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Characterization of tumour vasculature with dynamic contrast enhanced MRI and Gd-hyperbranched polyglycerols McPhee, Kelly Catherine 2012

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Characterization of Tumour Vasculature with Dynamic Contrast Enhanced MRI and Gd-Hyperbranched Polyglycerols  by Kelly Catherine McPhee B.Sc. Honours Physics, University of British Columbia, 2009  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  Master of Science in THE FACULTY OF GRADUATE STUDIES (Physics and Astronomy)  The University of British Columbia (Vancouver) March 2012 c Kelly Catherine McPhee, 2012  Abstract Tumour tissue is highly heterogeneous with disordered vasculature that is characteristically highly permeable relative to other normal tissue blood vessels. Noninvasive investigation of tumour vasculature may be achieved using Dynamic Contrast Enhanced MRI (DCE-MRI). Pharmacokinetic modelling of contrast agent uptake can provide information about blood flow and vessel permeability, but modelling is limited due to the ability of typical contrast agents such as Gd-DTPA to extravasate and accumulate in tumour tissue. The hypothesis motivating this work is that DCE-MRI measurements with both high and low molecular weight contrast agent uptake will allow for improved interpretation of the tumour microenvironment. A new high molecular weight contrast agent comprised of hyperbranched polyglycerol (HPG) molecules doubly labelled with gadolinium and a fluorescent marker is characterized, and used along side a standard low molecular weight contrast agent, Gadovist (Bayer Healthcare). Histological data reveals that HPG extravasates slowly from vasculature, and remains near blood vessels over the time-frame of a DCE-MRI experiment. HPG was also found to accumulate in tumour tissue over days, peaking at 2-4 days. HPG was found to be inappropriate for pharmacokinetic modelling, due to relatively low enhancement in the DCE-MRI data. Parameter maps showing bolus arrival time of HPG throughout the tumour show increased sensitivity to necrosis relative to Gadovist. Initial area under the HPG-concentration time curve was found to be correlated with vascular density. Modelling of DCE-MRI data should be performed with a model appropriate to the tissue, contrast agent, and data available. While simpler models are not able to distinguish blood flow from permeability, data quality is not necessarily ii  sufficient to justify the use of a more complex model. This problem is addressed in this work by modelling contrast agent uptake with system of increasingly complex models, and the Akaike information criterion was used to determine that a general two compartment exchange model was more appropriate than the extended Tofts model for pharmacokinetic modelling of DCE-MRI with a standard contrast agent.  iii  Preface Collaborators and Disclosures This project would not have been possible without the expertise of my supervisor, my collaborators, and the use of tools and methods developed within the collaborating labs. Dr. Jennifer Baker offered a wealth of knowledge about pre-clinical cancer research. She assisted with study design (Chapters 4 and 5, and prepared mice for MRI imaging. Dr. Baker provided great assistance and training for histology work. I performed the majority of tumour sectioning. Dr. Baker and I performed staining together. I performed cropping and analysis of histology images under her guidance. Custom analysis software for histology data collection and analysis was obtained from Alister Kyle and is cited as appropriate. Mice were obtained with implanted tumours and fiducial markers from BC Cancer Research Centre’s animal facility (ARC). Their care prior to transport to UBC was overseen by Dr. Baker. Mice were transferred to UBC’s animal research unit (ARU), and were cared for by the ARU staff. Custom MRI coils were built and maintained by Andrew Yung at the UBC 7T MRI centre. MRI data collection required the presence of several people. Dr. Jennifer Baker prepared mice for DCE-MRI studies. Dr. Baker, Dr. Reinsberg, and myself were present for nearly all animal imaging sessions. The Arterial Input Function (AIF) measured in this work (Section 3.2.1, and used for analysis in Chapters 4 and 5) falls under the research of Jennifer Moroz, a PhD candidate at the UBC 7T MRI centre. I assisted with some experiments, iv  however, the method is hers, and she performed the reconstruction of the data sets, and provided them to me. I fit the resulting group averaged AIF. Her work has been cited where relevant. Unless otherwise stated, software was developed for the data analysis in this work using MATLAB (Mathworks Inc), and was prepared by the author. All analysis of MRI data was performed by myself, with the exception of AIF measurements, as described above. The novel contrast agent used in this work was kindly provided by Dr. Katayoun Saatchi and Dr. Urs H¨afeli in UBC’s Faculty of Pharmacy. The use of this novel contrast agent is central to this thesis. Drs Saatchi and H¨afeli are co-authors on a recently accepted paper [1], and on work I presented at the Annual Meeting for the International Society for Magnetic Resonance In Medicine [2]. In the publication and in the presentation, data from pilot studies with HPG are presented. That data is not presented here again, but is summarized in Chapter 4. Two abstracts have been submitted with hopes to present at the 2012 Annual Meeting for the International Society for Magnetic Resonance in Medicine [3, 4]. The first abstract [4] describes the novel bolus arrival time measurement method described in Section 3.3.1, and the results using that method which are found in Chapter 4 (in particular, a figure similar to Figure 4.12). The second abstract [3] describes errors resulting from non-ideal selective excitation in 3D variable flip angle experiments, which is related to the information presented in Section 2.4.6. No other work has been submitted at this time. Ethics approval was obtained from the UBC Animal Care Committee (UBC Animal Care Certificate number A09-0943).  v  Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iv  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  vi  List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  x  List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xi  List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xiii  Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xv  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii 1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.2  Organization of this Thesis . . . . . . . . . . . . . . . . . . . . .  3  1.3  Magnetic Resonance Imaging Background . . . . . . . . . . . . .  4  1.3.1  Basic MR Principles . . . . . . . . . . . . . . . . . . . .  4  1.3.2  Spins in a Static Magnetic Field . . . . . . . . . . . . . .  6  1.3.3  Spins in a Time Varying Field . . . . . . . . . . . . . . .  6  1.3.4  Magnetic Resonance Imaging . . . . . . . . . . . . . . .  9  Exogenous Paramagnetic Contrast Media . . . . . . . . . . . . .  10  1.4.1  Relaxivity of Gadolinium Chelate Contrast agents . . . .  10  1.4.2  Measuring Contrast Agent Concentration In Vivo . . . . .  11  1.4  vi  1.5  1.6 2  12  1.5.1  Tracer Kinetics . . . . . . . . . . . . . . . . . . . . . . .  13  1.5.2  Issues Regarding Analysis . . . . . . . . . . . . . . . . .  15  Comparing Models . . . . . . . . . . . . . . . . . . . . . . . . .  16  Variable Flip Angle Fast Low-Angle Shot T1 Measurements in the Presence of Non-ideal Slice Profile and B1 Inhomogeneity . . . . . .  17  2.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  18  2.2  Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  20  2.3  Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  22  2.3.1  Simulations . . . . . . . . . . . . . . . . . . . . . . . . .  22  2.3.2  Phantom Experiments . . . . . . . . . . . . . . . . . . .  24  2.3.3  Correcting T1 Measurements . . . . . . . . . . . . . . . .  25  2.3.4  Using the B1SP Correction Method to Find T1 In Vivo . .  26  2.3.5  Data Analysis . . . . . . . . . . . . . . . . . . . . . . . .  27  Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  27  2.4.1  Errors in the Rephase Gradient . . . . . . . . . . . . . . .  27  2.4.2  Zero Crossing Location is T1 Dependant: Results from  2.4  2.5 3  Dynamic Contrast Enhanced MRI . . . . . . . . . . . . . . . . .  Simulation . . . . . . . . . . . . . . . . . . . . . . . . .  28  2.4.3  T1 Errors Due to Slice Profile: Results from Simulations .  29  2.4.4  Method Verification in Phantom Experiments . . . . . . .  29  2.4.5  Using the B1SP Correction Method to Find T1 In Vivo . .  32  2.4.6  3D VFA Experiments . . . . . . . . . . . . . . . . . . . .  32  Discussion and Conclusions . . . . . . . . . . . . . . . . . . . .  34  Analysis of DCE-MRI Data: Methods, Theory, and Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  36  3.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  36  3.2  Tools for DCE-MRI Analysis . . . . . . . . . . . . . . . . . . . .  36  3.2.1  Arterial Input Function . . . . . . . . . . . . . . . . . . .  36  Model-Free Analysis of DCE-MRI Data . . . . . . . . . . . . . .  39  3.3  3.3.1  Bolus Arrival Time and Identification of T2 * Artefacts: a Novel Method Employing Control Chart Decision Criteria  vii  39  3.3.2 3.4  3.5  4  Initial Area Under the Curve . . . . . . . . . . . . . . . .  42  Pharmacokinetic Modelling of the Contrast Bolus . . . . . . . . .  42  3.4.1  Two Compartment Exchange Model . . . . . . . . . . . .  42  3.4.2  Solutions to 2CXM . . . . . . . . . . . . . . . . . . . . .  43  3.4.3  Methods of Comparing Models . . . . . . . . . . . . . .  47  Sensitivity Analysis: Model Sensitivity to Accuracy of Contrast Agent Concentration Scaling . . . . . . . . . . . . . . . . . . . .  48  3.5.1  Methods  . . . . . . . . . . . . . . . . . . . . . . . . . .  49  3.5.2  Results . . . . . . . . . . . . . . . . . . . . . . . . . . .  49  3.5.3  Discussion and Conclusions . . . . . . . . . . . . . . . .  49  Characterization of New High Molecular Weight Contrast Agent via MRI and Histology . . . . . . . . . . . . . . . . . . . . . . . . . . . .  52  4.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  52  4.1.1  High Molecular Weight Agents in Literature . . . . . . .  53  4.1.2  A Novel High Molecular Weight Contrast Agent . . . . .  55  4.1.3  Pilot MRI and Histology Studies . . . . . . . . . . . . . .  55  4.1.4  Modelling Tracer Kinetics: Considerations . . . . . . . .  56  Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  57  4.2.1  Relaxivity . . . . . . . . . . . . . . . . . . . . . . . . . .  57  4.2.2  Overview of Experiments . . . . . . . . . . . . . . . . .  57  4.2.3  Apparatus and Protocols . . . . . . . . . . . . . . . . . .  58  4.2.4  Experiments . . . . . . . . . . . . . . . . . . . . . . . .  61  4.2.5  Magnetic Resonance Imaging . . . . . . . . . . . . . . .  62  4.2.6  Imunohistochemistry . . . . . . . . . . . . . . . . . . . .  64  4.2.7  Analysis of MRI Data . . . . . . . . . . . . . . . . . . .  67  Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  69  4.3.1  Relaxivity . . . . . . . . . . . . . . . . . . . . . . . . . .  69  4.3.2  Agreement of MR and Histology . . . . . . . . . . . . . .  70  4.3.3  Retention . . . . . . . . . . . . . . . . . . . . . . . . . .  70  4.3.4  Extravasation of HPG-GdF . . . . . . . . . . . . . . . . .  71  4.3.5  Bolus Arrival Time: Comparing HPG-GdF to Gadovist . .  73  4.3.6  IAUC60 . . . . . . . . . . . . . . . . . . . . . . . . . . .  73  4.2  4.3  viii  4.4  5  DCE-MRI Analysis . . . . . . . . . . . . . . . . . . . . .  74  4.3.8  Inspecting Concentration Time Curves . . . . . . . . . . .  74  Discussion and Conclusions . . . . . . . . . . . . . . . . . . . .  78  4.4.1  Retention . . . . . . . . . . . . . . . . . . . . . . . . . .  78  4.4.2  Extravasation . . . . . . . . . . . . . . . . . . . . . . . .  78  4.4.3  Comparing DCE-MRI Results from Two Contrast Agents  78  Characterization of Three Tumour Lines Using DCE-MRI with Both High and Low Molecular Weight Contrast Agents . . . . . . . . . .  82  5.1  Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  82  5.1.1  Tumours . . . . . . . . . . . . . . . . . . . . . . . . . .  83  Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  83  5.2.1  Mice . . . . . . . . . . . . . . . . . . . . . . . . . . . .  83  5.2.2  Magnetic Resonance Imaging . . . . . . . . . . . . . . .  84  5.2.3  Imunohistochemistry . . . . . . . . . . . . . . . . . . . .  85  5.2.4  Analysis of MRI Data and Pharmacokinetic Modelling . .  86  5.2.5  Statistics . . . . . . . . . . . . . . . . . . . . . . . . . .  87  Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  87  5.3.1  Distribution and Uptake of HPG-GdF . . . . . . . . . . .  88  5.3.2  Vascular Characteristics . . . . . . . . . . . . . . . . . .  90  5.3.3  Parameters Derived From DCE-MRI Data . . . . . . . . .  90  5.4  Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  95  5.5  Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  99  5.2  5.3  6  4.3.7  Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 100 6.1  Implications, and Considerations for Future Work . . . . . . . . . 102  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105  ix  List of Tables Table 2.1  T1 values (ms) measured by different methods . . . . . . . . .  31  Table 2.2  Flip angle map values calculated by different methods . . . . .  32  Table 2.3  T1 and flip angle map values for 3D VFA experiment . . . . .  33  Table 4.1  Summary of experiments and groups . . . . . . . . . . . . . .  62  Table 4.2  Thresholds for histology analysis . . . . . . . . . . . . . . . .  67  Table 4.3  Summary of pharmacokinetic parameters . . . . . . . . . . . .  69  Table 5.1  Summary of experiments and groups . . . . . . . . . . . . . .  84  Table 5.2  Thresholds for histology analysis . . . . . . . . . . . . . . . .  86  x  List of Figures Figure 1.1  Schematic diagram of the two compartment exchange model .  15  Figure 2.1  Pulses simulated . . . . . . . . . . . . . . . . . . . . . . . .  21  Figure 2.2  RF excitation pulses . . . . . . . . . . . . . . . . . . . . . .  22  Figure 2.3  Slice profiles from Bloch simulations using selective 1 ms Hermite excitation . . . . . . . . . . . . . . . . . . . . . . . . .  Figure 2.4  Surface of lookup table from simulations with varying T1 , and flip angle . . . . . . . . . . . . . . . . . . . . . . . . . . . .  Figure 2.5  23 24  Effect of slice rephase gradient differing from 50% at high and low T1 weighting . . . . . . . . . . . . . . . . . . . . . . . .  28  Figure 2.6  Zero crossing in VFA experiments depends on T1 weighting .  29  Figure 2.7  T1 values resulting from fitting simulated VFA experiments .  29  Figure 2.8  VFA curves for phantoms with simulated curves and best fit curves of the FLASH equation . . . . . . . . . . . . . . . . .  30  True T1 compared to measured values . . . . . . . . . . . . .  31  Figure 2.10 T1 errors due to slice profile and B1 in vivo . . . . . . . . . .  33  Figure 2.11 VFA curves from simulated and experimental 3D data . . . .  34  Figure 3.1  Custom tail coil for AIF measurement . . . . . . . . . . . . .  38  Figure 3.2  AIF data with its fit . . . . . . . . . . . . . . . . . . . . . . .  39  Figure 3.3  AIF fit curve and its components . . . . . . . . . . . . . . . .  39  Figure 3.4  Example of finding BAT with a control chart . . . . . . . . .  41  Figure 3.5  Errors in parameters due to concentration errors . . . . . . . .  50  Figure 3.6  Sensitivity of 2CXM model parameters to errors in concentration 51  Figure 4.1  Contrast agent injection procedure . . . . . . . . . . . . . . .  Figure 2.9  xi  59  Figure 4.2  Custom anaesthesia chamber . . . . . . . . . . . . . . . . . .  60  Figure 4.3  Fiducial markers for orientation . . . . . . . . . . . . . . . .  61  Figure 4.4  High resolution histology showing carbocyanine over CD31 .  66  Figure 4.5  High resolution histology showing HPG over CD31 . . . . . .  66  Figure 4.6  Relaxivity . . . . . . . . . . . . . . . . . . . . . . . . . . . .  70  Figure 4.7  Heterogeneous distribution of HPG shown in MR and Histology 70  Figure 4.8  Retention of HPG-GdF, measured with T1 . . . . . . . . . . .  Figure 4.9  T1 weighted images over 1 week following HPG-GdF admin-  71  istration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  71  Figure 4.10 Identifying perfused vasculature . . . . . . . . . . . . . . . .  72  Figure 4.11 Distance HPG-GdF travelled from CD31 objects . . . . . . .  72  Figure 4.12 Bolus arrival time with HMW agent indicates necroses . . . .  73  Figure 4.13 IAUC60 compared for Gadovist and HPG-GdF . . . . . . . .  74  Figure 4.14 Pharmacokinetic parameter maps: Gadovist . . . . . . . . . .  75  Figure 4.15 Goodness of fit for modelling HPG-GdF data with the uptake model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  75  Figure 4.16 Typical concentration time curves . . . . . . . . . . . . . . .  76  Figure 4.17 Inspecting Gadovist concentration time curves . . . . . . . .  77  Figure 5.1  Distance HPG-GdF travelled from vessels: compare tumour types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  88  Figure 5.2  HPG-GdF uptake from MR and Histology . . . . . . . . . . .  89  Figure 5.3  Comparing groups via histology . . . . . . . . . . . . . . . .  91  Figure 5.4  Vascular density compared to HPG-GdF fluorescence . . . . .  92  Figure 5.5  Comparing BAT . . . . . . . . . . . . . . . . . . . . . . . .  93  Figure 5.6  Comparing IAUC60 for both contrast agents . . . . . . . . .  94  Figure 5.7  IAUC60HPG correlated to vascular density . . . . . . . . . . .  95  Figure 5.8  Pharmacokinetic parameter maps from modelling Gadovist data with the 2CXM for all tumour lines . . . . . . . . . . . . . .  Figure 5.9  96  Goodness of fit for pharmacokinetic modelling of Gadovist DCE-MRI data for all tumour lines . . . . . . . . . . . . . .  xii  97  List of Abbreviations AIC  Akaiki Information Criterion  AIF  Arterial Input Function  BAT  Bolus Arrival Time  B0  the main magnetic field  B1  the transmit field  B1 map  see FA map  B1SP  B1 slice profile correction method, presented in Chapter 2  CA  Contrast Agent  DCE-MRI  Dynamic Contrast Enhanced Magnetic Resonance Imaging  EES  extravascular extracellular space  EPR  Enhanced Permeability and Retention effect  FLASH  Fast Low Angle Shot  FA map  flip angle map  Gd  Gadolinium  HMW  high molecular weight  HPG  hyperbranched polyglycerol xiii  HPG-GdF  hyperbranched polyglycerol double labelled with gadolinium, and Alexa 647 (a fluorescent marker)  IAUC60  initial area under the concentration time curve  Ktrans  volume transfer coefficient  MRI  Magnetic Resonance Imaging  αnom  nominal flip angle  RF  radio frequency  SNR  Signal to Noise Ratio  SS  Sum of Squares, or residual sum of squares  T1  spin-lattice relaxation time, or longitudinal relaxation time  T2  spin-spin relaxation time, or transverse relaxation time  TE  echo time  TR  repetition time  ve  EES volume fraction  VFA  variable flip angle  vp  plasma volume fraction  2CXM  two compartment exchange model  xiv  Glossary Akaiki information criterion provides a measure of relative goodness of fit of a  statistical model [5]. arterial input function a measurement of contrast agent concentration in a  supplying blood vessel. albumin  a protein found in blood serum  bolus arrival time the time at which the bolus of contrast agent arrives at the  point of interest in the tumour or tissue following injection. This is the time at when signal enhancement begins. B0  the main magnetic field.  B1  the applied magnetic field oscillating at the Larmour frequency used to excite spins. B1 is typically orthogonal to B0. Also known as the transmit field.  B1  refer to flip angle map map.  B1SP  B1 slice profile correction method, presented in Chapter 2 of this thesis.  Carbocyanine (DiOC7 (3)) is a fluorescent marker that, when injected  intravenously, label mitochondria of vascular and perivascular cells. In this work, it is administered five minutes prior to euthanasia, labelling blood vessels which are perfused within that five minutes. xv  CD31  a fluorescent marker used to label blood vessels. CD31 positive objects are groups of pixels in the stained image which are above a background threshold. Analysis methods define these as blood vessels.  echo time  (TE), time from the beginning of the pulse sequence to time when the spin echo occurs.  enhanced permeability and retention effect (EPR) the phenomenon of  accumulation of larger molecule in tumours has been described by some authors as the enhanced permeability and retention effect [6, 7] extravascular extracellular space the space outside blood vessels and cells. extravasation or to extravasate; to leak from a blood vessel. FLASH  Fast Low Angle Shot a gradient echo method with low flip angle.  flip angle map a map of values which may be multiplied by the nominal flip  angle to get the true flip angle at that point in the image. Gd  Gadoliniumthis is used in reference to Gadovist.  hyperbranched polyglycerol the molecule to which gadolinium and fluorescent  marker were attached to form the new high molecular weight contrast agent used in this work. HPG-GdF  hyperbranched polyglycerol double labelled with gadolinium, and Alexa 647 (a fluorescent marker)  intravascular stays within blood vessels Ktrans  volume transfer coefficient  necrosis  cell or tissue death due to injury or disease. Groups of cells which are dead or dying are termed necrotic.  nominal flip angle (αnom ) the intended flip angle chosen for a pulse sequence.  xvi  perfusion  flow, a perfused blood vessel is one in which blood is flowing.  radio frequency the frequency range from approximately 3 kHz to 300 GHz. relaxivity  the rate at which increasing concentration of a contrast agent changes 1/T1 or 1/T2. Relaxivity is expressed in units of  1 s·mM  1 ( concentration·time ).  repetition time the time between successive iterations of the pulse sequence (in  the same slice). T1  spin-lattice relaxation time, or longitudinal relaxation time.  T2  spin-spin relaxation time, or transverse relaxation time.  two compartment exchange model (2CXM), a general tracer kinetic model  which includes two spaces which the contrast agent may move between: the plasma space, and the extravascular extracellular space (EES). vasculature  network of blood vessels  xenografts  a surgical graft of foreign tissue in another tissue. In the context of this work, tumour cells from human tumours are implanted and grown in an immunocompromised mouse.  