas*Tumor1Vas.AlbHot-PSAlb_Tumor1/Tumor1Int*Tumor1Int.AlbHot) +(k_on_toAlb*Tumor1Int.Hot*Tumor1Int.Albumin/Tumor1Int-k_off_toAlb*Tumor1Int.AlbHot) - (lambdaPhys*Tumor1Int.AlbHot)33 d(Tumor1Int.AlbCold)/dt = (PSAlb_Tumor1/Tumor1Vas*Tumor1Vas.AlbCold-PSAlb_Tumor1/Tumor1Int*Tumor1Int.AlbCold) +(lambdaPhys*Tumor1Int.AlbHot) + (k_on_toAlb*Tumor1Int.Cold*Tumor1Int.Albumin/Tumor1Int-k_off_toAlb*Tumor1Int.AlbCold)34d(Tumor1Int.Albumin)/dt = -(k_on_toAlb*Tumor1Int.Hot*Tumor1Int.Albumin/Tumor1Int-k_off_toAlb*Tumor1Int.AlbHot) -(k_on_toAlb*Tumor1Int.Cold*Tumor1Int.Albumin/Tumor1Int-k_off_toAlb*Tumor1Int.AlbCold) +(PSAlb_Tumor1/Tumor1Vas*Tumor1Vas.Albumin-PSAlb_Tumor1/Tumor1Int*Tumor1Int.Albumin)35 d(Tumor1Bound.Hot)/dt = (k_on/Tumor1Int*Tumor1Int.Hot*Tumor1.R-k_off*Tumor1Bound.Hot) -(lambdaIntern_Tumor1*Tumor1Bound.Hot) - (lambdaPhys*Tumor1Bound.Hot)36 d(Tumor1Bound.Cold)/dt = (k_on/Tumor1Int*Tumor1.R*Tumor1Int.Cold-k_off*Tumor1Bound.Cold) -(lambdaIntern_Tumor1*Tumor1Bound.Cold) + (lambdaPhys*Tumor1Bound.Hot)37 d(Tumor1Intern.Hot)/dt = (lambdaIntern_Tumor1*Tumor1Bound.Hot) - (lambdaPhys*Tumor1Intern.Hot) -(lambdaRel_Tumor1*Tumor1Intern.Hot)38 d(Tumor1Intern.Cold)/dt = (lambdaIntern_Tumor1*Tumor1Bound.Cold) + (lambdaPhys*Tumor1Intern.Hot) -(lambdaRel_Tumor1*Tumor1Intern.Cold)39d(KidneyVas.Hot)/dt = -(lambdaPhys*KidneyVas.Hot) - (k_on_toAlb*KidneyVas.Hot*KidneyVas.Albumin/KidneyVas-k_off_toAlb*KidneyVas.AlbHot) + (F_Kidney/Art*Art.Hot) - (F_Kidney/KidneyVas*KidneyVas.Hot) - (GFR*phi/KidneyVas*KidneyVas.Hot) +(GFR*phi*(1-f_exc)/KidneyIntern*KidneyIntera.Hot)40d(KidneyVas.Cold)/dt = (lambdaPhys*KidneyVas.Hot) - (k_on_toAlb*KidneyVas.Cold*KidneyVas.Albumin/KidneyVas-k_off_toAlb*KidneyVas.AlbCold) + (F_Kidney/Art*Art.Cold) - (F_Kidney/KidneyVas*KidneyVas.Cold) -(GFR*phi/KidneyVas*KidneyVas.Cold) + (GFR*phi*(1-f_exc)/KidneyIntern*KidneyIntera.Cold)41 d(KidneyVas.AlbHot)/dt = (k_on_toAlb*KidneyVas.Hot*KidneyVas.Albumin/KidneyVas-k_off_toAlb*KidneyVas.AlbHot) -(lambdaPhys*KidneyVas.AlbHot) + (F_Kidney/Art*Art.AlbHot) - (F_Kidney/KidneyVas*KidneyVas.AlbHot)42 d(KidneyVas.AlbCold)/dt = (lambdaPhys*KidneyVas.AlbHot) + (k_on_toAlb*KidneyVas.Cold*KidneyVas.Albumin/KidneyVas-k_off_toAlb*KidneyVas.AlbCold) + (F_Kidney/Art*Art.AlbCold) - (F_Kidney/KidneyVas*KidneyVas.AlbCold)43d(KidneyVas.Albumin)/dt = -(k_on_toAlb*KidneyVas.Hot*KidneyVas.Albumin/KidneyVas-k_off_toAlb*KidneyVas.AlbHot) -(k_on_toAlb*KidneyVas.Cold*KidneyVas.Albumin/KidneyVas-k_off_toAlb*KidneyVas.AlbCold) + (F_Kidney/Art*Art.Albumin) -(F_Kidney/KidneyVas*KidneyVas.Albumin)44 d(KidneyInt.Hot)/dt = -(k_on/KidneyInt*KidneyInt.Hot*Kidney.R-k_off*KidneyBound.Hot) - (lambdaPhys*KidneyInt.Hot) +(GFR*phi/KidneyVas*KidneyVas.Hot) - (GFR*phi*(1-f_exc)/KidneyInt*KidneyInt.Hot) - (GFR*phi*f_exc/KidneyInt*KidneyInt.Hot)45 d(KidneyInt.Cold)/dt = -(k_on/KidneyInt*KidneyInt.Cold*Kidney.R-k_off*KidneyBound.Cold) + (lambdaPhys*KidneyInt.Hot) +(GFR*phi/KidneyVas*KidneyVas.Cold) - (GFR*phi*(1-f_exc)/KidneyInt*KidneyInt.Cold) - (GFR*phi*f_exc/KidneyInt*KidneyInt.Cold)46 d(KidneyBound.Hot)/dt = (k_on/KidneyInt*KidneyInt.Hot*Kidney.R-k_off*KidneyBound.Hot) - (lambdaIntern_Kidney*KidneyBound.Hot) -(lambdaPhys*KidneyBound.Hot)47 d(KidneyBound.Cold)/dt = (k_on/KidneyInt*KidneyInt.Cold*Kidney.R-k_off*KidneyBound.Cold) -(lambdaIntern_Kidney*KidneyBound.Cold) + (lambdaPhys*KidneyBound.Hot)48d(KidneyIntern.Hot)/dt = (lambdaIntern_Kidney*KidneyBound.Hot) - (lambdaPhys*KidneyIntern.Hot) -(lambdaRel_Kidney*KidneyIntern.Hot)49 d(KidneyIntern.Cold)/dt = (lambdaIntern_Kidney*KidneyBound.Cold) + (lambdaPhys*KidneyIntern.Hot) -(lambdaRel_Kidney*KidneyIntern.Cold)50 d(KidneyIntera.Hot)/dt = (GFR*phi*(1-f_exc)/KidneyInt*KidneyInt.Hot) - (GFR*phi*(1-f_exc)/KidneyIntern*KidneyIntera.Hot)51 d(KidneyIntera.Cold)/dt = (GFR*phi*(1-f_exc)/KidneyInt*KidneyInt.Cold) - (GFR*phi*(1-f_exc)/KidneyIntern*KidneyIntera.Cold)52d(HeartVas.Hot)/dt = -(lambdaPhys*HeartVas.Hot) - (k_on_toAlb*HeartVas.Hot*HeartVas.Albumin/HeartVas-k_off_toAlb*HeartVas.AlbHot) - (PS_Heart/HeartVas*HeartVas.Hot-PS_Heart/HeartInt*HeartInt.Hot) + (F_Heart/Art*Art.Hot) -(F_Heart/HeartVas*HeartVas.Hot)53d(HeartVas.Cold)/dt = (lambdaPhys*HeartVas.Hot) - (k_on_toAlb*HeartVas.Cold*HeartVas.Albumin/HeartVas-k_off_toAlb*HeartVas.AlbCold) - (PS_Heart/HeartVas*HeartVas.Cold-PS_Heart/HeartInt*HeartInt.Cold) + (F_Heart/Art*Art.Cold) -(F_Heart/HeartVas*HeartVas.Cold)54 d(HeartVas.AlbHot)/dt = (k_on_toAlb*HeartVas.Hot*HeartVas.Albumin/HeartVas-k_off_toAlb*HeartVas.AlbHot) -(lambdaPhys*HeartVas.AlbHot) + (F_Heart/Art*Art.AlbHot) - (F_Heart/HeartVas*HeartVas.AlbHot)55 d(HeartVas.AlbCold)/dt = (lambdaPhys*HeartVas.AlbHot) + (k_on_toAlb*HeartVas.Cold*HeartVas.Albumin/HeartVas-k_off_toAlb*HeartVas.AlbCold) + (F_Heart/Art*Art.AlbCold) - (F_Heart/HeartVas*HeartVas.AlbCold)56d(HeartVas.Albumin)/dt = -(k_on_toAlb*HeartVas.Hot*HeartVas.Albumin/HeartVas-k_off_toAlb*HeartVas.AlbHot) -(k_on_toAlb*HeartVas.Cold*HeartVas.Albumin/HeartVas-k_off_toAlb*HeartVas.AlbCold) + (F_Heart/Art*Art.Albumin) -(F_Heart/HeartVas*HeartVas.Albumin)57 d(HeartInt.Hot)/dt = (PS_Heart/HeartVas*HeartVas.Hot-PS_Heart/HeartInt*HeartInt.Hot) - (lambdaPhys*HeartInt.Hot)58 d(HeartInt.Cold)/dt = (PS_Heart/HeartVas*HeartVas.Cold-PS_Heart/HeartInt*HeartInt.Cold) + (lambdaPhys*HeartInt.Hot)59 d(SGVas.Hot)/dt = -(lambdaPhys*SGVas.Hot) - (k_on_toAlb*SGVas.Hot*SGVas.Albumin/SGVas-k_off_toAlb*SGVas.AlbHot) -(PS_SG/SGVas*SGVas.Hot-PS_SG/SGInt*SGInt.Hot) + (F_SG/Art*Art.Hot) - (F_SG/SGVas*SGVas.Hot)60 d(SGVas.Cold)/dt = (lambdaPhys*SGVas.Hot) - (k_on_toAlb*SGVas.Cold*SGVas.Albumin/SGVas-k_off_toAlb*SGVas.AlbCold) -(PS_SG/SGVas*SGVas.Cold-PS_SG/SGInt*SGInt.Cold) + (F_SG/Art*Art.Cold) - (F_SG/SGVas*SGVas.Cold)61 d(SGVas.AlbHot)/dt = (k_on_toAlb*SGVas.Hot*SGVas.Albumin/SGVas-k_off_toAlb*SGVas.AlbHot) - (lambdaPhys*SGVas.AlbHot) +(F_SG/Art*Art.AlbHot) - (F_SG/SGVas*SGVas.AlbHot)62 d(SGVas.AlbCold)/dt = (lambdaPhys*SGVas.AlbHot) + (k_on_toAlb*SGVas.Cold*SGVas.Albumin/SGVas-k_off_toAlb*SGVas.AlbCold) +(F_SG/Art*Art.AlbCold) - (F_SG/SGVas*SGVas.AlbCold)63 d(SGVas.Albumin)/dt = -(k_on_toAlb*SGVas.Hot*SGVas.Albumin/SGVas-k_off_toAlb*SGVas.AlbHot) -(k_on_toAlb*SGVas.Cold*SGVas.Albumin/SGVas-k_off_toAlb*SGVas.AlbCold) + (F_SG/Art*Art.Albumin) - (F_SG/SGVas*SGVas.Albumin)64 d(SGInt.Hot)/dt = (PS_SG/SGVas*SGVas.Hot-PS_SG/SGInt*SGInt.Hot) - (k_on/SGInt*SGInt.Hot*SG.R-k_off*SGBound.Hot) -(lambdaPhys*SGInt.Hot)65 d(SGInt.Cold)/dt = (PS_SG/SGVas*SGVas.Cold-PS_SG/SGInt*SGInt.Cold) - (k_on/SGInt*SGInt.Cold*SG.R-k_off*SGBound.Cold) +(lambdaPhys*SGInt.Hot)66 d(SGBound.Hot)/dt = (k_on/SGInt*SGInt.Hot*SG.R-k_off*SGBound.Hot) - (lambdaIntern_SG*SGBound.Hot) - (lambdaPhys*SGBound.Hot)67 d(SGBound.Cold)/dt = (k_on/SGInt*SGInt.Cold*SG.R-k_off*SGBound.Cold) - (lambdaIntern_SG*SGBound.Cold) +(lambdaPhys*SGBound.Hot)68 d(SGIntern.Hot)/dt = (lambdaIntern_SG*SGBound.Hot) - (lambdaPhys*SGIntern.Hot) - (lambdaRel_SG*SGIntern.Hot)69 d(SGIntern.Cold)/dt = (lambdaIntern_SG*SGBound.Cold) + (lambdaPhys*SGIntern.Hot) - (lambdaRel_SG*SGIntern.Cold)70 d(BoneVas.Hot)/dt = -(lambdaPhys*BoneVas.Hot) - (k_on_toAlb*BoneVas.Hot*BoneVas.Albumin/BoneVas-k_off_toAlb*BoneVas.AlbHot) -(PS_Bone/BoneVas*BoneVas.Hot-PS_Bone/BoneInt*BoneInt.Hot) + (F_Bone/Art*Art.Hot) - (F_Bone/BoneVas*BoneVas.Hot)71 d(BoneVas.Cold)/dt = (lambdaPhys*BoneVas.Hot) - (k_on_toAlb*BoneVas.Cold*BoneVas.Albumin/BoneVas-k_off_toAlb*BoneVas.AlbCold)- (PS_Bone/BoneVas*BoneVas.Cold-PS_Bone/BoneInt*BoneInt.Cold) + (F_Bone/Art*Art.Cold) - (F_Bone/BoneVas*BoneVas.Cold)72 d(BoneVas.AlbHot)/dt = (k_on_toAlb*BoneVas.Hot*BoneVas.Albumin/BoneVas-k_off_toAlb*BoneVas.AlbHot) -(lambdaPhys*BoneVas.AlbHot) + (F_Bone/Art*Art.AlbHot) - (F_Bone/BoneVas*BoneVas.AlbHot)73 d(BoneVas.AlbCold)/dt = (lambdaPhys*BoneVas.AlbHot) + (k_on_toAlb*BoneVas.Cold*BoneVas.Albumin/BoneVas-k_off_toAlb*BoneVas.AlbCold) + (F_Bone/Art*Art.AlbCold) - (F_Bone/BoneVas*BoneVas.AlbCold)74d(BoneVas.Albumin)/dt = -(k_on_toAlb*BoneVas.Hot*BoneVas.Albumin/BoneVas-k_off_toAlb*BoneVas.AlbHot) -(k_on_toAlb*BoneVas.Cold*BoneVas.Albumin/BoneVas-k_off_toAlb*BoneVas.AlbCold) + (F_Bone/Art*Art.Albumin) -(F_Bone/BoneVas*BoneVas.Albumin)75 d(BoneInt.Hot)/dt = (PS_Bone/BoneVas*BoneVas.Hot-PS_Bone/BoneInt*BoneInt.Hot) - (lambdaPhys*BoneInt.Hot)76 d(BoneInt.Cold)/dt = (PS_Bone/BoneVas*BoneVas.Cold-PS_Bone/BoneInt*BoneInt.Cold) + (lambdaPhys*BoneInt.Hot)77d(TumorRestVas.Hot)/dt = -(lambdaPhys*TumorRestVas.Hot) - (k_on_toAlb*TumorRestVas.Hot*TumorRestVas.Albumin/TumorRestVas-k_off_toAlb*TumorRestVas.AlbHot) - (PS_TumorRest/TumorRestVas*TumorRestVas.Hot-PS_TumorRest/TumorRestInt*TumorRestInt.Hot)+ (F_TumorRest/Art*Art.Hot) - (F_TumorRest/TumorRestVas*TumorRestVas.Hot)78d(TumorRestVas.Cold)/dt = (lambdaPhys*TumorRestVas.Hot) - (k_on_toAlb*TumorRestVas.Cold*TumorRestVas.Albumin/TumorRestVas-k_off_toAlb*TumorRestVas.AlbCold) - (PS_TumorRest/TumorRestVas*TumorRestVas.Cold-PS_TumorRest/TumorRestInt*TumorRestInt.Cold) + (F_TumorRest/Art*Art.Cold) - (F_TumorRest/TumorRestVas*TumorRestVas.Cold)79d(TumorRestVas.AlbHot)/dt = (k_on_toAlb*TumorRestVas.Hot*TumorRestVas.Albumin/TumorRestVas-k_off_toAlb*TumorRestVas.AlbHot)- (lambdaPhys*TumorRestVas.AlbHot) - (PSAlb_TumorRest/TumorRestVas*TumorRestVas.AlbHot-PSAlb_TumorRest/TumorRestInt*TumorRestInt.AlbHot) + (F_TumorRest/Art*Art.AlbHot) -(F_TumorRest/TumorRestVas*TumorRestVas.AlbHot)80d(TumorRestVas.AlbCold)/dt = (lambdaPhys*TumorRestVas.AlbHot) +(k_on_toAlb*TumorRestVas.Cold*TumorRestVas.Albumin/TumorRestVas-k_off_toAlb*TumorRestVas.AlbCold) -(PSAlb_TumorRest/TumorRestVas*TumorRestVas.AlbCold-PSAlb_TumorRest/TumorRestInt*TumorRestInt.AlbCold) +(F_TumorRest/Art*Art.AlbCold) - (F_TumorRest/TumorRestVas*TumorRestVas.AlbCold)81d(TumorRestVas.Albumin)/dt = -(k_on_toAlb*TumorRestVas.Hot*TumorRestVas.Albumin/TumorRestVas-k_off_toAlb*TumorRestVas.AlbHot) - (k_on_toAlb*TumorRestVas.Cold*TumorRestVas.Albumin/TumorRestVas-k_off_toAlb*TumorRestVas.AlbCold) + (F_TumorRest/Art*Art.Albumin) - (F_TumorRest/TumorRestVas*TumorRestVas.Albumin) -(PSAlb_TumorRest/TumorRestVas*TumorRestVas.Albumin-PSAlb_TumorRest/TumorRestInt*TumorRestInt.Albumin)82d(TumorRestInt.Hot)/dt = (PS_TumorRest/TumorRestVas*TumorRestVas.Hot-PS_TumorRest/TumorRestInt*TumorRestInt.Hot) -(k_on/TumorRestInt*TumorRestInt.Hot*TumorRest.R-k_off*TumorRestBound.Hot) - (lambdaPhys*TumorRestInt.Hot) -(k_on_toAlb*TumorRestInt.Hot*TumorRestInt.Albumin/TumorRestInt-k_off_toAlb*TumorRestInt.AlbHot)83d(TumorRestInt.Cold)/dt = (PS_TumorRest/TumorRestVas*TumorRestVas.Cold-PS_TumorRest/TumorRestInt*TumorRestInt.Cold) -(k_on/TumorRestInt*TumorRestInt.Cold*TumorRest.R-k_off*TumorRestBound.Cold) + (lambdaPhys*TumorRestInt.Hot) -(k_on_toAlb*TumorRestInt.Cold*TumorRestInt.Albumin/TumorRestInt-k_off_toAlb*TumorRestInt.AlbCold)84d(TumorRestInt.AlbHot)/dt = (PSAlb_TumorRest/TumorRestVas*TumorRestVas.AlbHot-PSAlb_TumorRest/TumorRestInt*TumorRestInt.AlbHot) + (k_on_toAlb*TumorRestInt.Hot*TumorRestInt.Albumin/TumorRestInt-k_off_toAlb*TumorRestInt.AlbHot) - (lambdaPhys*TumorRestInt.AlbHot)85d(TumorRestInt.AlbCold)/dt = (PSAlb_TumorRest/TumorRestVas*TumorRestVas.AlbCold-PSAlb_TumorRest/TumorRestInt*TumorRestInt.AlbCold) + (lambdaPhys*TumorRestInt.AlbHot) +(k_on_toAlb*TumorRestInt.Cold*TumorRestInt.Albumin/TumorRestInt-k_off_toAlb*TumorRestInt.AlbCold)86d(TumorRestInt.Albumin)/dt = -(k_on_toAlb*TumorRestInt.Hot*TumorRestInt.Albumin/TumorRestInt-k_off_toAlb*TumorRestInt.AlbHot) -(k_on_toAlb*TumorRestInt.Cold*TumorRestInt.Albumin/TumorRestInt-k_off_toAlb*TumorRestInt.AlbCold) +(PSAlb_TumorRest/TumorRestVas*TumorRestVas.Albumin-PSAlb_TumorRest/TumorRestInt*TumorRestInt.Albumin)87 d(TumorRestBound.Hot)/dt = (k_on/TumorRestInt*TumorRestInt.Hot*TumorRest.R-k_off*TumorRestBound.Hot) -(lambdaIntern_TumorRest*TumorRestBound.Hot) - (lambdaPhys*TumorRestBound.Hot)88 d(TumorRestBound.Cold)/dt = (k_on/TumorRestInt*TumorRestInt.Cold*TumorRest.R-k_off*TumorRestBound.Cold) -(lambdaIntern_TumorRest*TumorRestBound.Cold) + (lambdaPhys*TumorRestBound.Hot)89 