Computational modelling of anti-angiogenic therapies based on multiparametric molecular imaging data

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

Pharmacogenetics in Model-Based Optimization of Bevacizumab Therapy for Metastatic Colorectal Cancer

Vascular endothelial growth factor A (VEGF-A) and intercellular adhesion molecule 1 (ICAM-1) are significant regulators of angiogenesis, an important biological process involved in carcinogenesis. Bevacizumab, an anti-VEGF monoclonal antibody (MAB), is approved for the treatment of metastatic Colorectal cancer (mCRC), however clinical outcomes are highly variable. In the present study, we developed a pharmacokinetic (PK), a simplified quasi-steady state (QSS) and a pharmacokinetic/pharmacodynamic (PK/PD) model to identify potential sources of variability. A total of 46 mCRC patients, who received bevacizumab in combination with chemotherapy were studied. VEGF-A (rs2010963, rs1570360, rs699947) and ICAM-1 (rs5498, rs1799969) genes’ polymorphisms, age, gender, weight, and dosing scheme were investigated as possible co-variates of the model’s parameters. Polymorphisms, trough, and peak levels of bevacizumab, and free VEGF-A were determined in whole blood and serum. Data were analyzed using nonlinear mixed-effects modeling. The two-compartment PK model showed that clearance (CL) was significantly lower in patients with mutant ICAM-1 rs1799969 (p < 0.0001), inter-compartmental clearance (Q) was significantly higher with mutant VEGF-A rs1570360 (p < 0.0001), and lower in patients with mutant VEGF-A rs699947 (p < 0.0001). The binding QSS model also showed that mutant ICAM-1 rs1799969 was associated with a lower CL (p = 0.0177). Mutant VEGF-A rs699947 was associated with a lower free VEGF-A levels, prior to the next dose (p = 0.000445). The above results were confirmed by the PK/PD model. Findings of the present study indicated that variants of the genes regulating angiogenesis might affect PK and PD characteristics of bevacizumab, possibly influencing the clinical outcomes.

Multi-Scale Modeling and Oxygen Impact on Tumor Temporal Evolution: Application on Rectal Cancer During Radiotherapy

We present a multi-scale approach of tumor modeling in order to predict its evolution during radiotherapy. Within this context we focus on three different scales of tumor modeling: microscopic (individual cells in a voxel), mesoscopic (population of cells in a voxel) and macroscopic (whole tumor), with transition interfaces between these three scales. At the cellular level, the description is based on phase transfer probabilities in the cellular cycle. At the mesoscopic scale we represent populations of cells according to different stages in a cell cycle. Finally, at the macroscopic scale, the tumor description is based on the use of FDG PET image voxels. These three scales exist naturally: biological data are collected at the macroscopic scale, but the pathological behavior of the tumor is based on an abnormal cell-cycle at the microscopic scale. On the other hand, the introduction of a mesoscopic scale is essential in order to reduce the gap between the two extreme, in terms of resolution, description levels. It also reduces the computational burden of simulating a large number of individual cells. As an application of the proposed multi-scale model, we simulate the effect of oxygen on tumor evolution during radiotherapy. Two consecutive FDG PET images of 17 rectal cancer patients undergoing radiotherapy are used to simulate the tumor evolution during treatment. The simulated results are compared with those obtained on a third FDG PET image acquired two weeks after the beginning of the treatment.

An imaging-based computational model for simulating angiogenesis and tumour oxygenation dynamics

Tumour growth, angiogenesis and oxygenation vary substantially among tumours and significantly impact their treatment outcome. Imaging provides a unique means of investigating these tumour-specific characteristics. Here we propose a computational model to simulate tumour-specific oxygenation changes based on the molecular imaging data. Tumour oxygenation in the model is reflected by the perfused vessel density. Tumour growth depends on its doubling time (T d) and the imaged proliferation. Perfused vessel density recruitment rate depends on the perfused vessel density around the tumour (sMVDtissue) and the maximum VEGF concentration for complete vessel dysfunctionality (VEGFmax). The model parameters were benchmarked to reproduce the dynamics of tumour oxygenation over its entire lifecycle, which is the most challenging test. Tumour oxygenation dynamics were quantified using the peak pO2 (pO2peak) and the time to peak pO2 (t peak). Sensitivity of tumour oxygenation to model parameters was assessed by changing each parameter by 20%. t peak was found to be more sensitive to tumour cell line related doubling time (~30%) as compared to tissue vasculature density (~10%). On the other hand, pO2peak was found to be similarly influenced by the above tumour- and vasculature-associated parameters (~30-40%). Interestingly, both pO2peak and t peak were only marginally affected by VEGFmax (~5%). The development of a poorly oxygenated (hypoxic) core with tumour growth increased VEGF accumulation, thus disrupting the vessel perfusion as well as further increasing hypoxia with time. The model with its benchmarked parameters, is applied to hypoxia imaging data obtained using a [(64)Cu]Cu-ATSM PET scan of a mouse tumour and the temporal development of the vasculature and hypoxia maps are shown. The work underscores the importance of using tumour-specific input for analysing tumour evolution. An extended model incorporating therapeutic effects can serve as a powerful tool for analysing tumour response to anti-angiogenic therapies.