xvii  Acknowledgements I would like to thank Dr. Stefan Reinsberg, my supervisor, for his guidance and assistance throughout this process. Thank you to Dr. Jennifer Baker for the valuable skills and knowledge she provided. Thank you to Andrew Yung, Dr. Piotr Kozlowski, and everyone at the 7 T MRI centre for their support, advice, and assistance. I would like to thank my family, friends, and loved ones for their patience and support throughout my years at UBC.  xviii  Chapter 1  Introduction 1.1  Introduction  Angiogenesis is a key process in the development of tumours [8–13]. Oxygen and nutrients will only diffuse to distances on the order of tenths or hundredths of microns from blood vessesl. Therefore, once a tumour exceeds 1-2 mm3 in size, the blood supply available from surrounding healthy tissue is no longer sufficient, and new blood vessels must be generated [8, 10, 14]. This discovery is credited to Judah Folkman, nearly 50 years ago [14]. While angiogenesis is a highly ordered process in normal tissue, this is not the case in tumours where microvasculature is well known to be heterogeneous [15]. Because angiogenesis is critical to the progression of solid tumours, it is often targeted for intervention [8]. The tumour blood supply is the target of various anti-cancer treatments which impede tumour growth either by stopping the process of angiogenesis, or destroying existing tumour vasculature [16]. Non-invasive methods to assess the tumour microenvironment are necessary to provide understanding of cancer progression, for the development of cancer treatments, and for the monitoring of cancer treatments both in the clinic and laboratory [8, 9, 15, 17–20]. Magnetic Resonance Imaging (MRI) may be used for non-invasive monitoring of angiogenesis. Dynamic contrast enhanced MRI (DCEMRI) is commonly used in the clinic and research [17, 18, 21–24]. DCE-MRI is the focus of this work. Magnetic Resonance Imaging (MRI) is an established non-invasive imaging 1  tool for biological systems. MRI is based on the principles of nuclear magnetic resonance (NMR). When spin-1/2 particles are in a magnetic field, they align with that field. Applied oscillating radio frequency (RF) fields (an RF pulse) change the magnetization direction of those particles. After the oscillating field has been applied, the spins will relax back to the aligned state. This relaxation can be observed, and the signal acquired makes up MRI images. MRI has the benefits over other imaging techniques that high resolution three dimensional images can be obtained over a variety of contrasts and resolutions without the use of ionizing radiation. Because a large range of resolutions and contrasts can be obtained, MRI is highly versatile. Further, because it is non-invasive, it can be used to observe dynamic systems and in longitudinal studies, where invasive techniques would affect the system being observed. Tumour tissue is highly heterogeneous, both inter- and intra- tumour. Histological methods can provide highly accurate information about tumours, however, due to its invasive nature, a tumour cannot be assess before and after treatment. In pre-clinical research, groups of treated and untreated tumours may be compared, however, a non-invasive method which allows for assessment of changes in tumours due to treatment is preferable. DCE-MRI is a technique which involves the rapid collection of T1 weighted MRI images, during which a bolus of a contrast agent is injected into the subject, and the change in MR signal intensity is then monitored to infer the change in distribution of the agent over time. DCE-MRI methods are sensitive to blood supply in tissue. It has been demonstrated that quantitative information regarding the tumour microvasculature (such as the blood flow, or capillary wall permeability) can be obtained from the time course of the contrast agent accumulation. Pharmacokinetic modelling (for example, using the Tofts model [25]), has been recommended for the evaluation of antivascular and antiangiogenic compounds (anti-cancer drugs) [17, 18], and to evaluate treatment response in oncology [17, 19]. Assessment of tumours may be achieved using DCE-MRI [8, 9, 11, 15, 20]. Pharmacokinetic modelling of contrast agent uptake can provide information about blood flow and vessel permeability, but many models do not have the ability to separate the two, due to the ability of typical contrast agents such as Gd-DTPA to extravasate very quickly and accumulate in tumour tissue. A macromolecular contrast 2  media will extravasate from blood vessels slowly allowing for better estimates of permeability and blood flow. In this work, a novel, high molecular weight (HMW) contrast agent comprised of hyper-branched polyglycerol (HPG) molecules [1, 26] doubly labelled with a gadolinium and a fluorescent marker is investigated for this purpose. The attached gadolinium chelate allows for the assessment of HPG uptake using conventional DCE-MRI methods, while the fluorescent tag allows for histological confirmation of the distribution of the agent.  1.2  Organization of this Thesis  This thesis begins with brief background of MRI, DCE-MRI, and modelling of DCE-MRI data in this chapter. In order to obtain contrast agent concentration time curves from T1 -weighted DCE-MRI data, a baseline T1 map is first obtained. Further, inherent inaccuracies in data collection due to a non-ideal excitation profile and B1 inhomogeneity create errors in T1 measurements. This problem may be addressed with careful simulations and correction to measurements. A method for accurate T1 measurement in the presence of B1 inhomogeneity and non-ideal excitation profile is presented in Chapter 2. Once a concentration time curve has been obtained from DCE-MRI data, pharmacokinetic modelling is used to interpret that data. Chapter 3 provides a detailed discussion of pharmacokinetic modelling, as well introducing other methods used in this work to analyse DCE-MRI data. It is important to take into consideration the assumptions and limitations of any pharmacokinetic model, and the limitations of the data due to noise and time resolution. Further, it can be difficult to objectively choose the most appropriate model. These issues are considered, and effort is made to account for them in analysis of DCEMRI experiments. The methods in Chapters 2 and 3 are applied in Chapters 4 and 5 to a DCE-MRI study involving both a standard clinical low molecular weight agent, and a new high molecular weight agent, HPG-GdF. HPG-GdF is characterized and compared to a standard clinical low molecular weight contrast agent in Chapter 4. In Chapter 5, DCE-MRI data from both contrast agents, in conjunction with histology results are used to compare three tumour types in a pre-clinical rodent model.  3  1.3 1.3.1  Magnetic Resonance Imaging Background Basic MR Principles  A Classical Explanation All nuclei with an odd atomic mass number or odd atomic number possess an inherent angular momentum, or spin, and have a characteristic spin quantum number [27]. The spinning nucleus induces a magnetic field whose axis is the same as the axis of the spin, with magnitude and direction referred to as the magnetic moment, µ. This spin is called a magnetic dipole. At thermal equilibrium and without an external magnetic field, the ensemble of spins will be randomly oriented. However, when a static magnetic field, B0 , is applied, the magnetic dipoles tend to line up with that field, either in the parallel or anti-parallel state. The aligned state is the lower energy level, with the energy difference between the two states given by ∆E = γ h¯ B0  (1.1)  where γ is the gyromagnetic ratio which is specific to the nuclei. The rotating spins will experience a torque,N, due to B0 : N = µ × B0  (1.2)  and will precess around the axis of the magnetic field at their Larmour (or resonant) frequency, ω0 = γB0 .  (1.3)  This precession is analogous to the motion of a spinning top in the earth’s gravitational field. In the case of in vivo MRI imaging, the water proton (1 H nucleus) is the most commonly imaged nucleus due to its abundance in the human body. The gyromagnetic ratio of hydrogen is is 42.28 MHzT−1 . An applied pulse of a magnetic field oscillating with the resonant frequency of the spins will cause the spins to experience a torque around the axis of that field. The application of an RF pulse for certain times can be used to rotate the spins into  4  the -z direction, or into the x-y plane [27]. The pulse length required to rotate the spins with Larmour frequency ω0 by θ degrees is t = θ /ω0 . A Quantum Mechanical Explanation of Spins in a Magnetic Field Particles have spin according to their spin quantum number. The hydrogen atom has spin of 1/2. When a spin-1/2 particle at rest is placed in a static magnetic field, the Hamiltonian H becomes [28] H = −γB0 Sz = −  γB0 h¯ 2  1  0  0 −1  (1.4)  where Sz is the z component of the spin, and the magnetic field is along the z-axis. The eigenstates of the Hamiltonian are the same as those of Sz : χ+ , with energy E+ = −(γB0 )/2  (1.5)  χ− , with energy E− = +(γB0 )/2.  (1.6)  When the dipole moment is parallel to the field, the energy is lowest, just as in the classical interpretation. Here we have a time independent Hamiltonian, so the general solution to the time-dependent Schr¨odinger equation, i¯h  ∂χ = Hχ ∂t  (1.7)  can be expressed by: χ(t) =  aeiγB0t/¯h be−iγB0t/¯h  (1.8)  where constants a and b are determined by initial conditions, and are normalized. a and b may be rewritten as a = cos(α/2) and b = sin(α/2) with fixed angle α. The expectation of spin S as a function of time can be calculated Sx =  h¯ sin α cos(γB0t), 2  5  (1.9)  h¯ Sy = − sin α sin(γB0t), 2 h¯ Sx = cos α. 2  (1.10) (1.11)  Thus, we see S is tilted at a constant angle α and precesses about the field at the Larmour frequency ω = γB0  (1.12)  which is the same as in the classical case.  1.3.2  Spins in a Static Magnetic Field  From Boltzman statistics, it can be shown that the ratio of spins in the excited state, N− to spins in the ground state, N+ is N− = e−∆µ/kB T = e−¯hω0 /kB T N+  (1.13)  where µ is the magnetic dipole moment, kB is Boltzmann’s constant and T is temperature. Net magnetization is M0 = µ(N+ − N− ) = µN tanh(  µB ) kB T  (1.14)  where N = N+ + N− . At room temperature and at 1.5 Tesla (strength of a typical clinical MRI), N− /N+ is only slightly greater than 1. However, compared to Avagadro’s number (6.02 × 1023 ), it becomes obvious that this results in a sufficient number of aligned spins in the human body, and thus there is a net magnetization aligned with the magnetic field.  1.3.3  Spins in a Time Varying Field  The orientation of a coherent ensemble of spins can be altered by the application of a radio frequency (RF) field, applied for a finite time. Consider a sample in an external magnetic field B = B0 zˆ at t = −∞. Suppose at t = 0 a time varying magnetic field is added to B0 , such that the resultant field is B = B0 zˆ +2B1 cos(ωt)ˆx. Prior to the application of the oscillating field, the spins will precess about the zaxis at frequency ω0 , producing net magnetization M = M0 zˆ . However after the 6  oscillating magnetic field is applied, they will no longer precess around zˆ , but will instead precess around B at frequency ω. To simplify motion, a new reference frame with coordinates (x ,y ,z ) which rotates clockwise around the zˆ axis at frequency ω may be considered. This change of coordinates requires a transformation to our external field. It can be derived that the effective field B e f f becomes [29] B = (B0 −  ω )ˆz + B1 xˆ γ  (1.15)  For the particular case where the field’s oscillating frequency is equal to the Larmour frequency of the sample (ω = ω0 ), the zˆ component is 0, and thus the spins must rotate around the B e f f , tilting the new axis of precession to the xˆ axis of B. Spin-Lattice Relaxation Time, T1 A π radio frequency (RF) pulse will send spins into the excited state by inserting energy into the spin system, and reversing the net magnetization into the antiparallel direction (−ˆz) [27]. Due to interactions with the spins’ environment, they will relax back to the ground state, and the direction of the net magnetization slowly changes from the anti-parallel, to the parallel state. As the nucleus relaxes back to ground state, the energy must be released into the surroundings (or lattice). The spin-lattice relaxation follows the decay [30]: Mz (t) = M0 (1 − 2e−t/T1 )  (1.16)  with characteristic time T1 . Spin-lattice relaxation time varies depending on the field strength, the particle, and its environment. Spin-Spin Relaxation Time, T2 A π/2 RF pulse, moves the net magnetization into the x-y-plane, where the spins precess coherently. Because the spins are coherent, in the rotating frame, there is a net magnetization along the x axis. The spins interact with each other, causing random local inhomogeneity in the magnetic field, which will in turn change the local precession frequency [27]. If the magnitude of the local magnetic field is 7  greater than the applied magnetic field, the spins in that region will precess at some frequency greater than ω0 , and slower for a lower frequency. The results is a dephasing of the spins, and eventually a net zero magnetization in the x-y plane. The dacay of transverse magnetization in a frame rotating with the precession of the spins (x , y , z -frame) is described by [30] Mx y (t) = M0 e−t/T2  (1.17)  with characteristic decay time T2 . Typical T2 relaxation times in biological tissues range from a few microseconds in solids to a few seconds in liquids [27]. Effective Spin-Spin Relaxation, T∗2 Spin coherence is further affected by inhomogeneities in the applied magnetic field. That is, spin coherence is not solely dependent on inhomogeneities due to interactions with nearby spins, which cause the T2 relaxation. The relaxation caused by the combined effect of the spin-spin interactions and the inhomogeneities in the applied magnetic field is referred to as the effective transverse relaxation time, T∗2 [27]. Typical NMR Apparatus A typical NMR apparatus consists of an electromagnet (or sometimes a permanent magnet), producing the main magnetic field and a system of RF and receiver coils. The receiver coils are typically positioned such that a sample could be placed inside the coil. The axis of each the two sets of coils will be perpendicular to each other, and to the axis of the main magnetic field. To excite the spins in a sample, a pulse of AC current is applied to the RF coils. The length and frequency of the pulse determine how far the spins are rotated. A typical π pulse lasts τ = π/ω, and rotates the spins 180 degrees. The resulting relaxation of the spins in the sample induces a change in the magnetic field, and thus a current in the receiver coils.  8  1.3.4  Magnetic Resonance Imaging  Magnetic Resonance Imaging (MRI) is based on the same principles as NMR, only instead of taking a single measurement from a sample, MRI takes many measurements, which are used to create a three dimensional image of the object, with the image intensity proportional to the signal intensity at that location. Each pixel in an MR image corresponds to a three dimensional volume in the object, referred to as a voxel. An MR imaging system consists of the same basic components as an NMR apparatus: a main magnetic field source, RF coils, and receiver coils. There are also additional coils for producing magnetic field gradients. Gradients are necessary for the more complex pulse sequences used in MRI, and for spatially encoding the signal to create three dimensional images. The main magnetic field of an MRI system is produced by a large superconducting electromagnet, typically of strength 1.5-3 T (Tesla) in the clinic, and higher fields for research. The spin-echo pulse sequence, works much in the same way in MRI as for NMR experiments, only additional magnetic field gradients and pulses are applied to spatially select the volume which produces the signal. The sequence is applied many times, each time producing a signal for a new location. The time between consecutive pulse sequences is the repetition time, TR. The echo time and repetition time can be adjusted, and will determine image contrast. The relaxation dynamics are the same as for NMR, but Equations 1.16 and 1.17 can be rewritten in a more convenient form as [30] Mz = M0 (1 − 2e−T R/T1 )  (1.18)  Mxy = M0 e−T E/T2  (1.19)  In this form, the effect of TE and TR on the resulting image intensity is more apparent. Further, different pulse sequences can obtain different contrasts, and can be utilized to image various physiological and anatomical effects.  9  1.4  Exogenous Paramagnetic Contrast Media  Contrast between different tissues in an MR image is based on intrinsic differences in the NMR properties (i.e. relaxation times or proton density) between adjacent tissues. In many MRI applications, this difference is great enough, that by appropriately choosing the pulse sequence, neighbouring structures can be distinguished, and the resulting image contrast in sufficient for diagnostic purposes [31]. In NMR, contrast arises from tissue relaxation times, and one of the major advantages of MRI over x-ray based techniques is this intrinsic soft tissue contrast without the necessity of contrast agents. However, there are still important areas in which an exogenous (external) contrast agent is essential, in order to obtain sufficient contrast. This is typically the case when structures would otherwise be similar in appearance, to provide additional specificity in describing regions of abnormal signal, and to opacify or highlight spaces, or depict tissue vascularity and perfusion [31]. In order to act effectively, a contrast agent must be able to reduce T1 or T2 in tissues via affecting the amplitude and time scale of variation of local magnetic fields experienced by water molecules [31]. Paramagnetic agents attempt to do this. Molecules of the paramagnetic agents possess a large magnetic dipole moment, compared to the proton.  1.4.1  Relaxivity of Gadolinium Chelate Contrast agents  The majority of currently used contrast agents are stable chelates of gadolinium (III) [32]. Because this ion has the highest possible number (seven) of unpaired electrons, it is the most paramagnetic of stable metal ions [32]. The relationship between relaxation times and concentration of a paramagnetic contrast agent can be predicted by the Solomon Bloembergen equations [16, 32, 33]: 1 T1,obs 1 T2,obs  =  1 + r1 [Gd] T10  (1.20)  =  1 + r2 [Gd]. T20  (1.21)  The observed relaxation rates 1/T1,obs and 1/T2,obs are determined by relaxivity r1 and r2 (the spin-lattice and spin-spin relaxivity constants), and the relaxation rates, 10  1/T1,0 and 1/T2,0 , when no contrast agent is present. Relaxivity is dependent on field strength and chemical structure of the contrast agent [16, 32]. Concentration is usually expressed in molarity (in practice, mmol/L), and relaxivity is expressed as mM−1 s−1 . The paramagnetic relaxation of water protons is based on dipole-dipole interactions between proton spins, and fluctuations in the local magnetic field caused by unpaired electrons spins of the paramagnetic substance [32]. Paramagnetic relaxation rate enhancement consists of two main contributions [32]: inner sphere contributions due to interactions between GdIII electron spins with water protons, and outer sphere contributions from random translational diffusion of bulk solvent molecules around the paramagnetic ions. More generally, inner sphere and outer sphere are intra- and inter-molecular interactions respectively. Relaxivity due to these different spheres may be summed [32] to obtain the total relaxivity: ri = riIS + riOS ; i = 1, 2.  (1.22)  Overall, the relaxivity of gadolinium based contrast agents is influences by a large number of parameters, in particular, water proton exchange rate and rotation.  1.4.2  Measuring Contrast Agent Concentration In Vivo  In order to investigate the kinetic behaviour of a contrast agent, contrast agent concentrations must be determined from MRI signal intensities. Since we know from equations 1.20 and 1.21 that the contrast concentration is directly proportional to relaxation rate, a series of measurements of T1 in tissue could provide a method to monitor changes in concentration of the contrast agent [16]. The relationship between contrast agent concentration and the relative increase in signal intensity can be derived for any imaging sequence from the Bloch equations [16, 34]. The signal intensity from a Fast Low Angle Shot (FLASH) sequence (a gradient echo sequence with spoiling of the transverse magnetization) with flip angle α, repetition time TR and echo time TE is described by [16, 34]  S = S0  sin(α) · 1 − exp − TT1R 1 − cos(α) · exp − TT1R 11  exp −  TE T2∗  (1.23)  where S0 is a constant containing proton density, receiver gain, and image reconstruction settings. Assuming TE is sufficiently short, the T∗2 effects can be ignored (as this term goes to 1), and Equation 1.23 becomes  S = S0  sin(α) 1 − exp − TT1R 1 − cos(α)exp − TT1R  .  (1.24)  If the signal prior and post-contrast is known, and it is assumed that signal intensity is proportional to 1/T1 , it can be found that the relative increase in signal intensity following injection of the contrast agent is related to T1 of the contrast agent, and the pre-contrast T1 of the tissue [16]: SGd − S0 = r·ρ ·TR  1 T1Gd  −  1 T10  = r1 [Gd].  (1.25)  As such, the concentration of the contrast agent may be found, assuming constant relaxivity in blood and tissues. In practice, the conversion of the signal of a dynamic FLASH sequence to concentration may not be a simple as in Equation 1.25. Studies have shown that relaxivities are affected by macromolecular content [35, 36]. As a result, the assumption of constant relaxivity may be inaccurate, and relaxivity values measured in saline or water may be insufficient.  1.5  Dynamic Contrast Enhanced MRI  The use of extracellular contrast media has led to improved sensitivity of detection and delineation of tumours via MR imaging [16]. DCE-MRI may be used to characterize the structure and function of tumour microvasculature. A DCE-MRI experiment involves the injection of a contrast agent (such as gadolinium-DTPA) into the bloodstream of a subject which results in a shortening of relaxation times [16]. This results in signal enhancement (when using the appropriate imaging technique) in areas where the contrast agent is located: in this case, the blood vessels, and any surrounding tissue it has leaked into. By collecting a rapid series of MR images, dynamic information can be obtained. Specifically, perfusion (blood flow)  12  and vessel permeability information (or parameters related to these quantities) can be obtained. DCE-MRI methods are sensitive to blood supply of tumours, and have the ability to quantify features such as blood flow and capillary wall permeability [16]. The extravasation of contrast (transfer of contrast agent) from the capillaries into extracellular extra-vascular space depends on sufficient perfusion of feeding vasculature and extravasation of the agent from the vascular space [16]. Via pharmacokinetic modelling [16] of DCE-MRI, a parameter which describes this, Ktrans (also known as the volume transfer coefficient), is obtained. Ktrans can be interpreted differently depending on whether the case is dominated by capillary permeability or blood flow [16]. Many current models of single-tracer DCE-MRI experiments do not allow for the separation of flow and permeability information. Without separating these parameters, it is impossible to determine the mechanism behind temporal changes.  1.5.1  Tracer Kinetics  Tracer kinetics refers to the examination of the accumulation of contrast agent in tissues. The use of tracers to measure the kinetic properties in tissue has been powerful in medicine [31]. Tracer measurements of blood flow rely on several assumptions about the tracer, the means of administration, and its interaction with the tissue environment [31]. This section discusses tracer kinetics, and provides an introduction to pharmaocokinetic models of tracers. Arterial Input Function The arterial input function (AIF) refers to the concentration of the contrast agent within the arterial supply to tissue as a function of time [31]. An AIF is necessary for analysis of DCE-MRI data. The best results are obtained when the AIF is measured concurrently with the DCE-MRI study. However, this is not always possible. Sometimes a population average is used, or the AIF may be estimated mathematically. The use of a population averaged AIF is known to affect the accuracy of tissue parameters found in modelling [17].  