d(TumorRestIntern.Hot)/dt = (lambdaIntern_TumorRest*TumorRestBound.Hot) - (lambdaPhys*TumorRestIntern.Hot) -(lambdaRel_TumorRest*TumorRestIntern.Hot)90 d(TumorRestIntern.Cold)/dt = (lambdaIntern_TumorRest*TumorRestBound.Cold) + (lambdaPhys*TumorRestIntern.Hot) -(lambdaRel_TumorRest*TumorRestIntern.Cold)91d(SpleenVas.Hot)/dt = -(lambdaPhys*SpleenVas.Hot) - (k_on_toAlb*SpleenVas.Hot*SpleenVas.Albumin/SpleenVas-k_off_toAlb*SpleenVas.AlbHot) - (PS_Spleen/SpleenVas*SpleenVas.Hot-PS_Spleen/SpleenInt*SpleenInt.Hot) + (F_Spleen/Art*Art.Hot) -(F_Spleen/SpleenVas*SpleenVas.Hot)92d(SpleenVas.Cold)/dt = (lambdaPhys*SpleenVas.Hot) - (k_on_toAlb*SpleenVas.Cold*SpleenVas.Albumin/SpleenVas-k_off_toAlb*SpleenVas.AlbCold) - (PS_Spleen/SpleenVas*SpleenVas.Cold-PS_Spleen/SpleenInt*SpleenInt.Cold) + (F_Spleen/Art*Art.Cold)- (F_Spleen/SpleenVas*SpleenVas.Cold)93 d(SpleenVas.AlbHot)/dt = (k_on_toAlb*SpleenVas.Hot*SpleenVas.Albumin/SpleenVas-k_off_toAlb*SpleenVas.AlbHot) -(lambdaPhys*SpleenVas.AlbHot) + (F_Spleen/Art*Art.AlbHot) - (F_Spleen/SpleenVas*SpleenVas.AlbHot)94 d(SpleenVas.AlbCold)/dt = (lambdaPhys*SpleenVas.AlbHot) + (k_on_toAlb*SpleenVas.Cold*SpleenVas.Albumin/SpleenVas-k_off_toAlb*SpleenVas.AlbCold) + (F_Spleen/Art*Art.AlbCold) - (F_Spleen/SpleenVas*SpleenVas.AlbCold)95d(SpleenVas.Albumin)/dt = -(k_on_toAlb*SpleenVas.Hot*SpleenVas.Albumin/SpleenVas-k_off_toAlb*SpleenVas.AlbHot) -(k_on_toAlb*SpleenVas.Cold*SpleenVas.Albumin/SpleenVas-k_off_toAlb*SpleenVas.AlbCold) + (F_Spleen/Art*Art.Albumin) -(F_Spleen/SpleenVas*SpleenVas.Albumin)96 d(SpleenInt.Hot)/dt = (PS_Spleen/SpleenVas*SpleenVas.Hot-PS_Spleen/SpleenInt*SpleenInt.Hot) -(k_on/SpleenInt*SpleenInt.Hot*Spleen.R-k_off*SpleenBound.Hot) - (lambdaPhys*SpleenInt.Hot)97 d(SpleenInt.Cold)/dt = (PS_Spleen/SpleenVas*SpleenVas.Cold-PS_Spleen/SpleenInt*SpleenInt.Cold) -(k_on/SpleenInt*SpleenInt.Cold*Spleen.R-k_off*SpleenBound.Cold) + (lambdaPhys*SpleenInt.Hot)98 d(SpleenBound.Hot)/dt = (k_on/SpleenInt*SpleenInt.Hot*Spleen.R-k_off*SpleenBound.Hot) - (lambdaIntern_Spleen*SpleenBound.Hot) -(lambdaPhys*SpleenBound.Hot)99 d(SpleenBound.Cold)/dt = (k_on/SpleenInt*SpleenInt.Cold*Spleen.R-k_off*SpleenBound.Cold) -(lambdaIntern_Spleen*SpleenBound.Cold) + (lambdaPhys*SpleenBound.Hot)100 d(SpleenIntern.Hot)/dt = (lambdaIntern_Spleen*SpleenBound.Hot) - (lambdaPhys*SpleenIntern.Hot) -(lambdaRel_Spleen*SpleenIntern.Hot)101 d(SpleenIntern.Cold)/dt = (lambdaIntern_Spleen*SpleenBound.Cold) + (lambdaPhys*SpleenIntern.Hot) -(lambdaRel_Spleen*SpleenIntern.Cold)102d(LiverVas.Hot)/dt = -(lambdaPhys*LiverVas.Hot) - (k_on_toAlb*LiverVas.Hot*LiverVas.Albumin/LiverVas-k_off_toAlb*LiverVas.AlbHot) -(PS_Liver/LiverVas*LiverVas.Hot-PS_Liver/LiverInt*LiverInt.Hot) + (F_Liver/Art*Art.Hot) - (F_Liver/LiverVas*LiverVas.Hot) +(F_Spleen/SpleenVas*SpleenVas.Hot) + (F_GI/GIVas*GIVas.Hot)103d(LiverVas.Cold)/dt = (lambdaPhys*LiverVas.Hot) - (k_on_toAlb*LiverVas.Cold*LiverVas.Albumin/LiverVas-k_off_toAlb*LiverVas.AlbCold)- (PS_Liver/LiverVas*LiverVas.Cold-PS_Liver/LiverInt*LiverInt.Cold) + (F_Liver/Art*Art.Cold) - (F_Liver/LiverVas*LiverVas.Cold) +(F_Spleen/SpleenVas*SpleenVas.Cold) + (F_GI/GIVas*GIVas.Cold)104d(LiverVas.AlbHot)/dt = (k_on_toAlb*LiverVas.Hot*LiverVas.Albumin/LiverVas-k_off_toAlb*LiverVas.AlbHot) -(lambdaPhys*LiverVas.AlbHot) + (F_Liver/Art*Art.AlbHot) - (F_Liver/LiverVas*LiverVas.AlbHot) +(F_Spleen/SpleenVas*SpleenVas.AlbHot) + (F_GI/GIVas*GIVas.AlbHot)105d(LiverVas.AlbCold)/dt = (lambdaPhys*LiverVas.AlbHot) + (k_on_toAlb*LiverVas.Cold*LiverVas.Albumin/LiverVas-k_off_toAlb*LiverVas.AlbCold) + (F_Liver/Art*Art.AlbCold) - (F_Liver/LiverVas*LiverVas.AlbCold) +(F_Spleen/SpleenVas*SpleenVas.AlbCold) + (F_GI/GIVas*GIVas.AlbCold)106d(LiverVas.Albumin)/dt = -(k_on_toAlb*LiverVas.Hot*LiverVas.Albumin/LiverVas-k_off_toAlb*LiverVas.AlbHot) -(k_on_toAlb*LiverVas.Cold*LiverVas.Albumin/LiverVas-k_off_toAlb*LiverVas.AlbCold) + (F_Liver/Art*Art.Albumin) -(F_Liver/LiverVas*LiverVas.Albumin)107 