Image-driven pharmacokinetics: nanomedicine concentration across space and time

Clinical pharmacokinetics (PK) primarily measures the concentration of drugs in the blood. For nanomedicines it may be more relevant to determine concentration within a target tissue. The emerging field of image-driven PK, which utilizes clinically accepted molecular imaging technology, empirically and noninvasively, measures concentration in multiple tissues. Image-driven PK represents the intersection of PK and biodistribution, combining to provide models of concentration across space and time. Image-driven PK can be used both as a research tool and in the clinic. This review explores the history of pharmacokinetics, technologies used in molecular imaging (especially positron emission tomography) and research using image-driven pharmacokinetic analysis. When standardized, image-driven PK may have significant implications in preclinical development as well as clinical optimization of targeted nanomedicines.

Imaging Modalities to Assess Oxygen Status in Glioblastoma

Hypoxia, the result of an inadequacy between a disorganized and functionally impaired vasculature and the metabolic demand of tumor cells, is a feature of glioblastoma. Hypoxia promotes the aggressiveness of these tumors and, equally, negatively correlates with a decrease in outcome. Tools to characterize oxygen status are essential for the therapeutic management of patients with glioblastoma (i) to refine prognosis, (ii) to adapt the treatment regimen, and (iii) to assess the therapeutic efficacy. While methods that are focal and invasive in nature are of limited use, non-invasive imaging technologies have been developed. Each of these technologies is characterized by its singular advantages and limitations in terms of oxygenation status in glioblastoma. The aim of this short review is, first, to focus on the interest to characterize hypoxia for a better therapeutic management of patients and, second, to discuss recent and pertinent approaches for the assessment of oxygenation/hypoxia and their direct implication for patient care.

PET-specific parameters and radiotracers in theoretical tumour modelling

The innovation of computational techniques serves as an important step toward optimized, patient-specific management of cancer. In particular, in silico simulation of tumour growth and treatment response may eventually yield accurate information on disease progression, enhance the quality of cancer treatment, and explain why certain therapies are effective where others are not. In silico modelling is demonstrated to considerably benefit from information obtainable with PET and PET/CT. In particular, models have successfully integrated tumour glucose metabolism, cell proliferation, and cell oxygenation from multiple tracers in order to simulate tumour behaviour. With the development of novel radiotracers to image additional tumour phenomena, such as pH and gene expression, the value of PET and PET/CT data for use in tumour models will continue to grow. In this work, the use of PET and PET/CT information in in silico tumour models is reviewed. The various parameters that can be obtained using PET and PET/CT are detailed, as well as the radiotracers that may be used for this purpose, their utility, and limitations. The biophysical measures used to quantify PET and PET/CT data are also described. Finally, a list of in silico models that incorporate PET and/or PET/CT data is provided and reviewed.

Computational systems biology approaches to anti-angiogenic cancer therapeutics

Angiogenesis is an exquisitely regulated process that is required for physiological processes and is also important in numerous diseases. Tumors utilize angiogenesis to generate the vascular network needed to supply the cancer cells with nutrients and oxygen, and many cancer drugs aim to inhibit tumor angiogenesis. Anti-angiogenic therapy involves inhibiting multiple cell types, molecular targets, and intracellular signaling pathways. Computational tools are useful in guiding treatment strategies, predicting the response to treatment, and identifying new targets of interest. Here, we describe progress that has been made in applying mathematical modeling and bioinformatics approaches to study anti-angiogenic therapeutics in cancer.

Hypoxia in head and neck cancer in theory and practice: a PET-based imaging approach

Hypoxia plays an important role in tumour recurrence among head and neck cancer patients. The identification and quantification of hypoxic regions are therefore an essential aspect of disease management. Several predictive assays for tumour oxygenation status have been developed in the past with varying degrees of success. To date, functional imaging techniques employing positron emission tomography (PET) have been shown to be an important tool for both pretreatment assessment and tumour response evaluation during therapy. Hypoxia-specific PET markers have been implemented in several clinics to quantify hypoxic tumour subvolumes for dose painting and personalized treatment planning and delivery. Several new radiotracers are under investigation. PET-derived functional parameters and tracer pharmacokinetics serve as valuable input data for computational models aiming at simulating or interpreting PET acquired data, for the purposes of input into treatment planning or radio/chemotherapy response prediction programs. The present paper aims to cover the current status of hypoxia imaging in head and neck cancer together with the justification for the need and the role of computer models based on PET parameters in understanding patient-specific tumour behaviour.