13  Impulse Response Function In general, an impulse response function describes how a system responds (what out put the system provides) to a single stimulation (a delta function) [31]. For example, striking a bell would result in a ringing tone [31]. In the case of tracer kinetics, the impulse response function describes how contrast agent particles exit a system in responds to an ideal input - an instantaneous bolus - of contrast agent. Tissue Compartmentalization and Pharmacokinetic Modelling In order to quantify observed contrast agent kinetics in a way that provides physiologically meaningful parameters, a model of the tissue structure with parameters which affect the contrast agent distribution and accumulation must be defined [16]. Here we divide the tissue into three compartments: the vascular plasma space, the extracellular extravascular space (EES), and the intracellular space [25]. Other microscopic tissue components (membranes, fibrous tissue, etc) make up a fourth compartment. The intracellular and ’other’ volumes are referred to as intracellular space [16]. All clinically utilised MRI contrast agents do not pass into intracellular space of the tissue. Contrast agents discussed in this work are assumed to move only between two volumes: intravascular plasma space, and extravascular extracellular space. It is assumed that they may accurately be described by a two compartment exchange model. The two compartment exchange model discussed here describes intravascular plasma space and extravascular, extracellular space (EES space). Tissue is supplied with the contrast agent which can be estimated by the the arterial input function (AIF) from a supplying artery with flow F p . Once in the plasma space, the tracer diffuses into the EES via the capillary walls. The transfer rate depends on blood flow, and the permeability and surface area of the blood vessels. Next, contrast agent can diffuse back from EES to plasma and subsequently leaves plasma. A schematic diagram showing this exchange is shown in Figure 1.1. Parameters describing this exchange are the blood flow F p , and permeability surface area product PS. These determine transfer from plasma space to EES, the transfer back into plasma, and the elimination from the plasma respectively. The fractional volumes of plasma is denoted v p , and the fractional volume of EES is ve . The concentration  14  in tissue as a function of time, Ct (t), can be described by Ct (t) = Fp ·Cp (t) ∗ R2CXM  (1.26)  where Cp (t) is the concentration of the contrast in plasma of the feeding artery (estimated by the AIF), R2CXM (t) is the impulse response function of the tissue, Fp is the plasma perfusion, and ∗ is the convolution operator. The response function depends on the tissue model, and requires assumptions about the tissue environment, time resolution of data, and other factors. Further discussion of modelling is left to Chapter 3.  Figure 1.1: A schematic diagram of the two compartment exchange model. Vascular, or plasma space, v p , is shown, and extracellular, extravascular space is shown, ve .  1.5.2  Issues Regarding Analysis  Different pharmacokinetic models involve different assumptions, and thus the inappropriate choice of a model would introduce error into the resulting analysis. Comparisons of such models has been published (for example, Donaldson et al [17] and Buckley et al [37]). It is essential that the assumptions made in tracer kinetic model suit the data obtained, reflect data quality (contrast to noise, temporal resolution, scan duration), and physiology of tissue being investigated, and addresses questions posed in the study [37]. For example, the Tofts and modifiedTofts model are intended for use with low temporal-resolution data sets. Further, these models do not separate flow from permeability of the vessels, and instead measures K trans . If the purpose of the DCE-MRI study is to investigate the effect 15  on a tumour due to therapy, K trans may not change if flow and permeability change in opposite directions, and thus this model is ineffective [17].  1.6  Comparing Models  The Akaiki information criterion (AIC) [38] may be used to compare two models [5, 39]. As model complexity increases, often the fit quality will as well. However sum squared error is insufficient to determine if any new information is obtained. The AIC provides a means to determine if a more complex model is more appropriate. If it may be assumed that the scatter of points around the curve follow a Gaussian distribution, the AIC may be computed by: AIC = N · ln(SS/N) + 2K  (1.27)  where N is the number of data points, SS is the residual sum of squares, and K is the number of parameters in the model plus one.  16  Chapter 2  Variable Flip Angle Fast Low-Angle Shot T1 Measurements in the Presence of Non-ideal Slice Profile and B1 Inhomogeneity  The spin lattice relaxation time (T1 ) may be measured using a sequence of Fast Low Angle Shot images with different flip angles. In the presence of a slice select gradient, the relationship between signal, T1 , and flip angle of a fast low angle shot sequence deviates from the ideal case. If these deviations are not accounted for, T1 measurements performed with variable flip angle experiments will provide erroneous measurements. Variable flip angle methods further suffer in the presence of B1 inhomogeneity. With knowledge of the radio frequency excitation pulse shape and pulse length, Bloch simulations may be used to determine the flip angle through the slice plane, and the result17  ing signal may be simulated. In this chapter, a method to use singleor multi-slice 2D variable flip angle experiments for simultaneous B1 and T1 mapping is presented. This method is demonstrated with simulations, verified with phantom experiments, and in vivo examples are presented. I further demonstrate, through simulations, the effect the excitation profile will have on variable flip angle curves acquired with 3D experiments.  2.1  Introduction  An in vivo measurement of T1 is a required first step for measuring uptake of contrast agent in T1 weighted Dynamic Contrast Enhanced (DCE) MRI techniques. Change in MR signal intensity due to a contrast agent depends on both the initial T1 of the tissue, and the concentration of the contrast agent. Fast Low Angle Shot (FLASH) pulse sequences (also known as spoiled gradient echo) are used by numerous researchers for estimation of T1 (e.g. [40–43]). Multiple images are acquired with different repetition times, or flip angles. Such techniques are popular due to good SNR, low spatial distortion (compared to echo planar techniques), and low power deposition (compared to spin echo techniques) [43]. In the ideal case, the signal resulting from transverse magnetization in the steady state of spoiled gradient echo imaging sequence, where TE<<T2* is described by: S = S0 sin(α)  1 − exp(−T R/T1 ) 1 − cos(α) exp(−T R/T1 )  (2.1)  where α is flip angle, TR is repetition time, T1 is spin-lattice relaxation time, and S0 is a constant including scanner gain, coil reception profile, and proton density. Equation 2.1 will be henceforth referred to as the FLASH equation or ideal FLASH equation. T1 may be measured by performing a series of experiments with different repetition time (TR)s or flip angles, and fitting Equation 2.1 to the data. In this work, only variable flip angle (VFA) experiments with constant TR are discussed. In the presence of a slice selection gradient, the flip angle varies through the plane of the excited slice. This inhomogeneous excitation causes distortions in the 18  shape of the VFA signal curve, such that Equation 2.1 no longer applies. Errors in T1 measurements will be made if these effects are not accounted for. VFA methods further suffer from the presence of B1 field inhomogeneity. In the case where the ideal FLASH equation applies, the signal will null at a flip angle of 180◦ . However, the flip angle the user requests on the scanner (the nominal flip angle, αnom ), may not be the true flip angle, and may be incorrect by some factor due to improper system calibration. For FLASH experiments without a slice select gradient, the flip angle will be constant across the volume. B1 corrections may be made by simply finding the zero crossing in a VFA experiment, and scaling all nominal flip angles by a factor such that the zero crossing occurs at 180◦ [44]. Specifically, a linear regression is performed to find the signal null from three data points with nominal flip angles less then, equal to, and greater than 180◦ . For a zero crossing occurring at location η, the flip angles may then be corrected by a factor of 180/η. A map of these correction values is referred to in this work as a flip angle map. However, in the presence of slice select gradient, and a non-ideal slice profile, the signal null does not necessarily occur at 180◦ (as is show in Section 2.4.2). While using the method by Dowell and Tofts [44] achieves effective B1 mapping, the requirement of using a non-selective excitation is inconvenient: wrapping will occur in the slice select direction. This limits the possible orientation of slices, the geometry of objects which may be imaged, and the option for multi-slice imaging. The effect of slice profile on 2D single- and multi-slice MRI has been discussed in literature (for example [43, 45, 46]), and the adverse affects on T1 measurements have been noted. With knowledge of the radio frequency (RF) excitation pulse shape and pulse length, Bloch simulations may be used to determine the flip angle through the slice plane, and the resulting signal. In this chapter, a method to use single- or multi-slice variable flip angle experiments for simultaneous B1 and T1 mapping is presented. This B1SP (B1 and Slice Profile) correction to T1 measurements is demonstrated with simulations and verified with phantom experiments. In vivo examples are presented. Due to the effect of non-ideal pulse shape on signal intensities, 3D experiments are often used in place of 2D multi- or single-slice experiments. While it is typically understood that the signal in the outer slices will vary from the ideal case, differences occurring in all slices are shown here. Using both data and simulations, 19  T1 and flip angle (FA) map errors due to 3D experiments with selective excitation are demonstrated.  2.2  Theory  In order to simulate the signal resulting from a FLASH experiment, the excitation profile (or slice profile) must first be calculated. This requires solving the Bloch equations for a known RF excitation pulse. The evolution of the magnetization vector M(t) = [Mx (t), My (t), Mz (t)] may be described by the Bloch equations. The Bloch equations in the rotating frame are [47]:        Mx 0 −Ω ω1 sin(φ ) Mx (1/T1 )Mx d        Ω 0 −ω1 cos(φ ) My  +  (1/T 2)My  My  =  dt Mz −ω1 sin(φ ) ω1 cos(φ ) 0 Mz (1/T1 )(1 − Mz ) (2.2) where ω1 (t) is the nutation frequency of the the RF excitation pulse, φ is the phase of the RF excitation pulse, Ω is the frequency offset from the Larmour frequency. This may be simplified by assuming that T1 and T2 are long relative to the B1 pulse duration:      Mx 0 −Ω ω1 sin(φ ) Mx d      Ω 0 −ω1 cos(φ ) My  . My  =  dt Mz −ω1 sin(φ ) ω1 cos(φ ) 0 Mz  (2.3)  Knowing the RF excitation pulse, B1 (t), the nutation frequency is given by ω1 (t) = γB1 (t) (with the amplitude B1 determined by the nominal flip angle). The frequency offset due to location in the slice is determined by the location r, and gradient G, Ω = γ G · r. Here, the assumed initial conditions are: M0 = M0 zˆ = 1ˆz. The transverse magnetization profile resulting from an RF pulse of duration ∆t, in the presence of a gradient may be found by solving Equation 2.3 for a range of Ω values. The results of this simulation is M(z,t = t1 ), where time t1 is indicated in Figure 2.1. Next, a refocusing gradient (in the slice select direction) must also be simulated by multiplying the complex transverse magnetization by the complex exponential  20  Figure 2.1: The portion of the FLASH Sequence which is simulated by solving the Bloch equations. t1 indicates the magnetization simulated by the Bloch equation. t2 indicates the point where magnetization is simulated for following the rephase gradient. e−i∆tΩ(z)/2 , such that it is -50% of the gradient applied during the excitation (the effect of deviating from a 50% rephase gradient is investigated in Section 2.4.1). The result of this corresponds to magnetization at time t2 indicated on Figure 2.1. Examples of the transverse magnetization profiles resulting from simulating a 1 ms Hermite pulse (Figure 2.2) in the presence of a gradient are displayed in Figure 2.3. With the magnetization profile calculated, as above, the flip angle, α(n), and phase, φ (n), at all locations across the slice may then be found and used to calculate the signal resulting from an excitation with nominal flip angle αnom . The nonrectangular slice may be treated as a sum of many narrow rectangular slices, and the signal is integrated from the slice profile. First, the real and imaginary components must be summed individually: Sx = A  ∑  (1 − exp−T R/T1 ) sin(θ (n))cos(φ (n)) (1 − cos(θ (n)) exp−T R/T1 ) n=1  (2.4)  Sy = A  (1 − exp−T R/T1 ) sin(θ (n))sin(φ (n)) (1 − cos(θ (n)) exp−T R/T1 ) n=1  (2.5)  N  N  ∑  where Sx and Sy are the real and imaginary components, N is the number of samples, n, along the slice profile which are sampled at equally spaced intervals, and A is the constant of proportionality. To simulate a 2D experiment, this should be summed across the whole profile. For a 3D experiment, the excited slab is divided  21  into ranges for each slice, and the signal for each slice is summed accordingly. The total signal is calculated by: S=  2.3  Sx2 + Sy2 .  (2.6)  Methods  2.3.1  Simulations  First, excitation profiles for many flip angles were simulated and saved: Bloch simulations, as described by Equation 2.3, were performed to find M(z) following a 1 ms Hermite pulse (the Hermite pulse is shown in Figure 2.2). Simulations made use of the ordinary differential equation (ODE) solver, ode45, in MATLABTM (R2009a, The MathWorks Inc.). To obtain each profile, the solution of the Bloch equations was found at many frequency offsets: −10000 Hz ≤ Ω ≤ 10000 Hz, at 5 Hz resolution. Simulations were performed for flip angles ranging from 1 to 360◦ , at 0.1◦ resolution. Truncated Sinc Pulse 100  80  80 Amplitude, arbitrary units  Amplitude, arbitrary units  Hermite Pulse 100  60  40  20  40  20  0  0  −20  60  0  0.2  0.4  0.6  0.8  −20  1  0  0.2  0.4  0.6  0.8  1  time, ms  time, ms  Figure 2.2: The RF excitation pulse shapes used in this work were (left) the Hermite pulse, and (right) a truncated Sinc pulse (as available on the Bruker scanner). For this work, it is assumed that the echo time is sufficiently short that T2* may be ignored. It is also assumed that relaxation during the excitation pulse and rephase gradient is negligible. These slice profiles, Mx,y (z, αnom ), were then used to create look-up tables of the signal, S(αnom , T1 /T R) from 2D and 3D collections for T1 /TR ranging from 22  Figure 2.3: The simulated transverse magnetization profiles resulting from a selective 1 ms Hermite excitation pulse with a range of flip angles. 1/100 to 4000/100. Signal was computed by integrating magnetization profiles over different frequency ranges (Equations 2.4 to 2.6). To simulate signal from a 2D collection, signal was summed over the entire frequency range of the simulation (ranges were chosen such that Mx,y ≈ 0 at edges for all cases). For all excitation pulses used here, the My is an odd function, and Equation 2.5 sums to zero (for simulations of a 2D experiment). For the simulated 3D experiment, the signal for each slice was summed over frequency ranges corresponding to slice geometry in phantom experiments. The imaginary part of the signal does not necessarily sum to zero. To theoretically investigate the effects of inaccurate rephase gradients in 2D collections, the included rephase gradient was varied by different amounts ranging from 40% to 60%, and variable flip angle curves were plotted at different T1 weightings to observe the change in curve shape. The purpose of this investiga23  250 200  Signal (arbitrary units)  150 100 50 0 −50 −100 −150 0 500/100 1000/100 1500/100 2000/100 T1/TR  2500/100  0  50  100  150  200  Flip Angle (degrees)  Figure 2.4: The signal as a function of flip angle and T1 , resulting from simulations. tion is to see how sensitive the resulting signal curves are to errors in the rephase gradient, and to check if the 50% rephase gradient is perhaps not ideal.  2.3.2  Phantom Experiments  All imaging experiments were performed on a 7 T Bruker Biospec 70/30 scanner at room temperature with a combination of volume transmit (Tx) / surface receive (Rx) coil. Four test tube phantoms were made with different concentrations of gadolinium chelate contrast agent in saline (GadovistTM , Bayer Healthcare), to give a range of T1 relaxation times. Imaging was performed in both 2D and 3D acquisitions to compare to simulations. A FLASH variable flip angle experiment was used in a single slice acquisition (TR/TE = 100/2.75; matrix = 128 x 64; FOV = 4.26 x 2.7 x 0.1 cm3 ; 24  1 ms Hermite pulse excitation; gradient strength = 36 kHz/cm) and in two 3D acquisitions with the slab select gradient on (2.8 kHz/cm) and off (for both 3D experiments: TR/TE = 100/2.847; matrix = 128 x 64 x 16; FOV = 2.5000 x 2.5000 x 2.5000 cm3 ; 2 ms truncated Sinc excitation pulse). To examine the shape of VFA curves, images for a range nominal flip angles were acquired in all experiments: 10, 15, 20, 25, 30, 40, 50, 60, 70, 8, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180. For both 3D experiments, images with nominal flip angles of 190, 200, 210, and 215 were also acquired. An inversion recovery non-imaging experiment was performed on each phantom to confirm gold standard T1 values. The result is referred to as the true T1 .  2.3.3  Correcting T1 Measurements  To find accurate T1 measurements while accounting for slice profile, a variable flip angle data set sampling the whole curve must first be acquired to ensure that data will be obtained beyond the location of zero crossing. A single slice data set with a nominal flip angles ranging from 5◦ to up to 215◦ was collected (as described above). The VFA curve is then fitted (pixel by pixel) in a naive fashion, assuming that the ideal FLASH equation applies: the zero crossing is found, and used to scale the nominal flip angles, and then the ideal FLASH equation is fitted to a subset of the data (αnom = 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ , 80◦ , 100◦ , 120◦ ). Using a look up table, this value is mapped to a true T1 value. More specifically: 1. Data is collected. A 2D MRI data is collected with a nominal flip angles ranging from 5◦ to up to 215◦ . 2. Data is phased. All analysis is done pixel by pixel. The complex data for VFA curve for each pixel is plotted with the real part on the x-axis, and imaginary part on the y-axis. The slope is taken, and phased data is then: Sdephased = ℜ(S∗exp(i arctan(slope))). This results in the signal’s imaginary component being minimized, and removes sign ambiguity that occurs when using signal magnitude (signal magnitude cannot be negative, but the zero crossing must be identified). 3. The flip angles are scaled. The location of the signal null is found by taking 25  a linear fit of the three closest data points to the zero crossing, and interpolating. Taking the naive assumption that the zero crossing should occur at 180◦ , nominal flip angles are scaled according to the location of the zero crossing. 4. The phased data is fitted. This phase-corrected data, with scaled flip angles is fit to the ideal FLASH equation to obtain an uncorrected T1 . 5. A look-up table mapping the uncorrected T1 to the True T1 is created: • Simulated VFA curves (using the same nominal flip angles as the acquired data) are fit for T1 by the same routine above (steps 2-3). • This is repeated for many input T1 values, (ranging from 1 to 4000 ms here). The input T1 is taken as the true T1 . • A table is created of True T1 values, and the corresponding T1 resulting from the fit, T1,iFLASH f it , and zero crossing locations (see Figures 2.6 and 2.7). 6. T1 values are corrected. T1 fit values from step 4, are corrected using the table created in step 5. This new value is the B1SP corrected T1 value. 7. Flip angle maps are corrected. Knowing the data’s zero crossing location from step 3 and the true T1 from step 6, the true flip angle map value is found from the look-up table.  2.3.4  Using the B1SP Correction Method to Find T1 In Vivo  To demonstrate the utility of this method in vivo, a VFA experiment was performed. A subcutaneous tumour in a female non-obese diabetic/severe combined immunodeficient (NOD/SCID) mouse was imaged. A single slice FLASH variable flip angle experiment was performed (TR/TE = 500/2.75; αnom = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 150, 170, 180, 190, 200, 215; 1 ms Hermite pulse excitation). The zero crossing was found, and the curve was fit assuming the ideal FLASH equation, then corrected, as described above. T1 maps before and after were compared.  26  2.3.5  Data Analysis  All data analysis was performed using MATLAB  TM (R2009a,  The MathWorks  Inc.). The true T1 of each phantom was measured by fitting the non-imaging inversion recovery data. Regions of interest were drawn on all images selecting the phantoms. 2D VFA experiments were used to create T1 maps, and flip angle map with and without B1SP correction. To provide an alternative verification of T1 , and of the flip angle map, the T1 map and flip angle map were calculated from the 3D VFA experiment with nonselective excitation, using the same flip angles as the 2D experiment. T1 was fit assuming the ideal FLASH equation applies. The flip angle map was calculated according to Dowell and Tofts [44], but using the four flip angles closest to the zero crossing, from the given data set. The flip angle map calculated here was used to compare values found from the B1SP method. To evaluate errors in 3D measurements due to selective excitation, the T1 map, and flip angle map were calculated from the 3D VFA experiment with selective excitation, and compared to the values found from the non-selective VFA experiment.  2.4 2.4.1  Results Errors in the Rephase Gradient  Using a 1 ms hermite pulse excitation, the effect of varying the size of the slice rephase gradient a VFA FLASH experiment was simulated for TR/T1 = 100/100 (Figure 2.5 left), and TR/T1 = 100/2000 (Figure 2.5 right). Rephase gradients were varied from the standard 50% by up to ± 10% at high and low T1 weighting. Large deviations from the expected signal curve are observed. In particular, a large deviation is observed when deviating by ± 10%, relative to deviations ≤ ± 5%. Thus it is important for simulations, to accurately know the rephase gradient. Without the rephase gradient, intra-voxel dephasing and signal loss will occur. Though a 50% rephase gradient is usually assumed to be ideal, some authors have discussed the 27  use of rephase gradients varying from 50% for maximized rephasing (e.g. Section 3.1 of Bernstein, 2004 [30]). The rephase gradient should be optimized to maximize the refocusing of intravoxel dephasing, and therefore to maximize the resulting signal. The area of the rephase gradient may vary depending on flip angle, as is demonstrated in Figure 2.5. In particular, at flip angles larger than approximately 70◦ (and depending on T1 weighting), a rephase gradient less than 50% is ideal when using a 1 ms Hermite excitation.  Figure 2.5: Using a 1 ms hermite pulse, the effect of varying the size of the slice rephase gradient a VFA FLASH experiment was simulated for TR/T1 = 100/100 (left), and TR/T1 = 100/2000 (right). Rephase gradients were varied from the usual 50% by up to ± 10% at high and low T1 weighting.  2.4.2  Zero Crossing Location is T1 Dependant: Results from Simulation  The zero crossing was found on simulated T1 VFA curves for a range of T1 weightings, as shown in Figure 2.6. The location of the zero crossing shows the dependence on T1 weighting. It was found that the signal null occurs below 180◦ , and deviates further from 180◦ with longer T1 .  