d(LiverInt.Hot)/dt = (PS_Liver/LiverVas*LiverVas.Hot-PS_Liver/LiverInt*LiverInt.Hot) - (k_on/LiverInt*LiverInt.Hot*Liver.R-k_off*LiverBound.Hot) - (lambdaPhys*LiverInt.Hot)108 d(LiverInt.Cold)/dt = (PS_Liver/LiverVas*LiverVas.Cold-PS_Liver/LiverInt*LiverInt.Cold) - (k_on/LiverInt*LiverInt.Cold*Liver.R-k_off*LiverBound.Cold) + (lambdaPhys*LiverInt.Hot)109 d(LiverBound.Hot)/dt = (k_on/LiverInt*LiverInt.Hot*Liver.R-k_off*LiverBound.Hot) - (lambdaIntern_Liver*LiverBound.Hot) -(lambdaPhys*LiverBound.Hot)110 d(LiverBound.Cold)/dt = (k_on/LiverInt*LiverInt.Cold*Liver.R-k_off*LiverBound.Cold) - (lambdaIntern_Liver*LiverBound.Cold) +(lambdaPhys*LiverBound.Hot)111 d(LiverIntern.Hot)/dt = (lambdaIntern_Liver*LiverBound.Hot) - (lambdaPhys*LiverIntern.Hot) - (lambdaRel_Liver*LiverIntern.Hot)112 d(LiverIntern.Cold)/dt = (lambdaIntern_Liver*LiverBound.Cold) + (lambdaPhys*LiverIntern.Hot) - (lambdaRel_Liver*LiverIntern.Cold)113d(ProstateVas.Hot)/dt = -(lambdaPhys*ProstateVas.Hot) - (k_on_toAlb*ProstateVas.Hot*ProstateVas.Albumin/ProstateVas-k_off_toAlb*ProstateVas.AlbHot) - (PS_Prostate/ProstateVas*ProstateVas.Hot-PS_Prostate/ProstateInt*ProstateInt.Hot) +(F_Prostate/Art*Art.Hot) - (F_Prostate/ProstateVas*ProstateVas.Hot)114d(ProstateVas.Cold)/dt = (lambdaPhys*ProstateVas.Hot) - (k_on_toAlb*ProstateVas.Cold*ProstateVas.Albumin/ProstateVas-k_off_toAlb*ProstateVas.AlbCold) - (PS_Prostate/ProstateVas*ProstateVas.Cold-PS_Prostate/ProstateInt*ProstateInt.Cold) +(F_Prostate/Art*Art.Cold) - (F_Prostate/ProstateVas*ProstateVas.Cold)115 d(ProstateVas.AlbHot)/dt = (k_on_toAlb*ProstateVas.Hot*ProstateVas.Albumin/ProstateVas-k_off_toAlb*ProstateVas.AlbHot) -(lambdaPhys*ProstateVas.AlbHot) + (F_Prostate/Art*Art.AlbHot) - (F_Prostate/ProstateVas*ProstateVas.AlbHot)116 d(ProstateVas.AlbCold)/dt = (lambdaPhys*ProstateVas.AlbHot) + (k_on_toAlb*ProstateVas.Cold*ProstateVas.Albumin/ProstateVas-k_off_toAlb*ProstateVas.AlbCold) + (F_Prostate/Art*Art.AlbCold) - (F_Prostate/ProstateVas*ProstateVas.AlbCold)117d(ProstateVas.Albumin)/dt = -(k_on_toAlb*ProstateVas.Hot*ProstateVas.Albumin/ProstateVas-k_off_toAlb*ProstateVas.AlbHot) -(k_on_toAlb*ProstateVas.Cold*ProstateVas.Albumin/ProstateVas-k_off_toAlb*ProstateVas.AlbCold) + (F_Prostate/Art*Art.Albumin) -(F_Prostate/ProstateVas*ProstateVas.Albumin)118 d(ProstateInt.Hot)/dt = (PS_Prostate/ProstateVas*ProstateVas.Hot-PS_Prostate/ProstateInt*ProstateInt.Hot) -(k_on/ProstateInt*ProstateInt.Hot*Prostate.R-k_off*ProstateBound.Hot) - (lambdaPhys*ProstateInt.Hot)119 d(ProstateInt.Cold)/dt = (PS_Prostate/ProstateVas*ProstateVas.Cold-PS_Prostate/ProstateInt*ProstateInt.Cold) -(k_on/ProstateInt*ProstateInt.Cold*Prostate.R-k_off*ProstateBound.Cold) + (lambdaPhys*ProstateInt.Hot)120 d(ProstateBound.Hot)/dt = (k_on/ProstateInt*ProstateInt.Hot*Prostate.R-k_off*ProstateBound.Hot) -(lambdaIntern_Prostate*ProstateBound.Hot) - (lambdaPhys*ProstateBound.Hot)121 d(ProstateBound.Cold)/dt = (k_on/ProstateInt*ProstateInt.Cold*Prostate.R-k_off*ProstateBound.Cold) -(lambdaIntern_Prostate*ProstateBound.Cold) + (lambdaPhys*ProstateBound.Hot)122 d(ProstateIntern.Hot)/dt = (lambdaIntern_Prostate*ProstateBound.Hot) - (lambdaPhys*ProstateIntern.Hot) -(lambdaRel_Prostate*ProstateIntern.Hot)123 d(ProstateIntern.Cold)/dt = (lambdaIntern_Prostate*ProstateBound.Cold) + (lambdaPhys*ProstateIntern.Hot) -(lambdaRel_Prostate*ProstateIntern.Cold)124 d(GIVas.Hot)/dt = -(lambdaPhys*GIVas.Hot) - (k_on_toAlb*GIVas.Hot*GIVas.Albumin/GIVas-k_off_toAlb*GIVas.AlbHot) -(PS_GI/GIVas*GIVas.Hot-PS_GI/GIInt*GIInt.Hot) + (F_GI/Art*Art.Hot) - (F_GI/GIVas*GIVas.Hot)125 d(GIVas.Cold)/dt = (lambdaPhys*GIVas.Hot) - (k_on_toAlb*GIVas.Cold*GIVas.Albumin/GIVas-k_off_toAlb*GIVas.AlbCold) -(PS_GI/GIVas*GIVas.Cold-PS_GI/GIInt*GIInt.Cold) + (F_GI/Art*Art.Cold) - (F_GI/GIVas*GIVas.Cold)126 d(GIVas.AlbHot)/dt = (k_on_toAlb*GIVas.Hot*GIVas.Albumin/GIVas-k_off_toAlb*GIVas.AlbHot) - (lambdaPhys*GIVas.AlbHot) +(F_GI/Art*Art.AlbHot) - (F_GI/GIVas*GIVas.AlbHot)127 