Applications and challenges of using quantitative imaging data for biologically-based mathematical oncology

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David A Hormuth II, Guillermo Lorenzo


Quantitative imaging is being increasingly used to improve cancer diagnosis, monitoring, and treatment planning. In particular, the advent of multiparametric imaging has provided a noninvasive means to obtain a wealth of time- and spatially-resolved quantitative data about tumor morphology, architecture, vascularity, and dynamics. These unique data types collected over time can also be leveraged to predict the evolution of an individual patient’s tumor. Indeed, in recent years there has been extensive use of medical imaging data to inform, initialize, and calibrate biophysical models of tumor growth and treatment response [1,2]. These models aim to characterize patient or disease specific growth properties (e.g., diffusion, invasion, and proliferation rates) and patient or disease specific response to therapy (e.g., radiotherapy, chemotherapy, immunotherapy). There are even emerging methods to use model-based forecasts of response to enable physicians to optimally design the best managing strategy for each patient ́s tumor. Quantitative imaging has also been used to provide in vivo validation of modeling hypotheses, hence extending our understanding of tumor dynamics. In this mini- symposium we will discuss (1) translating pre-clinical models to clinical disease (2) modeling response to radiotherapy from in vitro to in vivo settings, (3) assessing the clinical utility of patient-specific response metrics, and (4) constructing imaging biomarkers grounded on mathematical models.

David A. Hormuth, II

The University of Texas at Austin, Austin, Texas USA
"Translating image driven models of response to radiation therapy from the pre-clinical to clinical setting"
Magnetic resonance imaging (MRI) is able to provide quantitative, non-invasive measurements of tissue and tumor properties related to perfusion, vascularity, proliferation, and cellularity that can be used to observe tumor growth throughout the course of therapy. We and others have leveraged this type of quantitative data to initialize and calibrate biologically-based models of tumor growth and response. Here, we investigate the use of diffusion weighted (DW-) MRI and dynamic contrast-enhanced (DCE-) MRI to non-invasively estimate tumor cellularity and vascularity, respectively, in high grade gliomas at the pre-clinical and clinical levels. At the pre-clinical level, we have developed a 3D, two-species reaction diffusion-based model describing the spatial-temporal evolution of tumor and blood volume fractions [1] during the course of fractionated radiation therapy. Images collected during therapy are used to calibrate tumor-specific growth and response parameters. These calibrated parameters are then used in a forward evaluation of the model to predict response following therapy. We observed less than 12.3% error in tumor volume predictions. At the voxel-level, we observed 6.6% and 14.1% in voxel-wise estimates of tumor and blood volume fraction, respectively. At the clinical level, we have developed a 3D reaction diffusion-based model describing the spatial-temporal evolution of tumor cellularity during and following chemoradiation. Using images collected at pre-treatment and at the 1-month post-chemoradiation visit, we calibrate for patient-specific model parameters. The calibrated parameters are then used to provide individualized predictions of tumor growth and treatment response. In a preliminary study with four patients, we observed less than 11.1% error in tumor volume predictions and 9.5% error at the voxel- level. These two studies demonstrate the utility of quantitative imaging data to initialize and calibrate mathematical models of tumor growth and response that can accurately predict both changes in tumor volume and intratumoral heterogeneity.