28  Zero crossing in VFA experiments depends on T1/TR 166  Location of Zero Crossing  164  Figure 2.6: The location of the zero crossing was investigated for different T1 weightings using the simulations of FLASH VFA experiments. No zero crossing occurred at 180◦ , and becomes smaller with increased T1 weighting.  162 160 158 156 154 152  0  1000/100  2000/100 True T1/TR  3000/100  Assessing errors in T1 measurement due to slice profile 2000 1800 1600  T1 from fitting  1400 1200 1000 800 600 400 200 0  2.4.3  0  1000  2000  3000 True T1, ms  4000  5000  6000  Figure 2.7: Simulations of VFA experiments with TR = 100 ms were fit assuming that the zero crossing should be 180◦ , and that the FLASH equation applies, to evaluate T1 errors. T1 estimates are significantly below true T1 values (the dotted line indicating unity is drawn for reference).  T1 Errors Due to Slice Profile: Results from Simulations  To assess errors made in T1 measurements due to naively fitting data from 2D FLASH variable flip angle experiments with the FLASH equation, it is fit to the simulated data (including flip angle scaling to adjust the zero crossing to 180◦ ). A one to one mapping was found between input and measured T1 (Figure 2.7). T1 values are vastly underestimated.  2.4.4  Method Verification in Phantom Experiments  The relationship in Figure 2.7 is used as a look-up table to correct T1 values found by naively fitting VFA curves from 2D experiments. To verify this method, and 29  5  2.5 simulation FLASH fit data  3 Signal, arbitrary units  5  TR/T1 = 100/104  x 10  2 1 0 −1 −2  50  100 Flip Angle, degrees  1 0.5 0 −0.5  −1.5  150  0  50  5  TR/T1 = 100/676  x 10  1.5 simulation FLASH fit data  Signal, arbitrary units  Signal, arbitrary units  simulation FLASH fit data  1.5  −1 0  4  10  TR/T1 = 100/507  x 10  2 Signal, arbitrary units  4  5  0  100 Flip Angle, degrees  150  TR/T1 = 100/1464  x 10  simulation FLASH fit data  1 0.5 0 −0.5  −5 0  50  100 Flip Angle, degrees  −1  150  0  50  100 Flip Angle, degrees  150  Figure 2.8: Data from phantom experiments agrees well with simulated curves. Simulations are for true T1 (rounded to nearest ms), as measured with a non-imaging inversion recovery experiment. Vertical scaling of simulations was adjusted to match data. Simulation curves were adjusted for B1 inhomogeneity in data, to align the location of the zero crossing with data. For reference, the best fit FLASH equation with FA scaled so that the zero crossings are aligned is also shown (dotted line). While the ideal FLASH equation seems to agree with the data, the errors in T1 values are significant. asses accuracy, this method was applied to phantom experiments, and T1 values were independently verified with non-imaging inversion recovery experiments. Four phantoms with different concentrations of saline doped with Gadovist were imaged. For the four phantoms, the T1 values found by the FLASH fit, inversion recovery (True T1 ), B1SP correction, and 3D non-selective FLASH VFA methods are compared in Table 2.1 (all times in ms). Values before and after the B1SP correction are plotted and (Figure 2.9) vs true T1 . T1 values from 2D experiments with no correction for slice profile underestimate true T1 values by approximately 50% . T1 values corrected with the B1SP method are about 20% lower than true T1 valuesd. B1SP corrected T1 is very close to values found by non-selective 3D 30  T1 values (ms) Measured by Different Methods Inversion Recovery Ideal FLASH fit B1SP Corrected Non-selective 3D VFA 105.0 ± 0.3 64 ± 1 71 ± 2 90 ± 2 507 ± 6 191 ± 4 340 ± 10 500 ± 100 680 ± 20 250 ± 10 530 ± 40 600 ± 200 1460 ± 10 400 ± 70 1200 ± 100 1200 ± 100 Table 2.1: True T1 values from inversion recovery are compared to fit values. Error values for T1 values found from imaging methods are 1 standard deviation within the region of interest. For the non-imaging inversion recover, error indicates the 95% confidence bound. VFA experiments, with longer T1 s agreeing within uncertainty. 1500 corrected T1 uncorrected T1 true T1  Estimated T1  1000  500  0 0  500  1000  1500  True T1  Figure 2.9: T1 estimates before and after the correction is applied are shown vs True T1 . Error bars represent the standard deviation of T1 values across the phantom. To verify the curve shapes resulting from simulations, the simulated VFA curves for the true T1 values were plotted with phantom data. Horizontal scaling was performed to align the zero crossing of the simulation with the nominal flip angle of the zero crossing in the data. Vertical scaling was performed to align the curve with the data. The simulations show good agreement to simulations of the true T1 value (Figure 2.8). Notice that while the FLASH curves seem to fit well, the T1 values are vastly underestimated, as is demonstrated in Table 2.1. The flip angle correction, without accounting for the slice profile effects, was very different between phantoms. With the B1SP correction, the T1 values in each 31  Flip Angle Map Values Calculated by Different Methods True T1 (ms) FLASH fit B1SP Corrected non-selective 3D VFA 105.0 1.23 ± 0.02 1.06 ± 0.02 1.10 ± 0.02 507 1.226 ± 0.009 1.082 ± 0.008 1.10 ± 0.02 680 1.156 ± 0.007 1.060 ± 0.006 1.11 ± 0.01 1460 1.33 ± 0.02 1.09 ± 0.02 1.10 ± 0.01 Table 2.2: Flip angle map correction values vary significantly with T1 . This trend is removed with the B1SP correction, and values become similar to true values phantom became very similar, and much closer to values found with the Dowell and Tofts method, as shown in Table 2.2. The values resulting from the ideal FLASH fit reflect that the location of the zero crossing depends on the T1 . Accounting for slice profile removes this dependence. Errors in this table indicate standard deviation within the ROI.  2.4.5  Using the B1SP Correction Method to Find T1 In Vivo  To demonstrate the utility of this method in vivo, a VFA experiment was performed. A subcutaneous tumour in a NOD/SCID mouse was imaged. The average T1 in the tumour assuming that the ideal FLASH case applies is 984 ms, and after the B1SP correction, is 1847 ms. The T1 maps are shown in Figure 2.10  2.4.6  3D VFA Experiments  For 3D data sets with selective excitation, no signal null occurs in the VFA signal magnitude curves. However, looking at the real part of these data sets, the signal null is observed. Further, the curve shape and zero crossing location depend on slice location. In the 2D case, the imaginary part of the signal is zero because the y-magentization profile is an odd function, and the sum of signal from this is then zero. However, in the 3D selection, the entire slice profile is not summed, but is divided up into slices, and each is summed separately. Experimental data, and corresponding simulations for a 3D VFA experiment with selective excitation (2 ms, truncated Sinc) for TR/T1 = 100/680 are shown in Figure 2.11. The shown curves are for a 16 slice 3D collection with 2.5 cm slab, and a gradient strength of 32  1000  1500  2000  2500  Figure 2.10: T1 maps of a tumour created assuming the ideal FLASH equation (left), and using the B1SP correction (right). T1 s are very different. Slice centre centre+3 centre+7  T1 VFA measurements Non-Selective Selective 560 ± 30 220 ± 30 560 ± 30 500 ± 100 570 ± 30 600 ± 500  FA map Non-Selective Selective 1.118 ± 0.009 1.02 ± 0.01 1.109 ± 0.009 1.13 ± 0.08 1.09 ± 0.01 1.1 ± 0.2  Table 2.3: T1 and FA map measurements are made from VFA data sets with selective and non-selective excitation. T1 measurement errors increase for slices further from the centre of the selected volume. 2800 Hz/cm. The centre slice is slice 8 of 16 slices, centre+1 would indicate slice 7, and so on. T1 and flip angle map values are calculated from both selective and non-selective acquisitions (Table 2.3), assuming the FLASH equation applies. While the T1 measurements with non-selective excitation have relatively constant standard deviations in T1 and FA map values, the values from the data set with selective excitation have much larger standard deviations (in addition to errors).  33  Figure 2.11: Simulations and data are show both real and magnitude data for VFA experiment (3D selective 2ms Sinc excitation with TR/T1 = 100/680). The centre slice is slice 8 of 16 slices, centre+1 indicates slice 7, and so on. No signal null occurs in the magnitude data. All curves displayed are normalized such that the maximum of each curve equals 1.  2.5  Discussion and Conclusions  Errors in FLASH VFA T1 measurements, and B1 mapping due to non-ideal slice selection were found to be significant. T1 is routinely underestimated, and B1 errors are routinely overestimated. For 2D variable flip angle experiments, the zero crossing was not found at 180◦ , but occurred sooner. As T1 weighting increases, the nominal flip angle of the zero crossing decreases further. The B1SP correction method presented here greatly improves T1 and B1 measurements. It has been demonstrated that accurate knowledge of slice rephase gradients is important for accurate simulations. Without the rephase gradient, intravoxel dephasing and signal loss will occur. The optimal rephase gradient will depend on the RF excitation, flip angle, and T1 weighting. At flip angles larger than approximately 70◦ (and depending on T1 weighting), a rephase gradient less than 50% provides a slightly enhanced signal when using a 1 ms Hermite excitation. However, the simulations required for the method presented here should reflect the pulse sequence used for data collection. For the scanner and pulse sequence used here, 34  a 50% refocussing gradient is always used. This is the standard setting on the 7 T Bruker Biospec 70/30. The simulations performed here do not suggest that deviating from a standard 50% rephase gradient would be beneficial when using a standard hermite pulse, due to large dependence on T1 and flip angle. The T1 and B1 measurement method presented here is advantageous over a 3D method with no slab select gradient because there is no concern about wrapping in the slice select direction, allowing more freedom in choosing geometry and orientation. The lookup table approach employed here is necessary, because the simulations are not easily invertible, are computationally costly, and the observed zero-crossing location is altered by both T1 and by B1 errors. Data and simulations show that a 3D VFA experiment used in place of a 2D multi-slice equivalent does not avoid gross T1 errors, mainly due to inhomogeneous excitation in large parts of the slab. Standard deviations increase towards the outer slices of the 3D selective VFA data. These outer slices are also furthest from the receive coil, and this may be an additional source of noise. Simulations of the Bloch equation taking into account RF excitation profiles may be used to recover T1 . However, the signal magnitude may not be fitted using these simulations because of strong coupling, unless prior knowledge of B1 exists. However, with knowledge of the true signal curve shape, and therefore also the true zero-crossing location, it may be possible to extract the correct T1 and B1 simultaneously, using the real part of the signal. Extension of the B1SP correction method to correct 3D data is left to future work.  35  Chapter 3  Analysis of DCE-MRI Data: Methods, Theory, and Sensitivity Analysis 3.1  Introduction  Dynamic Contrast Enhanced (DCE) MRI is an important tool for in vivo assessment of tumour vasculature. Temporal patterns of contrast enhancement in DCEMRI vary depending on the tumour microenvironment. DCE-MRI data may be analysed in various ways to assess the tumour micro environment. These methods include, but are not limited to, a pharmacokinetic model. In this chapter, analysis tools and methods for interpreting DCE-MRI data are presented and discussed.  3.2 3.2.1  Tools for DCE-MRI Analysis Arterial Input Function  The arterial input function (AIF) refers to the concentration of the contrast agent within the arterial supply to tissue as a function of time [31]. An AIF is necessary for pharmacokintic analysis of DCE-MRI data. The best results are obtained when the AIF is measured concurrently with the DCE-MRI study. However, this was not 36  possible in this work. Instead, the AIF was measured separately, and a population average used. The arterial input function used in this work was measured using 1 dimensional projection phase data [48, 49] of the tail of a mouse. While traditional methods derive concentration from magnitude data, phase varies linearly with gadolinium concentration (with slope rφ ), is independent of blood hematocrit, and errors due to T2 * will not occur. Further, the use of projection data allows for high time resolution in the collection. This method requires one 2D image acquired prior to contrast agent injection, and a series of 1D projections before, during and after the injection. The 2D image is required to remove signal in the projection image from tissue surrounding the vessel. A region of interest is drawn around the vessel, and the image outside the ROI is projected in the same direction as the projection images are obtained. This 1D projection is then subtracted from the projection time series, leaving only signal changes in the vessel: Svessel eiφvessel = S pro j (t) − Stissue eiφtissue .  (3.1)  The total phase phase from the contrast agent is then the initial phase (from the baseline images), φ0 , plus the change in phase due to the conctrast agent concentration [Gd] and calibration factor rφ : φ = rφ [Gd] + φ0 .  (3.2)  We assumed the calibration factor rφ = 1.20 ± 0.01 rad/mM (found for a TE of 5.399 ms [48]), may be scaled with changing TE, assuming rφ /T E = constant Data was collected using 7T Bruker Biospec 70/30 MRI system using a custom tail coil. To calibrate the phase-contrast agent relationship, 1-D Projection and 2D FLASH images were collected on a phantom for several phantoms containing concentrations of contrast agent between 2 and 10 mM. Phase information was determined directly from the free induction decay (FID) and unwrapped where appropriate. AIF experiments were projection images, and 2D FLASH images (TE/TR =  37  Figure 3.1: The apparatus with the custom saddle coil for the mouse tail is shown. 6.86 ms / 100 ms, 1x1 cm2 FOV, 256x1 and 256x256 matrix sizes respectively). Phase information was determined directly from the free induction decay (FID) and unwrapped ±2π radians at discontinuities. To use the AIF as an input to DCE-MRI models, a curve was fit to the AIFapproximating the analytical form as a triple exponential modulated by a sigmoid function, plus a Gaussian are summed: β1 −(t−τ1 )2 /(2σ 2 ) A1 e−a1t + A2 ea2t + A3 ea3t e + AIF(t) = √ 1 + e−b(t−t1 ) 2πσ  (3.3)  where β = 5.0 mM·s, σ = 3.0 s, τ = 12 s, A1 = 2.4 mM, a1 = 0.05 s−1 A2 = 0.7972 mM, a2 = 0.0036 s−1 , A3 = 0.1981 mM, a3 = 0.0008 s−1 , b = 0.4448 s−1 , t1 = 9.0 s. The AIF with its best fit line is shown in Figure 3.2 . To demonstrate how each part of the fit curve affects the fit, the curve is plotted along with each of its components in Figure 3.3  38  AIF 2.5 data fit  Contrast Concentration, mM  2  1.5  1  0.5  0  20  40  60  80 100 time, seconds  120  140  160  Figure 3.2: The AIF data is shown, with the best fit line. AIF fit curve, split into components  2  1st exp 2nd exp 3rd exp Gaussian AIF fit curve  1.8  Contrast Concentration, mM  1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0  10  20  30  40  50 60 70 time, seconds  80  90  100  110  120  Figure 3.3: To demonstrate how each part of the fit curve affects the fit, the curve is plotted along with each of its components.  3.3 3.3.1  Model-Free Analysis of DCE-MRI Data Bolus Arrival Time and Identification of T2 * Artefacts: a Novel Method Employing Control Chart Decision Criteria Student Version of MATLAB  The Bolus Arrival Time (BAT) is the time at which the contrast agent arrives at a location in the tumour following injection, and signal enhancement begins. In 39  any DCE-MRI data set, a number of scans will be collected before injection of the bolus of contrast agent. It is necessary to find the point in the dataset where the bolus arrival occurs for pharmacokinetic modelling of the data. This must be performed voxel-wise, as it should not be assumed that the contrast agent arrives in all areas of the tumour simultaneously. The BAT may be found by searching for the first enhancing time point in a contrast agent concentration time curve. In this work, this is done on a pixel by pixel basis. Changes from the mean concentration are found using a control chart decision criteria. The control chart, also known as Shewhart charts, was invented by Walter Shewhart as a means to determine if a process fails to remain under a state of control [50]. In this work, control charts are used to detect the time at which there is a change in contrast agent concentration from baseline, following the administration of a contrast agent. The decision criteria used here were based on the Western Electric decision rules [51] from MATLAB’s statistical toolbox (MATLABTM R2009a, The MathWorks Inc.). A change from baseline is detected when: 1. any given point falls outside of 3σ from the centre line (the average baseline concentration) 2. two out of three consecutive points fall outside of the 2σ limit on the same side of the centre line 3. four out of five consecutive points fall outside of the 1σ line, on the same side of the centre line 4. eight consecutive points all fall on one side of the centre line If the time series of a voxel did not meet the decision criteria indicating a change, it was deemed non-enhancing. Because the number of baseline scans in a DCEMRI data set was typically around 28, and the mean and standard deviation are sometimes unreliable, it was necessary to take extra measures to exclude erroneous choices of BAT. First, if the average contrast agent time curve for the whole tumour was viewed, and the onset point manually chosen, in order to ensure onset is never chosen more than two time points before this. Second, in order to eliminate erroneous choices, it was required that three time points in a row fail. These 40  three points must all indicate positive enhancement or all three indicate negative enhancement. Following the BAT, it is confirmed that ≥ 50% of the subsequent data points fall above the mean+3σ bound. Otherwise, the point is deemed non-enhancing. In voxels where the change indicated a negative gadolinium concentration, it was assumed that this is a T2 * effect, and timepoints in the concentration time curve are set to NAN until the third timepoint following the first positive enhancing point. These points will be inappropriate for modelling or IAUC60 calculation, however, after T2 * effecst have subsided, the data should not be disregarded. In all cases, the point prior to the first point of the consecutive set of points which indicates a change from the mean is taken as the BAT. Should more than one of the decision rules be violated, the one indicating the earliest BAT is chosen.  Concentration of Contrast Agent, mM  Control Chart Data Violation Center LCL/UCL  0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 −0.1  0  10  20  30  40 Scan Number  50  60  70  80  Figure 3.4: Time points in a contrast agent concentration time curve which deviate from the baseline condition are identified with a Control Chart To illustrate this method, an example is shown in Figure 3.4. In this example, the bolus arrival is found to occur at scan number 30. At 31, the change is identified by rule 1. At 32, rules 1 and 2 are met. By rule 1 being met at point 31, the previous point is then taken as the BAT. The centre (mean) line, and upper and lower control limits (±3σ ) are drawn for reference.  41  3.3.2  Initial Area Under the Curve  Initial area under the concentration time curve (IAUC) measures the uptake of the contrast agent in the first seconds following the bolus arrival. In this work, the initial area under the concentration time curve for 60 seconds following the bolus arrival (IAUC60) is calculated using a trapezoidal integration approximation, summing over the 60 seconds following the bolus arrival time. This calculation is performed pixel-by-pixel to create a parameter map.  3.4  Pharmacokinetic Modelling of the Contrast Bolus  Pharmacokinetic modelling has been recommended for the evaluation of antivascular and antiangiogenic compounds (anti-cancer drugs) [17, 18], and to evaluate treatment response in oncology [17, 19]. This section discusses various models which may be used to this end.  3.4.1  Two Compartment Exchange Model  The two compartment exchange model (2CXM) is a general tracer kinetic model which includes two spaces which the contrast agent may move between: the plasma space, and the extravascular extracellular space (EES), with volume fractions v p and ve respectively (Figure 1.1). ve and v p are fractional volumes with respect to the total volume of interest [17, 21, 22]. The intra-cellular volume is not accessible by the MR contrast agents used in this work, but does contribute to the total volume, and so ve + v p ≤ 1. The exchange of tracer across the barrier between plasma and EES is considered symmetric, and quantified by the permeability surface area product PS [22]. The system has a single inlet and outlet, and is considered to be in a stationary state. Thus the flow of plasmu Fp , in the arterial inlet equals the flow out the venous outlet. The model equations for the 2CXM may be derived from the principle of conservation of tracer mass [22, 52]. The out-flux of a compartment is proportional to the average concentration inside that compartment. This provides the venous outlet = FpCp , the plasma to EES flux = PSCp , and the EES to plasma flux = PSCe . Here we define the concentration in the feeding artery (also referred to as the AIF), as Ca , and thus tracer influx = FpCa . Applying conservation of mass provides us a 42  system of two equations for our two compartment exchange model: v pCp (t) = FpCa + PSCe − (Fp + PS)Cp  (3.4)  veCe (t) = PSCp − PSCe  (3.5)  where the parameter limits are: 0 ≤ Fp ≤ ∞ 0 ≤ PS ≤ ∞ 0 ≤ vp ≤ 1  (3.6)  0 ≤ ve ≤ 1 v p + ve ≤ 1 The total tissue concentration C(t) is defined as [22] C(t) = v pCp (t) + veCe (t)  (3.7)  and the initial condition for this model is C(t = 0) = 0, as t = 0 is taken as the time before tracer injection. The total concentration in tissue is related to the input Ca (t) by a convolution with the impulse response function (IRF) I(t) [22, 52]: C(t) = I(t) ∗Ca (t)  (3.8)  where ”∗” denotes the convolution.  3.4.2  Solutions to 2CXM  The 2CXM may be solved in the general, or in limiting cases. Here, the general 2CXM is solved, and then three special cases are discussed: the Tofts model, the modified (or extended) Tofts model, and the uptake model are presented. The Tofts model is frequently used for characterization of tumours, though authors do not necessarily use the same notation [18, 21–25].  