d(GIVas.AlbCold)/dt = (lambdaPhys*GIVas.AlbHot) + (k_on_toAlb*GIVas.Cold*GIVas.Albumin/GIVas-k_off_toAlb*GIVas.AlbCold) +(F_GI/Art*Art.AlbCold) - (F_GI/GIVas*GIVas.AlbCold)128 d(GIVas.Albumin)/dt = -(k_on_toAlb*GIVas.Hot*GIVas.Albumin/GIVas-k_off_toAlb*GIVas.AlbHot) -(k_on_toAlb*GIVas.Cold*GIVas.Albumin/GIVas-k_off_toAlb*GIVas.AlbCold) + (F_GI/Art*Art.Albumin) - (F_GI/GIVas*GIVas.Albumin)129 d(GIInt.Hot)/dt = (PS_GI/GIVas*GIVas.Hot-PS_GI/GIInt*GIInt.Hot) - (k_on/GIInt*GIInt.Hot*GI.R-k_off*GIBound.Hot) -(lambdaPhys*GIInt.Hot)130 d(GIInt.Cold)/dt = (PS_GI/GIVas*GIVas.Cold-PS_GI/GIInt*GIInt.Cold) - (k_on/GIInt*GIInt.Cold*GI.R-k_off*GIBound.Cold) +(lambdaPhys*GIInt.Hot)131 d(GIBound.Hot)/dt = (k_on/GIInt*GIInt.Hot*GI.R-k_off*GIBound.Hot) - (lambdaIntern_GI*GIBound.Hot) - (lambdaPhys*GIBound.Hot)132 d(GIBound.Cold)/dt = (k_on/GIInt*GIInt.Cold*GI.R-k_off*GIBound.Cold) - (lambdaIntern_GI*GIBound.Cold) + (lambdaPhys*GIBound.Hot)133 d(GIIntern.Hot)/dt = (lambdaIntern_GI*GIBound.Hot) - (lambdaPhys*GIIntern.Hot) - (lambdaRel_GI*GIIntern.Hot)134 d(GIIntern.Cold)/dt = (lambdaIntern_GI*GIBound.Cold) + (lambdaPhys*GIIntern.Hot) - (lambdaRel_GI*GIIntern.Cold)135 d(RestVas.Hot)/dt = -(lambdaPhys*RestVas.Hot) - (k_on_toAlb*RestVas.Hot*RestVas.Albumin/RestVas-k_off_toAlb*RestVas.AlbHot) -(PS_Rest/RestVas*RestVas.Hot-PS_Rest/RestInt*RestInt.Hot) + (F_Rest/Art*Art.Hot) - (F_Rest/RestVas*RestVas.Hot)136 d(RestVas.Cold)/dt = (lambdaPhys*RestVas.Hot) - (k_on_toAlb*RestVas.Cold*RestVas.Albumin/RestVas-k_off_toAlb*RestVas.AlbCold) -(PS_Rest/RestVas*RestVas.Cold-PS_Rest/RestInt*RestInt.Cold) + (F_Rest/Art*Art.Cold) - (F_Rest/RestVas*RestVas.Cold)137 d(RestVas.AlbHot)/dt = (k_on_toAlb*RestVas.Hot*RestVas.Albumin/RestVas-k_off_toAlb*RestVas.AlbHot) - (lambdaPhys*RestVas.AlbHot)+ (F_Rest/Art*Art.AlbHot) - (F_Rest/RestVas*RestVas.AlbHot)138 d(RestVas.AlbCold)/dt = (lambdaPhys*RestVas.AlbHot) + (k_on_toAlb*RestVas.Cold*RestVas.Albumin/RestVas-k_off_toAlb*RestVas.AlbCold) + (F_Rest/Art*Art.AlbCold) - (F_Rest/RestVas*RestVas.AlbCold)139d(RestVas.Albumin)/dt = -(k_on_toAlb*RestVas.Hot*RestVas.Albumin/RestVas-k_off_toAlb*RestVas.AlbHot) -(k_on_toAlb*RestVas.Cold*RestVas.Albumin/RestVas-k_off_toAlb*RestVas.AlbCold) + (F_Rest/Art*Art.Albumin) -(F_Rest/RestVas*RestVas.Albumin)140 d(RestInt.Hot)/dt = (PS_Rest/RestVas*RestVas.Hot-PS_Rest/RestInt*RestInt.Hot) - (lambdaPhys*RestInt.Hot)141 d(RestInt.Cold)/dt = (PS_Rest/RestVas*RestVas.Cold-PS_Rest/RestInt*RestInt.Cold) + (lambdaPhys*RestInt.Hot)142 d(SkinVas.Hot)/dt = -(lambdaPhys*SkinVas.Hot) - (k_on_toAlb*SkinVas.Hot*SkinVas.Albumin/SkinVas-k_off_toAlb*SkinVas.AlbHot) -(PS_Skin/SkinVas*SkinVas.Hot-PS_Skin/SkinVas*SkinInt.Hot) + (F_Skin/Art*Art.Hot) - (F_Skin/SkinVas*SkinVas.Hot)143 d(SkinVas.Cold)/dt = (lambdaPhys*SkinVas.Hot) - (k_on_toAlb*SkinVas.Cold*SkinVas.Albumin/SkinVas-k_off_toAlb*SkinVas.AlbCold) -(PS_Skin/SkinVas*SkinVas.Cold-PS_Skin/SkinInt*SkinInt.Cold) + (F_Skin/Art*Art.Cold) - (F_Skin/SkinVas*SkinVas.Cold)144 d(SkinVas.AlbHot)/dt = (k_on_toAlb*SkinVas.Hot*SkinVas.Albumin/SkinVas-k_off_toAlb*SkinVas.AlbHot) - (lambdaPhys*SkinVas.AlbHot)+ (F_Skin/Art*Art.AlbHot) - (F_Skin/SkinVas*SkinVas.AlbHot)145 d(SkinVas.AlbCold)/dt = (lambdaPhys*SkinVas.AlbHot) + (k_on_toAlb*SkinVas.Cold*SkinVas.Albumin/SkinVas-k_off_toAlb*SkinVas.AlbCold) + (F_Skin/Art*Art.AlbCold) - (F_Skin/SkinVas*SkinVas.AlbCold)146d(SkinVas.Albumin)/dt = -(k_on_toAlb*SkinVas.Hot*SkinVas.Albumin/SkinVas-k_off_toAlb*SkinVas.AlbHot) -(k_on_toAlb*SkinVas.Cold*SkinVas.Albumin/SkinVas-k_off_toAlb*SkinVas.AlbCold) + (F_Skin/Art*Art.Albumin) -(F_Skin/SkinVas*SkinVas.Albumin)147 d(SkinInt.Hot)/dt = (PS_Skin/SkinVas*SkinVas.Hot-PS_Skin/SkinVas*SkinInt.Hot) - (lambdaPhys*SkinInt.Hot)148 d(SkinInt.Cold)/dt = (PS_Skin/SkinVas*SkinVas.Cold-PS_Skin/SkinInt*SkinInt.Cold) + (lambdaPhys*SkinInt.Hot)149d(MuscleVas.Hot)/dt = -(lambdaPhys*MuscleVas.Hot) - (k_on_toAlb*MuscleVas.Hot*MuscleVas.Albumin/MuscleVas-k_off_toAlb*MuscleVas.AlbHot) - (PS_Muscle/MuscleVas*MuscleVas.Hot-PS_Muscle/MuscleInt*MuscleInt.Hot) + (F_Muscle/Art*Art.Hot) -(F_Muscle/MuscleVas*MuscleVas.Hot)150d(MuscleVas.Cold)/dt = (lambdaPhys*MuscleVas.Hot) - (k_on_toAlb*MuscleVas.Cold*MuscleVas.Albumin/MuscleVas-k_off_toAlb*MuscleVas.AlbCold) - (PS_Muscle/MuscleVas*MuscleVas.Cold-PS_Muscle/MuscleInt*MuscleInt.Cold) + (F_Muscle/Art*Art.Cold)- (F_Muscle/MuscleVas*MuscleVas.Cold)151 d(MuscleVas.AlbHot)/dt = (k_on_toAlb*MuscleVas.Hot*MuscleVas.Albumin/MuscleVas-k_off_toAlb*MuscleVas.AlbHot) -(lambdaPhys*MuscleVas.AlbHot) + (F_Muscle/Art*Art.AlbHot) - (F_Muscle/MuscleVas*MuscleVas.AlbHot)152 d(MuscleVas.AlbCold)/dt = (lambdaPhys*MuscleVas.AlbHot) + (k_on_toAlb*MuscleVas.Cold*MuscleVas.Albumin/MuscleVas-k_off_toAlb*MuscleVas.AlbCold) + (F_Muscle/Art*Art.AlbCold) - (F_Muscle/MuscleVas*MuscleVas.AlbCold)153d(MuscleVas.Albumin)/dt = -(k_on_toAlb*MuscleVas.Hot*MuscleVas.Albumin/MuscleVas-k_off_toAlb*MuscleVas.AlbHot) -(k_on_toAlb*MuscleVas.Cold*MuscleVas.Albumin/MuscleVas-k_off_toAlb*MuscleVas.AlbCold) + (F_Muscle/Art*Art.Albumin) -(F_Muscle/MuscleVas*MuscleVas.Albumin)154 d(MuscleInt.Hot)/dt = (PS_Muscle/MuscleVas*MuscleVas.Hot-PS_Muscle/MuscleInt*MuscleInt.Hot) - (lambdaPhys*MuscleInt.Hot)155 d(MuscleInt.Cold)/dt = (PS_Muscle/MuscleVas*MuscleVas.Cold-PS_Muscle/MuscleInt*MuscleInt.Cold) + (lambdaPhys*MuscleInt.Hot)156 d(BrainVas.Hot)/dt = -(lambdaPhys*BrainVas.Hot) - (k_on_toAlb*BrainVas.Hot*BrainVas.Albumin/BrainVas-k_off_toAlb*BrainVas.AlbHot)- (PS_Brain/BrainVas*BrainVas.Hot-PS_Brain/BrainInt*BrainInt.Hot) + (F_Brain/Art*Art.Hot) - (F_Brain/BrainVas*BrainVas.Hot)157d(BrainVas.Cold)/dt = (lambdaPhys*BrainVas.Hot) - (k_on_toAlb*BrainVas.Cold*BrainVas.Albumin/BrainVas-k_off_toAlb*BrainVas.AlbCold) - (PS_Brain/BrainVas*BrainVas.Cold-PS_Brain/BrainInt*BrainInt.Cold) + (F_Brain/Art*Art.Cold) -(F_Brain/BrainVas*BrainVas.Cold)158 d(BrainVas.AlbHot)/dt = (k_on_toAlb*BrainVas.Hot*BrainVas.Albumin/BrainVas-k_off_toAlb*BrainVas.AlbHot) -(lambdaPhys*BrainVas.AlbHot) + (F_Brain/Art*Art.AlbHot) - (F_Brain/BrainVas*BrainVas.AlbHot)159 d(BrainVas.AlbCold)/dt = (lambdaPhys*BrainVas.AlbHot) + (k_on_toAlb*BrainVas.Cold*BrainVas.Albumin/BrainVas-k_off_toAlb*BrainVas.AlbCold) + (F_Brain/Art*Art.AlbCold) - (F_Brain/BrainVas*BrainVas.AlbCold)160d(BrainVas.Albumin)/dt = -(k_on_toAlb*BrainVas.Hot*BrainVas.Albumin/BrainVas-k_off_toAlb*BrainVas.AlbHot) -(k_on_toAlb*BrainVas.Cold*BrainVas.Albumin/BrainVas-k_off_toAlb*BrainVas.AlbCold) + (F_Brain/Art*Art.Albumin) -(F_Brain/BrainVas*BrainVas.Albumin)161 d(BrainInt.Hot)/dt = (PS_Brain/BrainVas*BrainVas.Hot-PS_Brain/BrainInt*BrainInt.Hot) - (lambdaPhys*BrainInt.Hot)162 d(BrainInt.Cold)/dt = (PS_Brain/BrainVas*BrainVas.Cold-PS_Brain/BrainInt*BrainInt.Cold) + (lambdaPhys*BrainInt.Hot)163d(RedMarrowVas.Hot)/dt = -(lambdaPhys*RedMarrowVas.Hot) -(k_on_toAlb*RedMarrowVas.Hot*RedMarrowVas.Albumin/RedMarrowVas-k_off_toAlb*RedMarrowVas.AlbHot) -(PS_RedMarrow/RedMarrowVas*RedMarrowVas.Hot-PS_RedMarrow/RedMarrowInt*RedMarrowInt.Hot) + (F_RedMarrow/Art*Art.Hot) -(F_RedMarrow/RedMarrowVas*RedMarrowVas.Hot)164d(RedMarrowVas.Cold)/dt = (lambdaPhys*RedMarrowVas.Hot) -(k_on_toAlb*RedMarrowVas.Cold*RedMarrowVas.Albumin/RedMarrowVas-k_off_toAlb*RedMarrowVas.AlbCold) -(PS_RedMarrow/RedMarrowVas*RedMarrowVas.Cold-PS_RedMarrow/RedMarrowInt*RedMarrowInt.Cold) + (F_RedMarrow/Art*Art.Cold) -(F_RedMarrow/RedMarrowVas*RedMarrowVas.Cold)165d(RedMarrowVas.AlbHot)/dt = (k_on_toAlb*RedMarrowVas.Hot*RedMarrowVas.Albumin/RedMarrowVas-k_off_toAlb*RedMarrowVas.AlbHot) - (lambdaPhys*RedMarrowVas.AlbHot) + (F_RedMarrow/Art*Art.AlbHot) -(F_RedMarrow/RedMarrowVas*RedMarrowVas.AlbHot)166d(RedMarrowVas.AlbCold)/dt = (lambdaPhys*RedMarrowVas.AlbHot) +(k_on_toAlb*RedMarrowVas.Cold*RedMarrowVas.Albumin/RedMarrowVas-k_off_toAlb*RedMarrowVas.AlbCold) +(F_RedMarrow/Art*Art.AlbCold) - (F_RedMarrow/RedMarrowVas*RedMarrowVas.AlbCold)167d(RedMarrowVas.Albumin)/dt = -(k_on_toAlb*RedMarrowVas.Hot*RedMarrowVas.Albumin/RedMarrowVas-k_off_toAlb*RedMarrowVas.AlbHot) - (k_on_toAlb*RedMarrowVas.Cold*RedMarrowVas.Albumin/RedMarrowVas-k_off_toAlb*RedMarrowVas.AlbCold) + (F_RedMarrow/Art*Art.Albumin) - (F_RedMarrow/RedMarrowVas*RedMarrowVas.Albumin)168 d(RedMarrowInt.Hot)/dt = (PS_RedMarrow/RedMarrowVas*RedMarrowVas.Hot-PS_RedMarrow/RedMarrowInt*RedMarrowInt.Hot) -(lambdaPhys*RedMarrowInt.Hot)169 d(RedMarrowInt.Cold)/dt = (PS_RedMarrow/RedMarrowVas*RedMarrowVas.Cold-PS_RedMarrow/RedMarrowInt*RedMarrowInt.Cold) +(lambdaPhys*RedMarrowInt.Hot)170d(LungsVas.Hot)/dt = -(lambdaPhys*LungsVas.Hot) - (k_on_toAlb*LungsVas.Hot*LungsVas.Albumin/LungsVas-k_off_toAlb*LungsVas.AlbHot) - (PS_Lungs/LungsVas*LungsVas.Hot-PS_Lungs/LungsInt*LungsInt.Hot) -(F_Lungs/LungsVas*LungsVas.Hot) + (F_Lungs/Vein*Vein.Hot)171d(LungsVas.Cold)/dt = (lambdaPhys*LungsVas.Hot) - (k_on_toAlb*LungsVas.Cold*LungsVas.Albumin/LungsVas-k_off_toAlb*LungsVas.AlbCold) - (PS_Lungs/LungsVas*LungsVas.Cold-PS_Lungs/LungsInt*LungsInt.Cold) -(F_Lungs/LungsVas*LungsVas.Cold) + (F_Lungs/Vein*Vein.Cold)172 d(LungsVas.AlbHot)/dt = (k_on_toAlb*LungsVas.Hot*LungsVas.Albumin/LungsVas-k_off_toAlb*LungsVas.AlbHot) -(lambdaPhys*LungsVas.AlbHot) - (F_Lungs/LungsVas*LungsVas.AlbHot) + (F_Lungs/Vein*Vein.AlbHot)173 d(LungsVas.AlbCold)/dt = (lambdaPhys*LungsVas.AlbHot) + (k_on_toAlb*LungsVas.Cold*LungsVas.Albumin/LungsVas-k_off_toAlb*LungsVas.AlbCold) - (F_Lungs/LungsVas*LungsVas.AlbCold) + (F_Lungs/Vein*Vein.AlbCold)174d(LungsVas.Albumin)/dt = -(k_on_toAlb*LungsVas.Hot*LungsVas.Albumin/LungsVas-k_off_toAlb*LungsVas.AlbHot) -(k_on_toAlb*LungsVas.Cold*LungsVas.Albumin/LungsVas-k_off_toAlb*LungsVas.AlbCold) + (F_Lungs/Vein*Vein.Albumin) -(F_Lungs/LungsVas*LungsVas.Albumin)175 d(LungsInt.Hot)/dt = (PS_Lungs/LungsVas*LungsVas.Hot-PS_Lungs/LungsInt*LungsInt.Hot) - (lambdaPhys*LungsInt.Hot)176 d(LungsInt.Cold)/dt = (PS_Lungs/LungsVas*LungsVas.Cold-PS_Lungs/LungsInt*LungsInt.Cold) + (lambdaPhys*LungsInt.Hot)177d(AdiposeVas.Hot)/dt = -(lambdaPhys*AdiposeVas.Hot) - (k_on_toAlb*AdiposeVas.Hot*AdiposeVas.Albumin/AdiposeVas-k_off_toAlb*AdiposeVas.AlbHot) - (PS_Adipose/AdiposeVas*AdiposeVas.Hot-PS_Adipose/AdiposeInt*AdiposeInt.Hot) +(F_Adipose/Art*Art.Hot) - (F_Adipose/AdiposeVas*AdiposeVas.Hot)d(AdiposeVas.Cold)/dt = (lambdaPhys*AdiposeVas.Hot) - (k_on_toAlb*AdiposeVas.Cold*AdiposeVas.Albumin/AdiposeVas-178 k_off_toAlb*AdiposeVas.AlbCold) - (PS_Adipose/AdiposeVas*AdiposeVas.Cold-PS_Adipose/AdiposeInt*AdiposeInt.Cold) +(F_Adipose/Art*Art.Cold) - (F_Adipose/AdiposeVas*AdiposeVas.Cold)179 d(AdiposeVas.AlbHot)/dt = (k_on_toAlb*AdiposeVas.Hot*AdiposeVas.Albumin/AdiposeVas-k_off_toAlb*AdiposeVas.AlbHot) -(lambdaPhys*AdiposeVas.AlbHot) + (F_Adipose/Art*Art.AlbHot) - (F_Adipose/AdiposeVas*AdiposeVas.AlbHot)180 d(AdiposeVas.AlbCold)/dt = (lambdaPhys*AdiposeVas.AlbHot) + (k_on_toAlb*AdiposeVas.Cold*AdiposeVas.Albumin/AdiposeVas-k_off_toAlb*AdiposeVas.AlbCold) + (F_Adipose/Art*Art.AlbCold) - (F_Adipose/AdiposeVas*AdiposeVas.AlbCold)181d(AdiposeVas.Albumin)/dt = -(k_on_toAlb*AdiposeVas.Hot*AdiposeVas.Albumin/AdiposeVas-k_off_toAlb*AdiposeVas.AlbHot) -(k_on_toAlb*AdiposeVas.Cold*AdiposeVas.Albumin/AdiposeVas-k_off_toAlb*AdiposeVas.AlbCold) + (F_Adipose/Art*Art.Albumin) -(F_Adipose/AdiposeVas*AdiposeVas.Albumin)182 d(AdiposeInt.Hot)/dt = (PS_Adipose/AdiposeVas*AdiposeVas.Hot-PS_Adipose/AdiposeInt*AdiposeInt.Hot) - (lambdaPhys*AdiposeInt.Hot)183 d(AdiposeInt.Cold)/dt = (PS_Adipose/AdiposeVas*AdiposeVas.Cold-PS_Adipose/AdiposeInt*AdiposeInt.Cold) +(lambdaPhys*AdiposeInt.Hot)Report generated by SimBiology v. 6.4 (R2022b) on 11-Jul-2023 11:26:07
Thesis/Dissertation
eng
Biomedical Engineering
Vancouver : University of British Columbia Library
Attribution-NoDerivatives 4.0 International
Graduate
Rahmim, Arman
Use of physiologically based radiopharmacokinetic (PBRPK) models to simulate radiopharmaceutical therapies
Text