Sarah Brüningk

Institute of Molecular Systems Biology, ETH Zurich, Zurich Switzerland
"Intermittent radiotherapy as alternative treatment for recurrent high grade gliomas: A modelling study based on longitudinal tumour measurements"
Recurrent high grade glioma patients are faced with a poor prognosis for which there cur- rently exists no curative treatment option. In contrast to prescribing high dose hypofrac- tionated stereotactic radiosurgery (HFRS, 5x ≥ 6 Gy in daily intervals) with curative intent, we suggest a personalized, palliative treatment strategy aiming for tumour volume management by delivering intermittent high dose treatment every six weeks (iRT, ≥ 6 Gy per fraction). We performed a simulation analysis to compare HFRS, iRT and iRT plus boost (3x ≥ 6 Gy on consecutive days, delivered at time of progression) based on a simple mathematical model of tumour growth, radiation response and patient specific resistance to additional treatments (PD-L1 inhibitor and vascular disruptive agents). Our model uses only two patient specific parameters describing the surviving fraction fol- lowing each HFRS treatment fraction, and the rate of resistance evolution. Tumour growth rate and the efficacy of non-HFSR treatments were estimated for the patient population as a whole. Model parameters were fit from clinical tumour growth response curves of 16 patients of the Phase 1/2 clinical trial NCT02313272 that combined HFSR with beva- cizumab (10 mg/kg, every 2 weeks) and pembrolizumab (100 or 200 mg, every 3 weeks). Tumour volume was assessed by T1-weighted contrast enhanced magnetic resonance imag- ing at four to ten (median six) time points per patient. The obtained parameters were used to estimate the growth response of alternative iRT and iRT+boost treatments for up to 5-10 treatment fractions. Treatment efficacy was scored based on time to regrowth to the last recorded tumour volume per patient. The median coefficient of determination of the model fits was 0.93(0.67,0.99). The model predictions indicated that iRT may delay time to progression only for a subset of eleven patients, whereas iRT+boost treatment was equal or superior to HFSR in 15 out of 16 cases. For up to ten intermittently delivered fractions, iRT+boost was predicted to be marginally significantly better (p = 0.048) than HFRS. This simulation did not include other aspects of iRT, such as synergistic action with im- munotherapy through repeated antigen sampling, or the flexibility to treat both distal and primary lesions. Despite choosing this worst case estimate, our results suggest that iRT+boost may be a promising treatment alternative for recurrent high grade glioma patients.

Andrea Hawkins-Daarud

Precision Neurotherapeutics Innovation Program, Mayo Clinic, USA
"Assessing clinical utility of a model based patient-specific response metric for glioblastoma incorporating uncertainty quantification from image acquisition and segmentation"
Glioblastomas are lethal primary brain tumors known for their heterogeneity and invasiveness. A growing literature has been developed demonstrating the clinical relevance of a biomathematical model, the Proliferation- Invasion (PI) model, of glioblastoma growth. Of interest here is the development of a treatment response metric, Days Gained (DG). This metric is based on individual tumor kinetics of cellular diffusion and proliferation estimated through segmented volumes of hyperintense regions on T1-weighted gadolinium enhanced (T1Gd) and T2-weighted magnetic resonance images (MRIs). This metric was shown to be prognostic of time to progression and to be more prognostic of outcome than standard response metrics. While promising, the original paper did not account for uncertainty in the calculation of the DG metric leaving the robustness and the ultimate utility of this response metric in question. Using the Bayesian framework, we consider the impact of two sources of uncertainty: 1) image acquisition and 2) interobserver error in image segmentation. We first utilize synthetic data to characterize what non-error variants are influencing the final uncertainty in the DG metric. We then consider the original patient cohort along with additional cohorts from the recurrent setting to investigate clinical patterns of uncertainty and to determine how robust this metric is for predicting time to progression and overall survival in multiple scenarios. Our results indicate that the key clinical variants are the time between pre-treatment images and the underlying tumor growth kinetics, matching our observations in the clinical cohort. In the original cohort, we demonstrated that for this cohort there was a continuous range of cutoffs between 94 and 105 for which the prediction of the time to progression and was over 80% reliable [3]. While further validation must be done, this work represents a key step in ascertaining the clinical utility of this metric.

Victor M. Perez-Garcia

Universidad de Castilla – La Mancha, Spain
"If you have mathematical models then you have imaging biomarkers: Applications to gliomas, lung cancer, breast cancer and head & neck cancer"
The ultimate goal of mathematical models fed with imaging and molecular/clinical data is to provide prediction machines allowing to get precise estimates for patient survival, time to relapse, and to set up personalized therapeutic schedules. However, this is a very complex task due to our limited knowledge of the many biological processes involved and the scarce amount of information available today for patients. A more accessible goal is to use mathematical models to obtain qualitative information allowing to classify patients in classes according to features found to be relevant in the modelling. When those features can be obtained from medical images, we speak of imaging biomarkers. In this talk I will present different types of mathematical models and discuss how each modelling approach leads to the finding of imaging biomarkers that turn out to be true when tested on real patients imaging data. Specifically I will present: MRI-based biomarkers in glioblastoma based on either partial differential equations or discrete mesoscopic simulators [1-3], prognostic PET-based biomarkers based on the peak activity validated for lung and breast cancer [4] and PET-based prognosis biomarkers based on scaling laws for lung cancer, breast cancer, gliomas, and head & neck cancer [5]. These imaging biomarkers are all easy to implement in clinical practice since they do not require model simulations but just measurement of meaningful quantities on the images.

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