43  General Solution to the 2CXM The IRF of the 2CXM is a bi-exponential function [22] I(t) = F+ eK+ + F− eK−  (3.9)  The expressions for F± and K± are well known [22, 53–56]: Fp (v p + ve )τ∓ τ± − 1 F± = ±Fp τ+ − τ−  K± =  (3.10) (3.11)  where the two parameters τ± are given by τ± =  E − Ee + e 2E  1±  1−4  Ee(1 − E)(1 − e) (E − Ee + e)2  (3.12)  e is the extravascular fraction of the extracellular volume: e=  ve ve + v p  (3.13)  E=  PS PS + Fp  (3.14)  and E, is the extraction fraction:  The parameters PS, Fp , ve , and v p may be obtained from parameters F± and K±  44  by: τ− =  F+ F− +1 F+ k+ F− + k−  (3.15)  k+ k− τ+ − τ− Fp = F+ (τ+ − 1) τ+ + τ− − 1 − τ+ τ− E= (τ+ + τ− )(τ+ + τ− − 1) − τ+ τ− τ+ + τ− − 1 − τ+ ∗ τ− e= τ+ + τ− − 1 Fp (v p + ve ) = k+ τ− τ+ = τ−  ve = e(v p + ve )  (3.16) (3.17) (3.18) (3.19) (3.20) (3.21)  v p = (v p + ve ) − ve Fp E PS = (1 − E)  (3.22) (3.23)  Tofts and Modified Tofts model The Tofts model (TM) [25] is given by: C(t) = K transCp ∗ e−K  trans t/v  (3.24)  e  where Cp is given by the AIF, C(t) is the total concentration in the voxel, Ktrans is the volume transfer coefficient, and ve and v p EES and plasma factions, as previously defined. The extended Tofts Model (ETM) has an additional ad hoc term for the intravascular component of the concentration: C(t) = v pCp + K transCp ∗ e−K  trans t/v  e  (3.25)  These are special cases of the 2CXM, where the impulse response function of  45  the tissue is given by [22]: I(t) = EFp e−t  EFp ve  (3.26)  for the Tofts model, and by [22]: I(t) = EFp e−t  EFp ve  + v p δ (t)  (3.27)  for the extended Tofts model. E in these equations is the extraction fraction, given by [22, 57]: E=  Ca −Cv Ca  (3.28)  Uptake Model The uptake model is the special case where leakage into the EES space is very slow, and therefore Ce << Cp , and PSCe → 0. Equations 3.5 reduce to: v pCp = FpCa − (Fp + PS)Cp  (3.29)  veCe = PSCp  (3.30) (3.31)  The resulting residue function is [53, 58, 59]: R(t) = e−t/Tp + E(1 − e−t/Tp )  (3.32)  The model is fully defined by parameters exchange fraction E: E=  PS , PS + Fp  (3.33)  flow Fp , and plasma transit time, Tp (the mean time the contrast agent spends in the plasma compartment). PS and v p may calculated [53]: EFp 1−E Tp Fp vp = 1−E  PS =  46  (3.34) (3.35)  and ve is not found in this model. E is the same as for the general solution. The mean transit times for each compartment are [53]: vp PS + Fp ve TE = PS vp TB = Fp Tp =  (3.36) (3.37) (3.38)  where TB is the mean transit time for an intravascular tracer.  3.4.3  Methods of Comparing Models  When comparing how well different models fit the given dataset, one must discriminate whether one mechanism or another better interprets the data. Sum squared error (SSE) may be insufficient for such a comparison. A more complicated model will usually fit the data better, simply because it has more inflection points, however, this does not necessarily mean that it is a better interpretation of the data [5]. Statistical means of comparing the models is necessary. When one model is a simpler case of a second model, these models are referred to as nested. In the case of using nested models, an F test is sufficient. An F test is based on hypothesis testing. However, the F test is invalid when models are not nested. Instead, the Akaiki information criterion (AIC) [38] may be used to compare two nested or non-nested models [5, 39]. The AIC was first described by Akaiki in 1974. The AIC is based on information theory (rather than hypothesis testing). This method may be used when fitting the exact same data (with identical weighting) with two different models [5]. Since hypothesis testing is not used, the AIC cannot be used to say that one model is ”significantly” better, or that a model should be ”rejected”. However, one can calculate the likelihood ratio of one model representing the data better than another (Equation3.41 ). If it may be assumed that the scatter of points around the curve follow a Gaussian distribution, the AIC may be computed by: AIC = N · ln(SS/N) + 2K  47  (3.39)  where N is the number of data points, SS is the residual sum of squares, and K is the number of parameters in the model plus one. When N is small compared to K, the second order (corrected) AIC should be used: AICc = AIC +  2K(K + 1) . N −K −1  (3.40)  It is recommended that the corrected value is always calculated [5], since the correction term will go approach zero when it is unnecessary. In this work it may be assumed that this is done. The model with the lower AICc score is the more appropriate model relative to other considered models. Note that only absolute difference in AIC matters (not relative difference). If units were chosen differently, the SS would be different, and the AIC would change accordingly. If the AIC values are quite similar, the probability that the best model (the model with the lowest AIC score) is chosen is calculated by [5]: P=  e−0.5∆ 1 + e−0.5∆  (3.41)  where delta is the difference between AICc values (∆ = AICc,A − AICc,B , where model B has the lower AIC score). This probability, however, only indicates the probability that this model is best relative to the alternatively considered model, and does not provide any indication that another model may or may not be more appropriate.  3.5  Sensitivity Analysis: Model Sensitivity to Accuracy of Contrast Agent Concentration Scaling  In order to asses the use of different models, and their limitations, a DCE-MRI data set was analysed with both the Modified Tofts, and general 2CXM models. Parameter maps are created. The results are compared using the AIC to determine the best model for the data set. To asses how errors in contrast agent concentration might affect the results, the pharmacokinetic modelling is performed with the original calculated concentration, double that concentration, and half that concentration.  48  3.5.1  Methods  DCE-MRI data was obtained on a 7 T Bruker Biospec 70/30 using a combination of volume (Tx) / surface (Rx) coil. DCE-MRI data was collected at 2.24 s time resolution (FLASH; TR/TE = 35/2.75; FA = 40; NR = 1200). T1 and DCE-MRI experiments are single slice, with 0.33 mm x 0.33 mm x 1 mm resolution. A precontrast T1 measurement, and flip angle map were performed using a single slice FLASH variable flip angle experiment (FLASH TR/TE = 500/2.75, FA = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 215) and data is fit with the method described in Chapter 2.  3.5.2  Results  By calculating the AIC, and using equation 3.41, the probability that the general 2CXM model is more appropriate than the extended Tofts model is found. For 90% of voxels within the tumour ROI, the probability than 2CXM is the better model is greater than 95%. For 89% of voxels, the probability that the general 2CXM is best is 1. Based on these results, the sensitivity analysis is only presented for the general 2CXM model. If concentration is changed by a factor, the resulting 2CXM fit parameters Fp , PS, ve and v p all scale by that same factor, as can be seen in Figure 3.6. This relationship is maintained for fits resulting in ve and v p fractions greater than 1.  3.5.3  Discussion and Conclusions  Scaling of tissue concentrations, or in the AIF concentration, results in 2CXM model parameters scaling equally. This relationship continues to scale ve and v p to values greater than 1. This suggests that flow and permeability measurements resulting from a successful fit should not be disregarded on the basis of ve , v p , or their sum being greater than 1. Further, this emphasized the need for an AIF to be obtained concurrent with any DCE-MRI study. Significantly different parameter values between scans, or subjects may be obtained on the basis of a poorly guessed AIF. Results of the sensitivity analysis suggest that either the concentration in tissue is over-estimated, or the AIF concentration is under-estimated. It has been 49  Figure 3.5: Parameters of the 2CXM model are found to be sensitive to scaling of the concentration curves. Units of Fp and PS are s−1 ; ve and v p are fractions and have no units. previously demonstrated that contrast agent relaxivity depends on the presence of macromolecules [35, 36]. The relaxivity used in this study to convert change in signal to contrast agent concentration was measured in saline. Concentration errors may also be due to errors in baseline T1 measurements. Despite the suggestion that there is an error in the scaling of concentration values, model parameters are still useful. The ratio of a parameter in one voxel relative to another voxel in the same tumour is accurate, and the ratio of any two parameters in the same voxel should be independent of scaling errors.  50  ve  vp vp found with adjusted [Gd]  2.5  2  1.5  1  0.5  e  v found with adjusted [Gd]  2.5  [Gd] X 2 [Gd] X 0.5 y = 2x y = 0.5x  0  0  0.2  0.4  0.6  ve  0.8  1  1.2  2  1.5  1  0.5  0  1.4  [Gd] X 2 [Gd] X 0.5 y = 2x y = 0.5x  0  0.2  0.4  0.6  PS found with adjusted [Gd]  0.01  0.005  0  0  0.002  0.004  Fp  1  1.2  PS  [Gd] X 2 [Gd] X 0.5 y = 2x y = 0.5x  p  F found with adjusted [Gd]  Fp 0.02  0.015  0.8  vp  0.006  0.008  0.014 0.012 0.01 0.008 0.006 0.004 0.002 0  0.01  [Gd] X 2 [Gd] X 0.5 y = 2x y = 0.5x  0  1  2  3  4  PS  5  6  7 −3  x 10  Figure 3.6: Parameters of the 2CXM model found when concentration is purposefully scaled are compared to the values found with the original calculation. Units of Fp and PS are s−1 ; ve and v p are fractions and have no units. The grey background indicates the location of the ROI.  51  Chapter 4  Characterization of New High Molecular Weight Contrast Agent via MRI and Histology 4.1  Introduction  The vascular network in tumour tissue is highly disordered, and is characteristically highly permeable relative to blood vessels in normal tissue. Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) may be used to non-noninvasively assess tumour vasculature [8, 9, 11, 15, 20]. Pharmacokinetic modelling of contrast agent uptake can provide information about blood flow and vessel permeability, but many models do not have the ability to separate the two, due to the ability of typical contrast agents such as Gd-DTPA to extravasate and accumulate in tumour tissue. A contrast agent which remains intra-vascular, or leaks very slowly could provide a means to measure blood flow in tumours. Measuring both high and low molecular weight contrast agent uptake may allow information which was not previously available to be extracted. In this work, a novel high molecular weight (HMW) contrast agent comprised of hyper-branched polyglycerol (HPG) molecules [1, 26] doubly labelled with gadolinium and a fluorescent marker (HPG-GdF) is investigated for this purpose.  52  By having both gadolinium and fluorescent markers, HPG-GdF uptake may be assessed with conventional DCE-MRI methods, and distribution may be confirmed with histology. Preliminary investigations with small numbers demonstrated that the agent remains intra-vascular for sufficient time that assumptions regarding the kinetics of the tracer may be made, and that the agent accumulates in the tumour over days [1, 2]. In this Chapter, distributions of HPG-GdF relative to vasculature are measured with histological methods, and larger groups. Retention of the agent in tumour tissue over days is assessed with daily T1 measurements. DCE-MRI experiments are performed with two different agents in the same tumour 24 hours apart to investigate the utility of a high molecular weight agent in conjunction with a low molecular weight agent. HT29 human colorectal xenografts were chosen for both this work, and pilot studies. This tumour line was chosen because it is known within our lab to have highly permeable blood vessels (e.g. [60]).  4.1.1  High Molecular Weight Agents in Literature  The use of high molecular weight agents in DCE-MRI is not novel, though it has not gained the attention of DCE-MRI with conventional low molecular weight agents. A number of of high molecular weight gadolinium based contrast agents have been discussed in literature. These agents are generally comprised of Gadolinium chelates attached to a larger molecule. For example, albumin complexes, MS325 (Gd chelates with reversible binding to blood albumin), Dextran-(gadoliniumDTPA) complexes, liposomes, or dendrimers [61]. Albumin-(Gd-DTPA) was first synthesized in 1987 [62], and was one of the earliest macromolecular agents. These complexes have an average molecular weight of 92 kDa and diameter of ∼6 nm [61]. Albumin is a vascular protein responsible for maintaining osmotic pressure within blood vessels [61]. Albumin based contrast agents have the problem of prolonged retention [61, 63]. Retention of Gadolinium carries toxicity concerns, and limits the use of this agent. MS-325 complexes are Gd-chelates with reversible binding to blood albumin [64, 65]. This agent reduces the retention problems experienced when using Albumin complexes [61]. These agents are injected in the free form (∼957 Da), and  53  bind to blood albumin (∼67 kDa), but may then be released and cleared from the body. However, binding may be incomplete, and results in an unknown distribution of free and bound MS-325. The binding also varies between species. Dextrans are polymers of glucose molecules, are inexpensive, and their safety is established - they are used as a synthetic plasma expander. Dextrans are typically 75 kDa, but range in size and shape complicates permeability estimates and provides inconsistent results [61]. Dendrimers are highly branched synthetically produced spherical polymers. They have a well defined structure, and can be produced to specific physical size in a consistent and reproducible manner. A number of groups have used high molecular weight agents for DCE-MRI. with varying success. One noteable flaw in some previous research is the use of the Tofts or extended Tofts model [25], in cases where it may not be valid. Henderson et. al. [66] used a dual contrast protocol (Gd-DTPA 0.6 kDa, and Gadomer17, 17 kDa) in pet dogs with spontaneous mammary tumours. They observed flow measurements which corresponded well with literature, and that permeability measurements were lower in HMW case. Feng et. al. [67] and Wu et. al. [68] investigated biodegradable high molecular weight agents using DCE-MRI in tumour models. They found high molecular weight agents effective for evaluating tumour angiogenesis with DCE-MRI. In both papers, the extended Tofts model was used for pharmacokinetic modelling of DCE-MRI data. The Tofts and extended Tofts model must be used with care when using a high molecular weight agent. If the image DCE-MRI series is too short, and the concentration of the agent in tumour tissue has not yet peaked, the assumptions made in these models are no longer valid, and an uptake model would be more appropriate. Extravasation of high molecular weight agents is investigated in cancer research, without MR imaging. For example, Dreher et. al. [69] investigated high molecular weight dextrans covalently linked to a fluorophore, in tumours. Distribution of the dextrans in tumour tissue was observed via a dorsal skin fold window chamber. They found that increasing molecular weights from 3.3 kDa to 2 MDa resulted a statistically significant reduction in vascular permeability by approximately two orders of magnitude. They reported heightened accumulation in solid tumours with concentrations highest near vasculature. Tumours may passively ac54  cumulate large molecules due to increased permeability of blood vessels, and a poorly developed lymphatic drainage [69]. The phenomenon of accumulation of larger molecule in tumours has been described as the enhanced permeability and retention effect EPR [6, 7].  4.1.2  A Novel High Molecular Weight Contrast Agent  This work investigates a new high molecular weight contrast agent: hyperbranched polyglycerol (HPG) molecules doubly labelled with Gd-DOTA, and a fluorescent marker. HPG molecules are recently described globular molecules with low polydispersity [1, 26]. HPG molecules are asymmetrical and highly biocompatible [70–73]. HPG has been previously tested as a human serum substitute [74] and as a drug delivery vehicle [1]. Due to the globular structure of HPG molecules, they are less viscous in solution than linear polymers. HPG was derivatized with p-NH2-benzyl-DOTA (Macrocyclics) and tagged with Alexa Fluor 647 (Invitrogen Life Technologies) in the Faculty of Pharmaceutical Sciences at UBC [1]. The resulting HPG molecule modified with Gadolinium and fluorescent marker (HPG-GdF) contained 20 µg Gd per mg HPG. Each HPGGdF molecule has approximately 300 Gd-DOTA chelates. The 448 kDa molecules are large in comparison to standard clinical contrast agents. For example, Bayer Healthcare’s Gadovist is reported as 607 Da. Dual labelling of this agent allows for histological analysis of HPG-GdF distribution following MRI studies.  4.1.3  Pilot MRI and Histology Studies  Prior to the work presented here, pilot studies investigating HPG-GdF were performed by the author and collaborators investigating HPG-GdF with MRI and histological methods using HT29 tumour bearing mice [1, 2]. It was found that HPGGdF accumulates in tumours, peaking between 1 hour and 6 days post-injection, followed by a decline. Comparing to the commercially available Glowing Galbumin (Gd-Albumin, BioPAL), HPG-GdF was found to have a greater impact on signal intensity in tumour tissue, and stronger fluorescence in histology. Histological data showing the distribution of HPG-GdF fluorescence relative to blood vessels comparing 2 minutes exposure to 60 minutes, 7 days and 15 days showed that the  55  agent stayed in or very close to blood vessels over the first few minutes following injection, and travelled further over time. Both MR and histology showed heterogeneous distribution of the agent on the time scale of a DCE-MRI study. The number of subjects in these investigations is too small to draw firm conclusions. However, these findings provided motivation for study presented here.  4.1.4  Modelling Tracer Kinetics: Considerations  When performing pharmacokinetic analysis, it is necessary to ensure that the assumptions made in the given model are appropriate for the tissue being modelled, and for the time resolution and quality of the data to be modelled. These issues have been addressed in literature (e.g. References [17, 22, 37]). The popular Tofts and modified Tofts [25] pharmacokinetic models may make poor or incorrect assumptions about the tissue, and are often not objectively chosen. In particular, the Tofts model parameters may be interpreted many different ways depending on the assumptions which may be made regarding the tissue in question [22]. These issues are further confounded by the heterogeneous nature of the tumour microenvironment, which may result in different assumptions applying to different areas within the same tumour It has recently been suggested that analysis should be performed with a set of models with increasing complexity and the Akaiki information criterion (AIC) [38] may be used to determine the most appropriate model [22]. A more complicated model will usually result in an improved fit, simply because it has more inflection points. However, this does not necessarily indicate a better interpretation of the data [5]. The AIC provides a means of distinguishing an improved fit, taking into account the differences in model complexity. In this study, assumptions which may be made about the tissue and nature of the contrast agent were considered in choosing appropriate pharmacokinetic models for interpretation of DCE-MRI data. An uptake model was chosen for analysis of high molecular weight concentration curves, since the agent is expect to extravasate slowly. Data acquired using a low molecular weight contrast agent was analyzed with a three parameter (with the same form as the extended Tofts model), and a four parameter model (the general two compartment exchange model [22]), and  56  the AIC is used to determine the most appropriate model.  4.2  Methods  4.2.1  Relaxivity  Relaxivity is the ability of the contrast agent (CA) to change the R1 relaxation rate of surrounding water protons: ∆R1 =  1 1 − = r1 [CA] T1 T10  (4.1)  where r1 is the relaxivity. The T1 of HPG-GdF solutions were measured in a buffer solution at concentrations ranging from 5 to 20 mg/mL (corresponding to 0.1 to 0.4 mM). Non-imaging inversion recovery experiments were performed on each sample and fit for T1 . Linear regression was performed according to Equation 4.1 to find relaxivity. The T1 of Gadovist solutions were measured in saline solution, at concentrations ranging from 0.1 to 2 mM. Non-imaging inversion recovery experiments were performed on each sample and fit for T1 . Linear regression was performed according to Equation 4.1 to find relaxivity.  4.2.2  Overview of Experiments  Experiments performed in this study were aimed to achieve three goals: I. To assess retention and/or the possibility of accumulation of HPG-GdF in tumour tissue over days. This is achieved by performing T1 measurements on three mice, administering HPG-GdF to each of them, and performing subsequent T1 measurements daily for one week. Average tumour T1 is then compared. The tumours were collected for subsequent histological analysis. II. To assess (with histological methods) the time scale over which HPG-GdF leaks from blood vessels. Three groups of five mice are administered HPGGdF for 5, 20, and 60 minutes exposure. Histological methods are used to assess distribution of HPG-GdF fluorescence relative to vasculature. 57  III. To compare DCE-MRI analysis of HPG-GdF to a standard contrast agent and assess feasibility of using this agent in future studies. Six mice are imaged twice: in the first imaging session DCE-MRI is performed with a standard contrast agent; in the second session, DCE-MRI is performed with HPGGdF. The tumours were collected for subsequent histological analysis.  4.2.3  Apparatus and Protocols  Contrast Agents Two MRI contrast agents were used in this work: HPG doubly labelled with gadolinium and a fluorescent marker (HPG-GdF) (Faculty of Pharmaceutical Sciences, UBC), and Gadovist (Bayer Healthcare). HPG molecules have a mass of 448 kDa and are relatively large compared to Gadovist molecules, which have a mass of 607.4 Da. HPG-GdF contained 20 µg Gd per mg HPG, resulting in approximately 300 Gd-DOTA chelates. HPG was also tagged with Alexa 647 (Invitrogen Life Technologies). HPG-GdF was administered at 6 µL/g bolus i.v. dose at 100 mg/mL (0.2 mM). Gadovist (Bayer Healthcare) was administered as a 5 µL/g bolus i.v. dose at 60 mM. Mice and Tumours Female non obese diabetic/severe combined immuno-deficient (NOD/SCID) mice were used for in vivo experiments. Mice were bred and maintained in-house in accordance with the Canadian Council of Animal Care guidelines. Twenty four NOD/SCID mice were randomly assigned to three groups, and implanted with HT29 human colorectal carcinoma (American Type Culture Collection) xenografts subcutaneously on the sacral (lower back) region. Contrast Agent Injection Procedure Only small quantities of HPG-GdF were available for this study. For this work, an injection protocol was developed for a short bolus where quantities of contrast agent are restricted (Figure 4.1). For these DCE-MRI experiments, the injection is initiated from a power injector, outside the scanner room. This requires a long 58  Figure 4.1: In order to inject a bolus with high concentration and low volume, a series of tubes are connected, containing a dead volume, the contrast agent, and the saline flush. line of fluid, connecting the power injector to the IV line containing the contrast agent bolus. A butterfly needle is inserted into the tail vein when the mouse is prepared for the MR scan. This is attached to a short length of tube containing approximately 40 µL of heparin dilute in saline (heparin is an anti-coagulant), providing dead volume between the contrast agent and the subject. This line is then connected to a length of polyethylene tubing containing the contrast agent. The length of this tube is customized for each subject, to deliver the correct dose of contrast agent. This is followed by a long line of saline which reaches outside of the magnet room, and is attached to a power injector. The total injected volume is then the sum of 40 µL dead volume (heparinized saline), the contrast agent dose, and a 20 µL flush. Preparation of Mice for MR experiments The butterfly needle is inserted into the tail vein while the mouse is awake, using a custom anaesthesia chamber with a slot through which the tail can be held, as shown in Figure 4.2. Once inserted, the needle is secured with fast drying glue, and the mouse is anaesthetized with isofluorane. Mice remained anaesthetized throughout imaging. Mice are given approximately 0.5 mL of saline subcutaneously for hydration, 59  Figure 4.2: Custom chamber used for anaesthetizing mice while allowing access for the tail vein catheter to be inserted and eye lubricant is applied to prevent their eyes from drying during the scan. The anaesthetized mouse is positioned supine on the custom surface coil apparatus. The coil apparatus is fitted with a lid lined by a temperature controlled, water filled heating blanket. Temperature and respiration rate are monitored throughout imaging. Fiducial Markers for Correlation of MR and Histology In order to ensure reproducible orientation of MR images relative to tumour, and ensure orientation of histological tumour sections are along the same axis, a marker is required. While anatomical landmarks may sometimes be used for repeat MR imaging, positioning of the mouse and tumour growth over time may make this difficult to accomplish. Further, this will not ensure that the tumour may be frozen and sectioned in the same orientation. In order to correlate histological results with MR images, data must be acquired with the same (or as close as possible orientation). We use an implantable fiducial marker to achieve this. These methods have previously been described by Bains et. al. [75, 76], however, I will summarize the methods here. The markers are constructed from plastic tubing, approximately 1 mm in diameter, saline, and wax. The tubing is filled with saline, followed by the injection of molten paraffin wax. The ends of the tube are then cut to approximately 2 cm in length, and the ends are sealed. In addition to providing an axial orientation marker, the saline-paraffin interface is visible on MR images (Figure 4.3(b)) for through plane orientation. However, it was noted that the marker sometimes slides once the tumour is excised, so this interface may not be used reliably in sectioning for through plane orientation. Both MR images and histological sections are taken 60  perpendicular to the markers. The markers were implanted in a cranial-caudal orientation two days prior to tumour implantation. The tumours grow around, or next to the marker. Because of the fixed nature of an implanted marker (versus an external marker, glued or taped to the mouse), the MR images may be taken in the same orientation during each session, and errors in the angle relative to the marker at which tumours are sectioned may be minimized.  Figure 4.3: Fiducial markers are used for orientation. The marker is shown in the axial imaging plane (a). In the coronal plane (b), the wax/saline interface can be seen. The position of the marker can also be seen in histology images (c)  4.2.4  Experiments  All experiments followed a protocol approved by the UBC Committee on animal care. Groups Twenty four NOD/SCID HT29 tumour bearing mice were randomly assigned to three groups. These groups correspond to the goals of this study, as described in Section 4.2.2. Groups are summarized in Table 4.1. Group I (three mice) subjects were imaged on day 0 using a DCE-MRI protocol with HPG, and were subsequently imaged over one week for the purpose of observing retention of HPG. Each mouse received a 6 µL per gram dose of HPG for imaging. On subsequent days, the mice were re-imaged to obtain a T1 measurement, for the purpose of tracking retention of HPG-GdF over one week. T1 maps were computed. ROI averaged T1 is for each subject was found, and the group 61  Table 4.1: Summary of Experiments and Groups Group I II(a) II(b) II(c) III  Tumour line HT29 HT29 HT29 HT29 HT29  N 3 5 5 5 6  Study Description HPG-GdF retention study Extravasation study, 5 min; No MRI Extravasation study, 20 min; No MRI Extravasation study, 60 min; No MRI DCE-MRI with Gadovist on D0; HPG-GdF on D1  average on each day was compared. All tumours were collected and frozen following the final scan, without waking from anaesthesia. Mice were administered Carbocyanine following the final scan, 5 minutes prior to euthanasia. Group II (15 mice in three groups of five) were not imaged with MR, but received a 6 µL per gram dose of HPG, and were euthanized at 5, 20, or 60 minutes, and tumours collected for histological analysis to assess extravastion of HPG at each time point. All tumours were collected and frozen following the final scan, without waking from anaesthesia. A sixteenth mouse received no HPG, but the tumour was collected and sections were imaged for native fluorescence to assess background levels. All mice, except the 5 minute group, were administered carbocyanine (perfusion marker), 5 minutes prior to euthanasia. Histological sections were analysed for distribution of HPG relative to blood vessels, relative to perfused blood vessels, and total tumour uptake. Histological data from Group I was also compared. Data from Group III was added to the mice euthanized at 60 minutes. Groups III (six mice) were imaged in two sessions 24-48 hours apart using a DCE-MRI protocol. The first imaging day, the low molecular weight contrast agent, Gadovist, was used (5 µL per gram dose). On the second day, the high molecular weight contrast agent, HPG-GdF, was used (6 µL per gram dose). All tumours were collected and frozen following the final scan (60-70 minutes postinjection of HPG), without waking from anaesthesia.  4.2.5  Magnetic Resonance Imaging  All MRI experiments were performed at the UBC MRI Research Centre on a 7 T Bruker Biospec 70/30 scanner at room temperature with a combination of volume (Tx) / surface (Rx) coil. 62  Group I: Retention of HPG During the first scanning session, T1 mapping and flip angle mapping was performed, followed by a DCE-MRI experiment using HPG-GdF as the contrast agent, and repeated T1 measurement. Each imaging session began with axial RARE T2-weighted images for morphological reference and orientation. T1 measurements, and flip angle mapping were performed using a multi-slice FLASH variable flip angle experiment (FLASH; TR/TE = 500/2.75, FA = 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ , 70◦ , 80◦ , 90◦ , 100◦ , 110◦ , 120◦ , 130◦ , 140◦ , 150◦ , 160◦ , 170◦ , 180◦ , 190◦ , 200◦ , 215◦ ) and data was fit with the method described in Chapter 2. DCE-MRI data was collected at 2.24 s time resolution (FLASH; TR/TE = 35/2.75; FA = 40◦ ; NR = 1200). T1 and DCE-MRI experiments all have identical geometry (Matrix = 128 x 64 x 3; voxel size = 0.33 mm x 0.297 mm x 1.5 mm; 2.5 mm slice separation). A follow-up T1 measurement was performed (FLASH; TR/TE = 35/2.75; FA = 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ , 80◦ , 100◦ , 120◦ ), where the flip angle map was assumed to be the same as the pre-contrast measurement. All images were oriented perpendicular to their fiducial marker. The variable flip angle experiment for T1 measurement and flip angle map was repeated daily for seven days post-injection (with day 6 skipped). On each imaging day, slice location and orientation is adjusted to best match previous days. Group II: Extravasation Group II received no MR imaging. Tumours were collected for histological analysis only. Group III: DCE-MRI Subjects were imaged in two sessions (24-48 hours apart), with identical protocols, but different contrast agents: Gadovist during the first session, HPG-GdF in the second. The protocol is very similar to that of Group I, but is single slice (instead of three slices). Each imaging session included axial RARE T2-weighted images for morphological reference and orientation. T1 measurements, and flip angle mapping were performed using a single slice FLASH variable flip angle experi63  ment (FLASH TR/TE = 500/2.75, FA = 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ , 70◦ , 80◦ , 90◦ , 100◦ , 110◦ , 120◦ , 130◦ , 140◦ , 150◦ , 160◦ , 170◦ , 180◦ , 190◦ , 200◦ , 215◦ , Matrix = 128 x 64) and data was fit with the method described in Chapter 2. DCE-MRI data was collected at 2.24 s time resolution (FLASH; TR/TE = 35/2.75; FA = 40◦ ; NR = 1200). T1 and DCE-MRI experiments were single slice, with 0.33 mm x 0.297 mm x 1.5 mm resolution. A follow-up T1 measurement was performed (FLASH; TR/TE = 35/2.75; FA = 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ , 80◦ , 100◦ , 120◦ ), where the flip angle map was not re-produced. All images were oriented perpendicular to their fiducial marker, and the slice location was adjusted to match on subsequent imaging days.  4.2.6  Imunohistochemistry  Histology was used in this work to identify blood vessels, perfused blood vessels, and HPG-GdF distribution at different time points. Immunohistochemistry and imaging methods were based on those previously reported in Bains et. al. [75]. All MR-imaged tumours were cryosectioned to have histological images that correspond to the MR image. Tumours from subjects who were not imaged with MRI were sectioned at 1 mm and 5 mm depth. Sectioning and Staining Tumours were collected at indicated time points, embedded vertically in optimum cutting temperature (Tissue-TEK) using their fiducial markers for guidance, and immediately frozen. Tumour cryosections were cut with a Cryostar HM560 (Microm International GmbH). Three 20 µm cryosections were collected 1.5 mm (Group III), or 2.5 mm apart (Group I), centred at the depth corresponding with MR imaging, in addition to a fourth section at a 1 mm depth. Tumours from mice without MR imaging were sectioned at 1 mm, and 5 mm depth. Sections were dried, then imaged for carbocyanine (DiOC7 (3)) and HPG-GdF native fluorescence and then fixed in acetone-methanol for 10 min. Sections were subsequently stained and re-imaged for CD31 using fluorescent-tagged antibodies to PECAM/CD31 [77], and for nuclear density using Hoechst 3342 fluorescent nuclear dyes [78].  64  Image Collection and Analysis Whole tumour sections were imaged and digitized, as described by Kyle et. al. [79]. The imaging system included a fluorescence microscope, motorized x-yz robotic stage, monochrome CCD video camera, frame grabber, and Macintosh computer running customized NIH-Image software (NIH 2007 http://rsb.info.nih.gov/nihimage). The microscope focused on the slide with a 10× magnification; the field of view was imaged with the camera; the x-y stage moved the slide, allowing tiling of adjacent fields of view, to image the whole tumour section at 0.75 µm resolution. Images were reduced to 1.5 µm resolution for cropping and analysis. Whole tumour images are then stacked and manually aligned. Hoechst images were used to create cropping masks to identify necrotic and viable tissue areas. The Hoechst image is manually cropped in three sequential steps: first to the tumour boundary; second, artefacts (including folding, tearing, and staining artefacts) were removed from the boundary cropped image; third, necrotic areas were identified and also removed. The set of three cropped images are then used as masks to identify whole tumour, and viable (versus necrotic) tissue. Necrotic tissue areas may be identified by the difference between the second and third image. Positive staining is defined as those pixels with an intensity meeting or exceeding a minimum threshold which is determined to include positive staining and which is several fold greater than background levels. Objects are defined as groups of adjacent positive pixels greater than 5 pixels in size. Background levels are assess by average intensity from a tumour which was imaged, but not stained, and from average intensity in stained tumours in areas where no positive staining is observed. Analysis is performed with custom NIH software [78]. Carbocyanines are fluorescent markers that, when injected intravenously, label mitochondria of vascular and perivascular cells, thereby identifying perfused blood vessels. In these experiments, unless otherwise noted, Carbocyanine was administered five minutes prior to tumour excision as a marker of blood vessel perfusion at the time of excision. In this work, blood vessels are identified by CD31 positive objects. Perfused blood vessels are identified as CD31 objects which are overlapped by a minimum of 20% by Carbocyanine objects. Background and threshold levels are reported it Table 4.2. Figure 4.4 shows a CD31 image overlaid with a  65  Figure 4.4: A high resolution image of carbocyanine fluorescence (blue) is overlaid onto the corresponding CD31 (red) image. Examples of vessels identified as perfused and unperfused are indicated. The scale bar indicates 120 µm.  Figure 4.5: A high resolution image of HPG (cyan) is overlaid onto the corresponding CD31 (red) image. The scale bar indicates 120 µm. carbocyanine image, demonstrating objects identified as perfused and un-perfused blood vessels. HPG extravasation is assessed by examining its location relative to blood vessels, and from perfused blood vessels: pixels from the HPG-GdF fluorescence image are sorted according to distance from CD31 objects, and from CD31 objects positive for Carbocyanine, and their average HPG fluorescence intensity is reported. Blood vessel density is reported using the average distance of tissue from vasculature. An example of colourized overlaid CD31 (red) and HPG (cyan) images is shown in Figure 4.5. Necrotic fraction is calculated by total number of pixels in images removed by necrosis cropping relative to total number of pixels within the tumour boundary in whole tumour images. Total necrotic area is identified by the difference between the image cropped for artefacts and that image cropped for necrosis.  66  Table 4.2: Thresholds for Histology Analysis Stain CD31 Carbocyanine HPG-GdF  4.2.7  Average Background 3.7 1.4 1.04  Threshold for Positive Staining 22 15 N/A  Analysis of MRI Data  Regions of interest (ROI) were drawn on T2-weighted RARE images to select the tumour using ImageJ (NIH). All other analysis of MR data is performed in MATLAB (Mathworks Inc). T1 and flip angle maps were calculated from variable flip angle data, as described in Chapter 2. The method described in Chapter 2 is extended to calculate dynamic T1 values from the DCE-MRI data series. Knowing the flip angle map, signal as a function of T1 may be simulated. The ratio of signal at each time point in the DCE series relative to the average signal from the baseline scans, S/Sbaseline maps to T1 T1 /T1,baseline . Knowing the relaxivity of the contrast agent, this is converted into a concentration time curve. Bolus arrival time maps are created for each data set using the method described in Section 3.3.1. This method also identifies T2 * artefacts. Time points affected by T2 * artefacts are flagged as Not-a-Number (NaN), but the remaining time points are kept for pharmakokinetic analysis. Maps of the initial area under the concentration time curve for 60 seconds (IAUC60) were calculated for each DCE-MRI data set. IAUC60 values for voxels affected by T2 * artefacts are not calculated, as the initial concentration values are unknown. For pharmacokinetic modelling, the time resolution of the concentration time curves was reduced by a factor of 4 due to high noise. Concentration time curves were fit with various models. Model fitting was performed in Matlab using custom software which utilized the Levenberg-Marquard-Fletcher method for solving of non-linear equations [80]. The modified Tofts model, and the two-compartment exchange model were fit to curves for Gadovist data; curves for HPG-GdF were fit using an uptake model (see below in Section 4.2.7 for details and further details  67  of pharmacokinetic modelling, including derivations may be found in Chapter 3 Section 3.4). The Akaiki Information Criterion (AIC) [38] was used to determine the most suitable model for modelling the concentration time curves for the low molecular weight data (see Section 3.4.3 for details). Parameters resulting from modelling are summarized in Table 4.3. Parameter maps are displayed overlaid onto corresponding grey scale RARE T2-weighted images for morphological reference when such images are available. Pharmacokinetic Models Concentration time curves derived from DCE-MRI data from Gadovist were fit with both the three parameter modified Tofts model, and four parameter, general two compartment exchange model (2CXM): Three Parameter Model C(t) = Cp (t) ∗ I(t)  (4.2)  I(t) = v1 δ (t) + v2 ke−kt  (4.3)  C(t) = Cp (t) ∗ I(t)  (4.4)  I(t) = F+ eK+ + F− eK−  (4.5)  where  Four Parameter Model  where  (where ∗ is the convolution, Cp (t) is the AIF, and I(t) is the impulse response function of the tissue) and AIC values are used to determine the most appropriate model. A group averaged AIF was used for this work (Refer to Section 3.2.1 for details). Parameters from the three parameter model may be converted to vascular fraction v p = v1 , EES fraction ve = v2 , and transfer constant Ktrans = kv2 . Parameters from the four parameter model may be converted into flow F p , permeability surface area product PS, volume fractions ve and v p (refer to Section 3.4.2). Due to the intravascular nature of HPG, the models used for Gadovist concentration time curves are inappropriate. HPG concentration time curves are instead  68  Table 4.3: Summary of Pharmacokinetic Parameters Parameter E Fp PS ve vp Tp  Definition PS extraction fraction E = PS+F p plasma flow permeability surface area product (flux from vascular to EES space) extravascular extracellular space fraction plasma space fraction (ve +v p ≤ 1) transit time in plasma space  fit by an uptake model [53, 58, 59]: C(t) = FpCp (t) ∗ I(t)  (4.6)  I(t) = Fp [e−t/Tp + E(1 − e−t/Tp )]  (4.7)  where  where Tp is the plasma transit time (the mean time the contrast agent spends in the plasma compartment), and other parameters are as described above. Further details of pharmacokinetic modelling are included in Chapter 3. Parameter maps are displayed overlaid onto corresponding grey scale axial RARE T2-weighted images for morphological reference.  4.3 4.3.1  Results Relaxivity  Non-imaging inversion recovery was used to measure the R1 relaxation rate of HPG-GdF samples in buffered solution (Figure 4.6, left), and of Gadovist dilute in saline (Figure 4.6, right). Relaxivity of HPG-GdF was measured to be 421 s−1 mM−1 . Relaxivity of Gadovist was found to be 4.9±0.5 s−1 mM−1 . Though the relaxivity of HPG-GdF is many times higher than that of Gadovist, the concentrations of HPG-GdF used were two orders of magnitude lower than that of Gadovist.  69  Relaxivity of HPG−GdF is 422 s−1mM−1  Relaxivity of Gadovist is 4.9 s−1mM−1  25  12  10  20  1/T1 (s−1)  1/T1 (s−1)  8 15  10  6  4 5  0  2  0  0.01  0.02  0.03  0.04  0  0.05  HPG−GdF concentration (mM)  0  0.5  1  1.5  2  Gadovist concentration (mM)  Figure 4.6: Non-imaging inversion recovery was used to measure the R1 relaxation rate of HPG-GdF samples in buffered solution (left), and of Gadovist dilute in saline (right). Relaxivity of HPG was found to be 421 s−1 mM−1 . Relaxivity of Gadovist was found to be 421 s−1 mM−1 .  4.3.2  Agreement of MR and Histology  Heterogeneous uptake of HPG is evident in both MR and histology. The ∆ R1 map (1/s) for subject no. 1 (Group III) is shown in Figure 4.7 with the corresponding HPG fluorescence image. Notice that dark areas in the centre of the tumour are seen in both images, as well as a brighter rim. Also, an upper right lobe has strong HPG fluorescence surrounding it, which corresponds well to bright areas in the ∆ R1 map.  Figure 4.7: ∆ R1 (1/s) (right) and corresponding fluorescence image (left) both show heterogeneous distribution of HPG.  4.3.3  Retention  T1 maps were computed for three mice over one week following exposure to HPGGdF. Regions of interest (ROI) were drawn around tumours, and the tumour av70  erage T1 was calculated from T1 maps. Group averaged T1 values are shown in Figure 4.8. The minimum average T1 in tumours was found to occur 2-3 days after after injection of HPG-GdF. Tumour averaged T1 values do not return to baseline values within the 7 days of follow-up imaging. RARE images from the same time points are shown in Figure 4.9. Enhancement is heterogeneous within the tumour, and continues to change over several days. Changes in T1 following HPG administration 2.5  T1 (s)  2 1.5 1 0.5 0  baseline+40min  +1d  +2d +3d timepoint  +4d  +5d  +7d  Figure 4.8: Retention of HPG-GdF is assessed via T1 . ROI average T1 values were computed at multiple time points, and averaged across all three subjects. T1 decreases in the presence of HPG-GdF, with a minimum at 2-4 days.  Figure 4.9: RARE images from indicated time points show heterogeneous signal enhancement in the tumour following HPG-GdF administration.  4.3.4  Extravasation of HPG-GdF  HPG-GdF native fluoresence images showed heterogeneous distribution of HPG molecules within tumours. HPG-GdF native fluorescence was mapped for whole 71  tumour sections according to distance to nearest CD31 objects and to nearest CD31 objects positive for carbocyanine, as shown in Figure 4.11. HPG molecules traveled further from vessels at longer time points. Little difference was observed from 5 to 20 minutes. The distribution of HPG-GdF fluorescence relative to CD31 objects positive for Carbocyanine showed that HPG-GdF was found closer to vessels which were perfused in the five minutes prior to tumour excision.  Figure 4.10: CD31 (red) and HPG-GdF (cyan) images are used together to map extravasation of HPG-GdF. A full tumour section and zoomed in section are shown. Notice CD31 objects with and without overlapping HPG-GdF. The scale bars indicates 1 cm on the whole tumour section image, and 120 µm on the high resolution image. Location of HPG relative to vasculature  10  12 Signal Intensity, Arbitrary Units  Signal Intensity, Arbitrary Units  12  Location of HPG relative to perfused vasculature  7 days 60 min 20 min 5 min Control  8 6 4 2 0 0  10  7 days 60 min 20 min Control  8 6 4 2 0 0 10 20 30 40 50 Distance from nearest carbo +ve CD31 object (µm)  10 20 30 40 50 Distance from nearest CD31 object (µm)  Figure 4.11: The distribution of HPG-GdF relative to CD31 objects (vessels), and to CD31 objects positive for carbocyanine (perfused vessels). At longer time points, HPG-GdF travels further from vessels.  72  4.3.5  Bolus Arrival Time: Comparing HPG-GdF to Gadovist  Images of BAT for both low and high molecular weight agents are shown in Figure 4.12 with corresponding histology images. Histology masks indicate viable tissue; images of histology sections were cropped to tumour boundaries, and necrotic tissue was removed. Regions of necrosis visually correspond to areas of delayed BAT with low molecular weight, and delayed or non-enhancing regions with the HMW agent.  Figure 4.12: Bolus arrival (indicated in seconds from the beginning of the DCE-MRI series) for HPG-GdF and Gadovist are compared to histology. The scale bar indicates 3 mm. All images are of identical scaling. Each column contains images from the same tumour (subject no. 1-6 of Group III, in order from left to right)  4.3.6  IAUC60  IAUC60 maps were calculated for each subject in Group III for both contrast agents. IAUC60 maps for each of the six tumours in Group III are shown overlaying axial anatomical images in Figure 4.13. Areas of low uptake visually correspond in the paired images. IAUC60 values for HPG-GdF are low relative to IAUC60 values for maps from Gadovist data. IAUC60 images have similar features in paired images, even though IAUC60 values are three orders of magnitude lower for HPG-GdF.  73  Figure 4.13: IAUC60 (mM·min) for HPG-GdF and Gadovist are compared, with each column containing parameter from the same tumour (for Group III subjects no. 1-6 ordered left to right). The scale bar indicates 3 mm. All images are of identical scaling.  4.3.7  DCE-MRI Analysis  Using the AIC, the 2CXM model was found to be most appropriate in 81% ±7% of voxels over the three parameter model. As a result, only results of the 2CXM model are discussed. Parameter maps, and the corresponding R2 goodness of fit maps are presented in Figure 4.14 (Gadovist data). Parameter maps are shown overlaying T2 weighted RARE images for reference. Pharmacokinetic modelling of HPG-GdF data was not successful. The majority of voxels were non-enhancing, and due to relatively low signal enhancement in enhancing pixels, goodness of fit values were unreasonably low. R2 goodness of fit is much lower for modelling of HPG-GdF concentration time curves relative to R2 from modelling Gadovist data (Figure 4.15). Because of poor fitting performance, the resulting parameter maps were disregarded.  4.3.8  Inspecting Concentration Time Curves  Signal enhancement due to Gadovist is much higher relative to enhancement due to HPG-GdF. Typical concentration time curves for single voxels are shown in Figure 4.16 for both HPG-GdF and Gadovist. The concentrations of HPG-GdF are low and the noise level is higher relative to Gadovist. Concentration time curves are shown for subject no. 4 (Group III) as a parameter map in Figure 4.17. Within each concentration time curve map, all curves  74  Figure 4.14: PS (1/s), F p (1/s), ve , and ve parameter maps (and the corresponding R2 goodness of fit) resulting from modelling Gadovist concentration time curves with the general two compartment exchange model (4 parameters) are presented for Group III (subjects no. 1-6, left to right). Images for the same tumour are in columns. The scale bar indicates 3 mm.  Figure 4.15: R2 goodness of fit maps resulting from modelling HPG-GdF concentration curves with the uptake model are presented (Group III). The scale bar indicates 3 mm. Tumours are ordered identically to in Figure 4.14  75  Typical Concentration Curve for Gadovist  −4  5  0.12  x 10  Typical Concentration Curve for HPG  4.5  (b)  0.08  4 3.5  [HPG] (mM)  (a)  [Gadovist] (mM)  0.1  0.06  0.04  3 2.5 2 1.5  0.02  1 0 0.5 −0.02  0  500  1000  1500  2000  0  2500  Time (s)  0  500  1000  1500  2000  2500  Time (s)  Figure 4.16: Typical concentration time curves for single voxels for Gadovist (a) and HPG-GdF (b) are shown. Notice the concentrations of HPGGdF are low relative to Gadovist, and the noise level is higher. Time curves are for single voxels. have identical scaling to ensure relative uptake may be compared between voxels (though HPG-GdF curves are not identically scaled to Gadovist curves). Corresponding parameters maps are shown along side concentration time curves. Non-enhancing regions in the HPG-GdF concentration time curve correspond to poorly/slowly enhancing regions in the Gadovist time curves (Figure 4.17). Different areas of each map show curves with very different shapes. In particular, the curves in the Gadovist plots near the rim peak much sooner than those near the centre.  76  77 (b) HPG-GdF  Figure 4.17: [Gadovist] (a) and [HPG-GdF] (b) time curves (for subject no. 4, Group III) are displayed as a parameter map with the corresponding maps for BAT, model parameters, and corresponding R2 goodness of fit are shown. Within each concentration time curve map, all curves have identical scaling to ensure relative uptake may be compared between voxels.  (a) Gadovist  4.4 4.4.1  Discussion and Conclusions Retention  Serial T1 measurements on Group I showed that HPG-GdF accumulates in in tumours over days, followed by a decrease at 2-4 days. Uncertainty in the time of the peak is due to the heterogeneous distribution of HPG-GdF. Further, the tumours change and grow over time, and thus T1 may change. A region of increased T1 occurred in some tumours, and is unexplained, but its location with respect to the image in each case suggests it may be an artefact occurring on Day 2. Due to the uptake of HPG molecules in tumours over days, HPG-GdF might be useful mostly in pre-clinical studies. However, because the distribution of HPGGdF is relatively static on the timescale of minutes on subsequent days, retention should not preclude the repeated use of the agent on subsequent days. However, its presence would disturb anatomical details in T1 weighted images. Due to adverse health affects of Gadolinium, clinically used contrast agents are desired to clear from the body within hours, not weeks.  4.4.2  Extravasation  Histology shows that HPG-GdF remains primarily intravascular over several minutes, and stays near the vasculature as it begins to leak out of blood vessels. HPGGdF distributes further from vessels over time, and remains in the tumour for days. After 7 days, the distribution of HPG-GdF does not equilibrate, but remains heterogeneous in both MR and histological images.  4.4.3  Comparing DCE-MRI Results from Two Contrast Agents  Bolus Arrival Time and IAUC60: Comparing HPG-GdF to Gadovist Regions of histology indicating large areas of necrosis visually correspond to areas where HPG-GdF does not penetrate, and to areas where the arrival of a conventional contrast agent is delayed. Thus, BAT is not only an important input parameter for pharmacokinetic modelling, but also a reproducible, phenomenological 78  parameter in its own right. In necrotic areas, the contrast agent is likely to reach the area via diffusion instead of delivery through blood vessels, and thus HPGGdF is not likely reach into large areas of necrosis due to its slow extravasation from blood vessels. Identification of necrotic areas is important cancer research. Effective identification of the BAT is important for pharmacokinetic modelling of DCE-MRI data. If modelling were to be performed using the same BAT for the whole tumour, errors in pharmacokinetic model parameters may be introduced, particularly in large necrotic areas. Delayed bolus arrival time may also indicate transient hypoxia. HPG-GdF was found overlaying CD31 positive objects which are not positive for Carbocyanine. Carbocyanine was administered 5 minutes prior to tumour excision and will therefore only mark vessels perfused within that time. Due to the relatively low levels of fluorescence in HPG-GdF images, analysis to investigate this hypothesis was not possible. Evidence is only anecdotal, from viewing histology images. The BAT and IAUC60 both identify areas of low (or negligible) uptake within the tumour. While BAT provides information about regions of low uptake, it is only complimentary to IAUC60 information. The IAUC60 allows for differentiation between areas of the tumour where BAT is not delayed. Areas with very similar BAT may have very different IAUC60 values (as determined by viewing parameter maps). Pharmacokinetic Modelling Gadovist concentration time curves were fit twice, using two different models. Probabilities calculated from compared AIC values for the paired fits voxel-wise within each ROI showed that the four parameter 2CXM provided improved fits relative to the three parameter extended Tofts model in 81% ±7% of voxels in each tumour ROI. Due to the prevalence of the 2CXM, only these results are discussed. Areas in 2CXM parameter maps with unrealistic parameters (e.g. unreasonably high ve or v p ) correspond to very poor R2 goodness of fit values (R2 < 0.5). However, tumour average ve and v p values were still unreasonably high. The results of the sensitivity analysis presented in Chapter 3 may explain the non-physical model results: scaling of concentration time curves resulted in identical scaling of 2CXM  79  parameters. Parameter maps calculated where the [CA] was doubled suggest that either the concentration of Gadovist in tissue is overestimated, or the AIF concentration is underestimated. Errors in relaxivity would result in incorrect scaling of the concentration time curve. Relaxivity has been reported to increase in the presence of macromolecules [35, 36]. The relaxivity measurement in this study was performed with saline solutions. If AIF and tissue concentrations are measured with T1 based methods, and it may be assumed that relaxivity in blood and tissue are equivalent, this error is a simple scaling factor, and cancel out of both sides of modelling equations, [81]. This is not the case here, as the AIF was measured using phase data. Fitting the uptake model to HPG-GdF concentration time curves was unsuccessful, as determined by low R2 goodness of fit parameter maps (Figure 4.15). The signal enhancement due to the presence of HPG-GdF was small relative to enhancement due to Gadovist. This resulted in noisier concentration time curves, and created difficulty in fitting. Concentration time curves that appeared to be well fit had low goodness of fit values due to the noise levels in the data. Either a higher dose, or enhanced relaxivity would be required to improve results in future experiments. However, due to the large size of the agent, and the slow extravasation, it may simply extravasate too slowly for the purposes desired here. In these experiments, time resolution was down-sampled from the acquired 2.24 s to 8.96 s to reduce noise. Large regions of the tumours did not enhance at all. Another contributing factor is that an AIF was not collected for HPG-GdF. Instead, it was assumed that AIF scales with dose, and therefore, the AIF measured with Gadovist could be scaled. Because the extravasation rates of these two agents are very different, this assumption is not ideal. Concentration time curves as a parameter map (Figure 4.17) provide additional information about the tumour microenvironment. Non-enhancing regions in the HPG-GdF concentration time curve correspond to poorly (or slowly) enhancing regions in the Gadovist time curves (Figure 4.17). Concentration time curves that have not yet peaked at the end of the DCE-MRI scan series correspond to poorly fit (or failed fit) data from the DCE-MRI series. If contrast agent concentration is still rising at the end of the scan series, the assumption that the tracer flux from the EES space back to the plasma space is non-zero may not be valid. An uptake 80  model may be more appropriate in these areas.  81  Chapter 5  Characterization of Three Tumour Lines Using DCE-MRI with Both High and Low Molecular Weight Contrast Agents 5.1  Introduction  In Chapter 4, a new high molecular weight agent comprised of hyper-branched polyglycerol doubly labelled with gadolinium and a fluorescent marker was investigated for use in DCE-MRI. In this chapter, this high molecular weight agent was used in conjunction with a conventional contrast agent to compare three tumour lines. Two human colorectal tumour lines, HT29 (this data was also presented in Chapter 4) and HCT116, and one breast cancer line, MDA-435-LCC6Her2 , are compared. Both histological and DCE-MRI parameters are used to investigate differences between tumour models in the tumour microenvironment.  82  5.1.1  Tumours  HT29 and HCT116 have been previously compared within our lab [60]. Vascular density was found to be relatively lower in HCT116. The proportion of vessels positive for a perfusion marker was found to be lower in HT29. Differences in vascular function were found via histological methods: in the HT29 tumours, a 500 kDa FITC-dextran was found to diffuse further from vasculature with time. The study here is intended to explore differences that may be found with DCEMRI with a macromolecular contrast agent.  5.2  Methods  The methods described here are very similar to those used in Chapter 4, for Group III. However, here, three tumour lines are used, and additional histological analysis is performed. To avoid repetition, the methods in this chapter are less detailed than in Chapter 4. All experiments followed a protocol approved by the UBC Committee on animal care.  5.2.1  Mice  Female non obese diabetic/severe combined immuno-deficient (NOD/SCID) were used for in vivo experiments. Mice were bred and maintained in-house in accordance with the Canadian Council of Animal Care guidelines. Eighteen NOD/SCID mice were implanted with tumour xenografts subcutaneously on the sacral (lower back) region. Tumours where implanted next to fiducial markers which allow for reproducing orientation in MR on subsequent days, and to obtain histological sections in an orientation which correspond to the MR imaging plane (further details may be found in Section 4.2.3 and in References [75, 76]). Groups Eighteen female NOD/SCID mice were randomly assigned to three groups, and implanted with tumour xenograft subcutaneously on the lower back region. The tumour type determined the group: HT29 human colorectal carcinoma xenografts  83  Table 5.1: Summary of Experiments and Groups Group HT29 HCT MDA  Tumour line HT29 HCT116 MDA-435-LCC6Her2  N 6 6 6  Study Description All groups: DCE-MRI with Gadovist on D0; HPG-GdF on D1; Tumours collected for Histo  (HT29 Group); HCT116 human colorectal carcinoma xenografts (HCT Group); MDA-435-LCC6Her2 human breast xenograft (MDA Group). When tumours reached ≥ 300 mm3 in size, they were ready for imaging. Groups are summarized in Table 5.1 for convenience. All three groups (six mice each) were imaged in two sessions 24-48 hours apart using a DCE-MRI protocol. During the first imaging session, a low molecular weight contrast agent, Gadovist (Bayer Healthcare), was used. During the second session, the high molecular weight contrast agent, HPG-GdF (UBC, Faculty of Pharmacy), was used. All tumours were collected and frozen following the final scan, without waking from anaesthesia. Tumours were collected at 60-70 minutes post-injection of HPG-GdF, and 5 minutes following administration of carbocyanine (a perfusion marker). Tumours were embedded in optimum cutting temperature (Tissue-TEK) and immediately frozen.  5.2.2  Magnetic Resonance Imaging  Each imaging session consisted of axial RARE T1-weighted images for morphological reference and orientation, a variable flip angle experiment for T1 and flip angle mapping, a DCE-MRI series, and a follow up T1 measurement. T1 measurements, and flip angle mapping are performed using a single slice FLASH variable flip angle experiment (FLASH; TR/TE = 500/2.75; FA = 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ , 70◦ , 80◦ , 90◦ , 100◦ , 110◦ , 120◦ , 130◦ , 140◦ , 150◦ , 160◦ , 170◦ , 180◦ , 190◦ , 200◦ , 215◦ ) and data is fit with the method to account for slice profile effects (as described in Chapter 2). DCE-MRI data is collected at 2.24 s time resolution (FLASH; TR/TE = 35/2.75; FA = 40◦ ; NR = 1200). T1 and DCEMRI experiments are single slice, with 0.33 mm x 0.297 mm x 1 mm resolution. A  84  follow up T1 measurement is performed (FLASH; TR/TE = 35/2.75; FA = 10◦ , 20◦ , 30◦ , 40◦ , 50◦ , 60◦ , 80◦ , 100◦ , 120◦ ), where the flip angle map is not re-produced. All slices are oriented perpendicular to the fiducial marker, and the slice location is adjusted to match on subsequent imaging days.  5.2.3  Imunohistochemistry  Histology was used in this work to identify blood vessels, perfused blood vessels, and HPG-GdF distribution at different time points. All tumours were cryosectioned to obtain cryosections corresponding to the MR image: Three 20 µm cryosections were collected 1.5 mm apart, centred at the depth corresponding with MR imaging. Due to the easily compressible nature of the tissue, the shape of the tumour section may be distorted following excision and freezing, relative to its shape during the MRI. As a result, the image location in MR can only be estimated. Images of sections were compared to MR images to choose the one which best corresponds. Results discussed here are only from the section which is manually identified to correspond. Images were obtained for HPG-GdF, carbocyanine (marking perfused blood vessels), CD31 (staining for vasculature), and Hoechst (staining for cell nuclei for identification and cropping of necrotic and viable tissue areas). Tumour cryosections were stained and images obtained, as described in Chapter 4 (Section 4.2.6). Details of staining and image acquisition are therefore not reproduced in detail here. Histological data was analysed to investigate HPG-GdF extravasation as described in Section 4.2.6. In addition to analysis performed in Chapter 4, blood vessel density, fraction of perfused vessels and necrotic fraction were calculated. Blood vessel density is reported using the average distance in tissue from nearest CD31 object. Density of perfused blood vessels is likewise reported by average distance in tissue from nearest CD31 object positive for Carbocyanine. Fraction of perfused vessels is calculated by the number of CD31 objects positive for Carbocyanine relative to the number of CD31 objects in whole tumour images. Necrotic fraction is calculated as the number of pixels in images cropped to remove necrosis as a fraction of the number of pixels in whole tumour images. Thresholds used to  85  Table 5.2: Thresholds for Histology Analysis Tumour Type HT29  MDA  HCT116  Stain CD31 Carbocyanine HPG-GdF CD31 Carbocyanine HPG-GdF CD31 Carbocyanine HPG-GdF  Avg Background 3.7 1.4 1.04 4.6 1.8 1.13 2.9 0.49 1.08  Threshold for +ve Staining 22 15 N/A 22 27 N/A 26 20 N/A  identify positive staining are reported in Table 5.2.  5.2.4  Analysis of MRI Data and Pharmacokinetic Modelling  Analysis of MRI data was identical to that described in Section 4.2.7, and thus is only described briefly here. T1 and flip angle mapping were performed using the VFA experiment, and method described in Chapter 2. This method was extended to calculate dynamic T1 from DCE-MRI data. Pre- and post-contrast VFA experiments were used to calculate T1 before, and approximately 40 minutes after administration of the contrast agent. Change in R1 (R1 = 1/T1 ) is calculated pixel by pixel and averaged within each ROI. Bolus arrival time (BAT) (as described in Section 3.3.1) and IAUC60 maps (as described in Section 3.3.2) were calculated from concentration time curves derived from DCE-MRI data. Concentration time curves, derived from DCE-MRI data, were fit with various models. The time resolution of the concentration time curves was reduced by a factor of 4 to reduce noise. Curves for the low molecular weight agent were fit by the modified Tofts model, and the general four parameter two-compartment exchange model (2CXM). Refer to Section 3.4 for details of different models. Concentration time curves for the high molecular weight agent were not modelled due to relatively low signal enhancement, and noisy concentration time curves, as demonstrated in  86  Chapter 4. The Akaiki Information Criterion (AIC) [38] was used to determine the most suitable model for modelling the Gadovist concentration time curves (see Section 3.4.3 for further information on the AIC). A lower AIC value indicates an improved fit, and the probability that one is more likely than the other to represent the data is given by Equation 3.41. To determine the best model for each subject, the number of voxels where each model is most probable are calculated for each tumour. Model fitting was performed in Matlab using custom software which utilized the Levenberg-Marquard-Fletcher method [80]. For group comparison, resulting pharmacokinetic parameters are expressed as ROI averaged values.. Voxels where the R2 goodness of fit is less than 0.5 were disregarded for this calculation. Group averaged values are calculated and averaging ROI averaged values across all subjects in each group.  5.2.5  Statistics  Statistical analysis was performed using Matlab’s Statistical toolbox. Groups were compared with a two sample Student T-test. The null hypothesis states that two groups from independent random samples are from the same distribution, and have the same mean and variance. This is tested against the possibility that the groups have non-equal means. The test provides a p-value, which is the probability that the data would be obtained assuming the null hypothesis is true. A significant difference is detected when p<0.05 (the probability of the null hypothesis is less than 5%). Different parameters are tested for correlation using the Spearman’s rank correlation and 95% confidence interval. This test assesses how well the relationship between variables can be described using a monotonic function. Unlike the Pearson’s test, the relationship need not be linear (it will give the same results comparing X to Y as X to Y3 , etc).  5.3  Results  MRI and corresponding histological data were obtained for eighteen mice (six per tumour line) to assess differences in the tumour microenvironment between tumour 87  types. Six complete data sets (two DCE-MRI data sets, and corresponding histology) were used for analysis of the HT29 group. Five complete data sets were available for analysis of the MDA-435-LCC6Her2 group. Histology corresponding to MR images was unavailable for one subject (no. 5 of MDA-435-LCC6Her2 group). Three complete data sets were available for analysis of the HCT116 group. DCEMRI data with HPG-GdF was unavailable for one subject (no. 6 of HCT group) in the HCT group due to premature injection of the contrast agent. Histology data was unavailable for one subject due to loss of tumour sections (no. 4 of HCT group). One subject did not receive carbocyanine (no. 1 of HCT group). Subjects with incomplete data sets were not disregarded.  5.3.1  Distribution and Uptake of HPG-GdF  The distribution of HPG-GdF relative to vessels was investigated in order to assess a differences in vascular permeability to macromolecules between tumour models. HPG-GdF native fluorescence was mapped according to distance from nearest CD31 object (Figure 5.1). The distribution does not suggest a significant difference in extravasation of HPG-GdF between tumour models. Location of HPG relative to blood vessels  Location of HPG relative to perfused blood vessels 6 HT29 HCT 5 MDA−LCC6  6 HT29 HCT MDA−LCC6  Signal Intensity, Arbitrary Units  Signal Intensity, Arbitrary Units  5 4 3 2 1 0 0  4 3 2 1  20  40  60  80  0 0  100  Distance from nearest CD31 object (µm)  20  40  60  80  100  Distance from nearest CD31 object (µm)  Figure 5.1: The distribution of HPG-GdF relative to CD31 objects (vessels), and to CD31 objects positive for carbocyanine (perfused vessels). Uptake of HPG-GdF in tumours was assessed both by average HPG-GdF fluorescence in tissue, and by ROI averaged ∆R1 , and the results compared. Average 88  HPG-GdF fluoresecence (corrected for background) was found to be significantly lower in HCT116 relative to MDA-435-LCC6Her2 (p = 0.01) and HT29 (p = 0.002) tumours xenografts (Figure 5.2(a)). ∆R1 due to HPG-GdF (Figure 5.2(b)) is highest in MDA tumours relative to HCT (p = 0.07) and HT29 (p = 0.006). ∆R1 due to HPG-GdF suggests uptake is lower in HT29 than HCT (p = 0.02), conflicting with results from average HPG-GdF fluorescence. However, histology results are for viable tumour tissue only, and exclude necrosis and surrounding tissue. MR images are much lower resolution, include necrotic areas, and may include small amounts of surrounding tissue, though ROIs are drawn to include only tumour tissue. Using Spearman’s Rank Coefficient, the average HPG-GdF signal from histological sections was not found to be correlated with ROI averaged ∆R1 (p = 0.8). Average HPG Signal  ∆R1 due to HPG (1/s) 0.35  (b)  1.2 1  0.3 ∆R1 (1/s)  (a)  Average Signal (Arbitrary Units)  0.4 1.4  0.8 0.6  0.25 0.2 0.15 0.1 0.05  0.4  0 0.2 HT29  MDA−LCC6  HCT116  HT29  MDA−LCC6  HCT116  HPG Uptake Determined by MR and Histology 0.4  (c) ∆R1 (s−1)  0.3  HT29 MDA HCT  0.2  0.1  0 0  0.5 1 Average HPG Signal (arbitrary units)  1.5  Figure 5.2: (a) Average HPG-GdF native fluorescence in viable tissue is averaged in each histological image (60-70 minutes exposure), and groups are compared via a box and whisker plot, with raw data points overlaid. (b) Tumour averaged ∆R1 due to HPG-GdF (approximately 40 minutes exposure). (c) HPG-GdF fluorescence is plotted against ∆ R1 . Error bars indicate ±1 standard deviation.  89  5.3.2  Vascular Characteristics  Vascular characteristics were assessed and compared between tumour groups. These results offer a means of comparison for MRI derived parameters. Vascular density was found to be significantly lower in HCT116, relative to HT29 (p = 3 × 10−4 ) and MDA-435-LCC6Her2 (p = 8 × 10−6 ), as indicated by a larger average distance of tissue from nearest CD31 object (Figure 5.3(a)). HT29 and MDA-435-LCC6Her2 have similar vascular density (p = 0.3). Density of perfused vasculature, as indicated by average distance from nearest CD31 object positive for Carbocyanine (Figure 5.3(b)), follows the same trend as vascular density. However, due to high standard deviation within HT29 group, there is no significant difference found for HT29 relative to other groups (p > 0.3). MDA-435-LCC6Her2 were found to have significantly higher density of perfused vessels relative to HCT (p = 0.003). The fraction of perfused vessels was calculated by the number of CD31 objects positive for carbocyanine in viable tumour tissue relative to the total number of CD31 objects. HT29 tumour xenografts had relatively larger fraction of carbocyanine positive CD31 objects, relative to MDA-435-LCC6Her2 (p = 0.05) and HCT116 (0.006). HCT116 has a lower fraction than MDA-435-LCC6Her2 (Figure 5.3d) (p = 0.09,). Density of perfused vasculature was compared to average HPG-GdF fluorescence (Figure 5.4(a)) with Spearman’s Rank test, and are correlated with significance level p = 0.07. HPG-GdF fluorescence was also found to be correlated with vascular density (p = 0.005) (Figure 5.4(b)). Data is from tumour sections corresponding to MR images.  5.3.3  Parameters Derived From DCE-MRI Data  BAT Bolus arrival times were measured for all DCE-MRI data sets pixel by pixel within regions of interest (Figure 5.5). BAT maps reveal large areas of non-enhancing pixels in many tumours. In the HPG-GdF data sets, BAT values are very similar (as assessed by visual comparison of parameter maps) to those of the Gadovist data  90  Average Distance to Nearest Vessel  Average Distance to Nearest Perfused Vessel 160  140  (b)  120 100 80 60 40 20 0  HT29  MDA−LCC6  Average Distance to Nearest Carbo +ve CD31 Object (µm)  (a)  Average Distance to Nearest CD31 Object (µm)  160  140 120 100 80 60 40 20 0  HCT116  Necrosis Fraction  HCT116  0.8  0.6  0.7  (d)  0.6  0.5 Fraction  Necrosis Fraction  MDA−LCC6  Fraction of Carbocyanine +ve CD31 Objects  0.7  (c)  HT29  0.4 0.3  0.5 0.4 0.3  0.2  0.2  0.1 0  0.1 HT29  MDA−LCC6  0  HCT116  HT29  MDA−LCC6  HCT116  Figure 5.3: (a) Vascular density, as measured by average distance to nearest CD31 positive object. (b) Density of perfused vasculature, as measured by average distance to nearest CD31 object positive for Carbocyanine. (c) Necrotic fraction, as measured by number of pixels in necrotic regions over number of pixels in the whole tumour. (d) Fraction of CD31 objects which are positive for carbocyanine. Error bars indicate ±1 standard deviation. Each of the respective parameters is assessed in individual tumour sections, and then averaged over all tumours in each group. sets in voxels where enhancement occurs. Regions where the BAT of Gadovist is delayed show some delay in the HPG-GdF data sets, or do not enhance at all. IAUC60 IAUC60 maps were calculated for all tumours (Figure 5.6). IAUC60 values for HPG-GdF are much lower relative to Gadovist. For both contrast agents, IAUC60 parameter maps tend to show higher values at the tumour rim relative to centre. ROI averaged IAUC60 values from Gadovist data in the MDA-435-LCC6Her2 tumours are significantly higher relative to HCT116 (p = 0.02), and higher relative to HT29 xenografts (p = 0.06). The IAUC60Gadovist values are similar for two colorectal 91  Perfused Vascular Density Compared to HPG Fluorescence  Vascular Density Compared to HPG Fluorescence −3  6  x 10  HT29 MDA HCT116  5  (b)  4 3 2 1 0 0  0.5 1 Average HPG Signal (arbitrary units)  1.5  Inverse Squared Average Distance to Nearest CD31 Obj (µm−2)  (a)  Inverse Squared Average Distance to Nearest Carbo +ve CD31 Obj (µm−2)  −4  1  x 10  0.8  HT29 MDA HCT116  0.6 0.4 0.2 0 0  0.5 1 1.5 Average HPG Signal (arbitrary units)  Figure 5.4: A linear trend is observed between inverse squared mean distance from nearest carbocyanine positive CD31 object (a) and average HPGGdF fluorescence and from nearest CD31 object (b). xenografts (p = 0.3). ROI averaged IAUC60 values from HPG-GdF data are highest in MDA-435-LCC6Her2 tumour xenografts. IAUC60HPG are significantly higher for MDA-435-LCC6Her2 relative to HT29 (p = 0.02) and HCT116 (p = 0.002). Tumour averaged IAUC60HPG values for HT29 and HCT116 are similar (p = 0.2). Tumour averaged IAUC60 values show a linear relationship with the the inverse square of the mean distance to the nearest CD31 object in tissue (Figure 5.7. This provides a parameter an approximation density per cross sectional area. Tumour averaged IAUC60 values are compared to vascular density (average distance in tissue to nearest CD31 object) using the Spearman’s rank correlation (Figure 5.7). IAUC60HPG correlated to vascular density (p = 0.0002). Correlation of IAUC60HPG with average distance to nearest carbocyanine positive CD31 object in tissue was not as strong (p = 0.05). No correlation was found between IAUC60Gadovist with either average distance to nearest CD31 object (p = 0.1) or carbocyanine positive CD31 object (p = 0.4). ROI averaged IAUC60Gadovist and IAUC60HPG were found to be correlated (p=0.03) using Spearman’s rank correlation (Figure 5.6(e)). Pharmacokinetic Analysis Pharmacokinetic analysis was performed on Gadovist data with two models, and fitting was compared with the AIC to determine the probability that one model 92  HT29 MDA  HCT  (b)  HT29  MDA  HCT  (a)  Figure 5.5: BAT (in seconds from beginning of DCE-MRI scan series) found from Gadovist (a) and HPG-GdF (b) concentration time curves for all 18 tumours. The scale bar indicates 3 mm. Subjects appear in the same order in (a) and (b). is more appropriate than the other. In all tumour lines, the 2CXM model was found to be the most appropriate model. The 2CXM model best fit 81% ±7%, 92% ±4% and 95% ±6% of voxels in HT29, HCT116, and MDA-435-LCC6Her2 tumours respectively. Due to the prevalence of 2CXM model over the extended Tofts model, only 2CXM results are discussed. F p and PS parameter maps, and corresponding R2 goodness of fit maps are shown in Figures 5.8 and 5.9. ROI average PS values from the 2CXM model were compared between groups (Figure 5.8(c)). Results from the Gadovist data showed that MDA-435-LCC6Her2 had significantly higher PS than HT29 (p<0.03), and higher than HCT116 (p<0.06). No significant difference in PS was found between HCT116 and HT29 tumour xenografts (p = 0.5). Tumour average F p values from the 2CXM were compared between groups  93  HT29 MDA  HCT  (b)  HT29  MDA  HCT  (a)  IAUC60 (Gadovist)  6  −4  IAUC60 (HPG)  −4  (d)  0.4 0.35  x 10  (e)  5 IAUC60 (mM⋅s)  IAUC60 (mM⋅s)  0.3 0.25 0.2 0.15  4 3 2  0.1 0.05 0  HT29  MDA−LCC6  HCT116  6  x 10  5 IAUC60 HPG (mM⋅s)  (c)  4 3 2  1  1  0  0 0  HT29  MDA−LCC6  HCT116  HT20 MDA−LCC6 HCT 0.1 0.2 0.3 0.4 IAUC60 Gadovist (mM⋅s)  0.5  Figure 5.6: IAUC60 (mM·min) calculated from Gadovist (a) and HPG-GdF (b) concentration time curves for all 18 tumours. The scale bar indicates 3 mm. Group averages are examined in (c) and (d). The relationship between tumour averaged IAUC60 for HPG-GdF vs. Gadovist is examined in (e), but are not correlated. IAUC60 of HPG-GdF is low relative to Gadovist in all tumour lines. MDA-435-LCC6Her2 tumours have higher average IAUC60 values with both HPG-GdF and Gadovist relative to the other tumour types. The HCT group is the least heterogeneous. (Figure 5.8(d)). MDA-435-LCC6Her2 had significantly higher perfusion than HT29 (p = 0.03), and higher than HCT116 (p = 0.08). HCT116 did not have significantly higher average perfusion than HT29 (p = 0.03). 94  −4  IAUC60 HPG (mM⋅s)  6  x 10  HT29 MDA HCT  5 4 3 2 1 0 0  0.2 0.4 0.6 0.8 (Avg Distance to CD31 obj)−2 (1/µm2)  1 −3  x 10  Figure 5.7: Inverse square of average distance to the nearest CD31 object (approximately vascular density per cross sectional area) is significantly correlated with IAUC60HPG (p = 0.0002).  Tumour averaged F p and PS values reflect a trend which is obvious from viewing the parameter maps (Figure 5.8(a-b)). These parameters suggest MDA-435LCC6Her2 has the best vascular function. HT29 and MDA-435-LCC6Her2 tumours did not show significantly different vascular densities, though HT29 had relatively higher necrosis fraction and vascular parameters are only calculated in viable tumour tissue.  5.4  Discussion  Histological analysis revealed a higher vascular density in HT29 relative to HCT116 tumour xenografts. This agrees with previous work [60]. The distribution of HPGGdF relative to vasculature at 60 minutes was found to be similar between tumour types, which disagrees with previous work indicating that HT29 tumours have increased permeability to macromolecules relative to HCT116 [60]. However, extravasation of HPG-GdF was only one time point, and results may differ for a longer exposure, or for different molecules. Further, increased average HPG-GdF fluorescence in tissue (Figure 5.2(a)) suggests that HT29 tumours were leakier, though this may be due to differences in vascular density (Figure 5.3(a)). Uptake of HPG-GdF assessed by average HPG-GdF fluorescence in tissue does not agree with ∆R1 . Average HPG-GdF fluorescence in tissue (Figure 5.2(a)) shows lower tumour uptake in HCT116 tumours relative to HT29 and MDA-435LCC6Her2 tumour xenografts for 60 minutes exposure. However ROI averaged ∆R1 (Figure 5.2(b)) shows lower uptake in HT29 relative to HCT116 (p = 0.002) and MDA-435-LCC6Her2 (p = 0.006) for approximately 40 minutes exposure. Using Spearman’s Rank Coefficient, the average HPG-GdF signal from histological sections is not well correlated to ROI averaged ∆R1 (p = 0.8) in corresponding images. 95  (a)  MDA  HCT  HT29  F p (1/s) from modelling Gadovist data with the 2CXM  (b)  MDA  HCT  HT29  PS (1/s) from modelling Gadovist data with the 2CXM  (c)  (d)  PS (Gadovist)  −3  2  x 10  Fp (Gadovist)  −3  4  x 10  3.5 3 Fp (1/s)  PS (1/s)  1.5  1  2.5 2 1.5  0.5  1 0.5  0  HT29  MDA  0  HCT116  HT29  MDA  HCT116  Figure 5.8: F p (1/s) (a) and PS (1/s) (b) maps from modelling Gadovist data with the 2CXM are shown for all 18 tumours. The scale bar indicates 3 mm. Group averaged PS (1/s) (c) and F p (1/s) (d) resulting from modelling Gadovist concentration time curves with the 2CXM. There are variety of reasons why these values may not be correlated. Histology results are for viable tumour tissue only, and exclude necrosis and surrounding tissue. MR images are much lower resolution (approx 0.33 mm compared to 1.5 µm), include necrotic areas, and may include small amounts of surrounding tissue, though  96  HT29 HCT MDA Figure 5.9: R2 goodness of fit values from pharmacokinetic modelling of Gadovist data with the four parameter 2CXM model, and (b) of HPGGdF with the uptake model. Maps are shown for all tumours. The scale bar indicates 3 mm. Tumours are displayed in the same order as other figures. ROIs were drawn to include only tumour tissue. High natural background fluorescence was observed at the same wavelength as fluorescence of HPG-GdF in necrotic regions; therefore, it was not possible to quantify the presence of HPGGdF in necrotic regions. Further, all group comparisons are averaged across the region of interest or tumour section, and do not necessarily represent the heterogeneous distribution, which is obvious from viewing ∆R1 or HPG-GdF fluorescence maps (Figure 4.7). Whole tumour section average fluorescence of HPG-GdF is only about double the background fluorescence at that wavelength. Due to the low level of fluoresence, it was not possible to perform analysis to look for CD31 object which are also positive for HPG-GdF. In this work, modelling of Gadovist concentration time curves was performed with two models: the three parameter extended Tofts model, and the four parameter 2CXM. The Akaike information criterion was used to discern the most appropriate model. The 2CXM was found to be the most appropriate model for these datasets, over the extended Tofts model. This approach provided an objective method of determining which of the two models was most appropriate. Pharmacokinetic analysis with the 2CXM of DCE-MRI experiments with Gadovist revealed that MDA-435-LCC6Her2 had significantly higher PS and F p than HT29, 97  and higher PS and F p than HCT116). No significant difference in PS or F p was found between HCT116 and HT29 tumour xenografts, though both were lower in HT29. This is contradictory to higher vascular density and higher fraction of perfused vessels in HT29 found in histology. MDA-435-LCC6Her2 tumours were shown to have the highest perfused vacular density, and highest vascular density, though they did not have the highest fraction of perfused vessels. This agrees with 2CXM results showing the significantly higher PS and F p , and the increased IAUC60 (with both Gadovist and HPG-GdF). Histological analysis showed that HCT116 tumour xenografts had the lowest vascular density, and smallest fraction of functional vessels. F p and PS from pharmacokinetic analysis did not show a significant difference between HT29 and HCT116 groups, however, this may be due to a vastly different necrotic fraction in each group (Figure 5.3(c)). Vascular density from histology only represents viable tissue, and does not include necrotic areas, while MR results are not able to exclude necrosis. HPG-GdF dynamic data provided interesting information in the form of IAUC60 and BAT maps. IAUC60HPG tumour averages were found to have significant correlation with vascular density (determined by mean distance to nearest CD31 object in histological sections corresponding to MR images). IAUC60HPG was also found to be linear with the inverse square of the mean distance to the nearest CD31 object. This inverse squared parameter approximates vascular density per cross sectional area. Further, non-enhancing voxels in HPG-GdF concentration time curves (identified by bolus arrival time analysis), are strongly suggestive of necrosis. MRI derived parameters were compared using ROI averages. Due to the heterogeneous nature of the tumours, this is not ideal. Further, the ability to confirm MRI parameter maps with histology is limited. Co-registration of MRI data on subsequent imaging sessions, and histological data were not performed in this work. Due to the compressible nature of the tumour, positioning of the surface coil altered its shape varied between imaging days, and relative to histology. With co-registration, it may be possible to draw further conclusions about the tumour microenvironment in MR data.  98  5.5  Conclusions  Overall, MDA tumours had highest IAUC60 (with both contrast agents), the least non-enhancing voxels in DCE-MRI (assessed via BAT maps), highest F p and PS values from pharmacokinetic modelling, and highest vascular (and perfused vascular) density in tissue. ROI averaged IAUC60 from both contrast agents, and pharmacokinetic parameters did not show differences in the two colorectal tumour models. Histological analysis showed significantly higher vascular density in HT29 (p = 0.0003). HT29 tumours had the highest fraction of perfused vessels. HCT tumours had ∼3 fold higher necrotic fraction than HT29, which may be the reason the pharmacokinetic parameters did not reflect histological results. While HPG-GdF offered BAT and IAUC60 parameter maps, ROI averages of those parameters were insufficient for differentiating between tumour types. If coregistration of histology, and the two imaging sessions were achieved, the HPGGdF MRI data may be better able to provide information about the tumour microenvironment.  99  Chapter 6  Discussion and Conclusions This work is motivated by the hypothesis that performing DCE-MRI with a high molecular weight contrast agent would provide information blood flow, giving a better understanding of the tumour microenvironment than may be provided by DCE-MRI with a conventional low molecular weight agent, and pharmacokinetic modelling with the extended Tofts model. To this end, hyperbranched polyglycerols doubly labelled with Gadolinium and Alexa-647 (HPG-GdF) are investigated in this thesis. The distribution and retention of the agent was assessed (Chapter 4). T1 measurements over one week following administration of HPG-GdF showed that the molecules accumulate in tumour tissue over days, followed by a decrease, with a peak at 2-4 days. Fluorescence images of histological sections from subjects with different exposure times showed that HPG-GdF remained primarily intravascular over several minutes, and remained near vasculature up to an hour later. Whole tumour section images of HPG-GdF fluorescence showed that the distribution remained heterogeneous one week following administration. Due to the retention and uptake of HPG-GdF molecules in tumour tissue over days, HPG-GdF may primarily be useful in pre-clinical studies. However, retention of the agent should not preclude the repeated use of this agent on subsequent days in pre-clinical studies. After a day, the distribution should remain relatively static on the scale of minutes, and should not disrupt new DCE-MRI measurements. HPG-GdF was found to be inappropriate for pharmacokinetic analysis of DCE100  MRI data, as determined by low R2 goodness of fit. Signal enhancement due to HPG-GdF was much lower than Gadovist, and thus the SNR of DCE-MRI data was lower. This is unfortunate, since HPG-GdF would be appropriate for an uptake model, which would provide a value for blood flow. A smaller version of HPGGdF may remain intravascular over short time periods, but extravasate less slowly that the agent used here, and with sufficient relaxivity, may be more appropriate for DCE-MRI studies. HPG-GdF proved useful for creating bolus arrival time and IAUC60 parameter maps. When comparing DCE-MRI results using HPG-GdF versus Gadovist, bolus arrival time maps for HPG-GdF data show increased sensitivity to necrotic areas. IAUC60 maps show similar features for the two contrast agents. However, regions of low enhancement with Gadovist are often non-enhancing in HPG-GdF data sets. IAUC60HPG tumour averages were found to have significant correlation with vascular density (determined by mean distance to nearest CD31 object in histological sections corresponding to MR images). IAUC60HPG was also found to be linear with vascular density (inverse square of the mean distance to the nearest CD31 object in tissue). Further, non-enhancing voxels in HPG-GdF concentration time curves (identified by bolus arrival time analysis), are strongly suggestive of necrosis. In order to determine the utility of HPG-GdF in a study comparing tumour types, MDA-435-LCC6Her2 , HT29, and HCT116 tumour models were compared with DCE-MRI with two agents, and with corresponding histology (Chapter 5). Results were used to examine differences in vascular characteristics of the three tumour models. Pharmacokinetic analysis with the 2CXM of DCE-MRI experiments with Gadovist revealed that MDA-435-LCC6Her2 had significantly higher PS and F p than HT29, and higher PS and F p than HCT116). MDA-435-LCC6Her2 also had highest IAUC60 in both Gadovist and HPG-GdF experiments. Histological analysis supported these results, showing MDA-435-LCC6Her2 tumours were shown to have the highest perfused vacular density, and highest vascular density. No significant difference in PS or F p was found between HCT116 and HT29 tumour models. Histological analysis showed that HCT116 tumour xenografts had the lowest vascular density, and smallest fraction of functional vessels. Histological analysis for extravasation of HPG-GdF did not indicate a difference between 101  tumour models in vascular permeability to macromolecules for a 60 minute exposure. Due to the compressible nature of tumour tissue, the shape of the tumour varied in MR images from different scanning sessions, and relative to histological analysis. If coregistration had been achieved, better analysis of the correlation of the different data sets may have been possible. Accurate knowledge of the T1 in tissue is necessary for calculation of the contrast agent concentration time curves. Errors in FLASH variable flip angle (VFA) T1 measurements, and B1 mapping due to non-ideal slice selection are significant, if not accounted for. A method to measure T1 and flip angle maps in the presence of non-ideal excitation profile is presented in Chapter 2. It was found that T1 is routinely underestimated, and B1 errors are routinely overestimated. For 2D variable flip angle experiments, the zero crossing is not found at 180◦ , but occurs sooner. As T1 weighting increases, the zero crossing decreases further. The presented correction method greatly improves T1 and B1 measurements, and is advantageous over a non-selective excitation because there is no concern about wrapping in the slice select direction, allowing for more freedom to choose the orientation of MR images. Further, both data and simulations show that a 3D VFA experiment used in place of a 2D multi-slice equivalent does not avoid gross T1 errors, mainly due to inhomogeneous excitation in large parts of the slab. The signal deviates from the expected in all but the centre-most slices due to the slice profile, and this deviation increases moving away from the centre of the excited slab.  6.1  Implications, and Considerations for Future Work  This work highlights and addresses several issues in pharmacokinetic analysis: First, pharmacokinetic analysis is highly sensitive to correct scaling of concentration time curves (as discussed in 3.5). Sensitivity analysis of the two compartment exchange model demonstrated the importance of accurate knowledge of concentration time curves, and concentration of the AIF. Scaling of tissue concentrations, or in the AIF concentration, results in 2CXM model parameters scaling equally. This relationship continues to scale ve and v p to values greater than 1. This  102  suggests that flow and permeability measurements resulting from a successful fit should not be disregarded on the basis of ve , v p , or their sum, being greater than one. Second, there is a need for an AIF measurement, concurrent with DCE-MRI data collection. Results of the sensitivity analysis suggest that either the concentration in tissue is over-estimated, or the AIF concentration is under-estimated. As pointed out in Section 3.5, incorrect scaling will result in scaled pharmacokinetic parameters. Significantly different parameter values between scans, or subjects may be obtained on the basis of a poorly guessed AIF. Third, when performing pharmacokinetic modelling of DCE-MRI data, the model should be carefully chosen (in 3). The assumptions of the model should be appropriate given the tissue being investigated, data quality, time resolution, and acquisition length (e.g. References [17, 22, 37]). For pharmacokinetic modelling of tumour tissue, the Tofts and modified Tofts models are popular [25], however, the assumptions made may poorly represent the tissue and data, and therefore may be incorrectly interpreted [22]. When used appropriately, these models have the drawback of not distinguishing blood flow from blood vessel permeability. The general two compartment exchange model separates blood flow from permeability, and makes fewer assumptions regarding the tissue in question, but increasing model complexity is not necessarily more appropriate. Time resolution and data quality are important to consider, but the choosing the most appropriate model may not be straightforward. To overcome this difficulty, the Akaiki Information Criterion (AIC) is used in this work to objectively discriminate if the extended Tofts model or the two compartment exchange model is more appropriate (Section 3.4.3). This approach was recently recommended by Sourbron et. al. [22]. The AIC provides an objective measure of improved fit, taking into account changes in model complexity. In this work, the 2CXM was deemed most appropriate over the three parameter extended Tofts model for analysis of Gadovist DCE-MI data, based on probabilities calculated using the AIC. Fourth, the macromolecular contrast agent investigated in this work extravasated too slowly to provide sufficient signal enhancement in DCE-MRI data for pharmacokinetic modelling. Increasing relaxivity, or reducing the molecule size may improve signal enhancement. 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