Fully Automatic Calibration of Tumor-Growth Models Using a Single mpMRI Scan

MRI-based digital twins to improve treatment response of breast cancer by optimizing neoadjuvant chemotherapy regimens

We developed a practical framework to construct digital twins for predicting and optimizing triple-negative breast cancer (TNBC) response to neoadjuvant chemotherapy (NAC). This study employed 105 TNBC patients from the ARTEMIS trial (NCT02276443, registered on 10/21/2014) who received Adriamycin/Cytoxan (A/C)-Taxol (T). Digital twins were established by calibrating a biology-based mathematical model to patient-specific MRI data, which accurately predicted pathological complete response (pCR) with an AUC of 0.82. We then used each patient's twin to theoretically optimize outcome by identifying their optimal A/C-T schedule from 128 options. The patient-specifically optimized treatment yielded a significant improvement in pCR rate of 20.95-24.76%. Retrospective validation was conducted by virtually treating the twins with AC-T schedules from historical trials and obtaining identical observations on outcomes: bi-weekly A/C-T outperforms tri-weekly A/C-T, and weekly/bi-weekly T outperforms tri-weekly T. This proof-of-principle study demonstrates that our digital twin framework provides a practical methodology to identify patient-specific TNBC treatment schedules.

Identifiability and model selection frameworks for models of high-grade glioma response to chemoradiation

We have developed a family of biology-based mathematical models of high-grade glioma (HGG), capturing the key features of tumour growth and response to chemoradiation. We now seek to quantify the accuracy of parameter estimation and determine, when given a virtual patient cohort, which model was used to generate the tumours. In this way, we systematically test both the parameter and model identifiability. Virtual patients are generated from unique growth parameters whose growth dynamics are determined by the model family. We then assessed the ability to recover model parameters and select the model used to generate the tumour. We then evaluated the accuracy of predictions using the selected model at four weeks post-chemoradiation. We observed median parameter errors from 0.04% to 72.96%. Our model selection framework selected the model that was used to generate the data in 82% of the cases. Finally, we predicted the growth of the virtual tumours using the selected model resulting in low error at the voxel-level (concordance correlation coefficient (CCC) ranged from 0.66 to 0.99) and global level (percentage error in total tumour cellularity ranged from -12.35% to 0.07%). These results demonstrate the reliability of our framework to identify the most appropriate model under noisy conditions expected in the clinical setting.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 2)'.

Personalized predictions of Glioblastoma infiltration: Mathematical models, Physics-Informed Neural Networks and multimodal scans

Predicting the infiltration of Glioblastoma (GBM) from medical MRI scans is crucial for understanding tumor growth dynamics and designing personalized radiotherapy treatment plans. Mathematical models of GBM growth can complement the data in the prediction of spatial distributions of tumor cells. However, this requires estimating patient-specific parameters of the model from clinical data, which is a challenging inverse problem due to limited temporal data and the limited time between imaging and diagnosis. This work proposes a method that uses Physics-Informed Neural Networks (PINNs) to estimate patient-specific parameters of a reaction-diffusion partial differential equation (PDE) model of GBM growth from a single 3D structural MRI snapshot. PINNs embed both the data and the PDE into a loss function, thus integrating theory and data. Key innovations include the identification and estimation of characteristic non-dimensional parameters, a pre-training step that utilizes the non-dimensional parameters and a fine-tuning step to determine the patient specific parameters. Additionally, the diffuse-domain method is employed to handle the complex brain geometry within the PINN framework. The method is validated on both synthetic and patient datasets, showing promise for personalized GBM treatment through parametric inference within clinically relevant timeframes.

Modeling free tumor growth: Discrete, continuum, and hybrid approaches to interpreting cancer development

Tumor growth dynamics serve as a critical aspect of understanding cancer progression and treatment response to mitigate one of the most pressing challenges in healthcare. The in silico approach to understanding tumor behavior computationally provides an efficient, cost-effective alternative to wet-lab examinations and are adaptable to different environmental conditions, time scales, and unique patient parameters. As a result, this paper explored modeling of free tumor growth in cancer, surveying contemporary literature on continuum, discrete, and hybrid approaches. Factors like predictive power and high-resolution simulation competed against drawbacks like simulation load and parameter feasibility in these models. Understanding tumor behavior in different scenarios and contexts became the first step in advancing cancer research and revolutionizing clinical outcomes.

Designing clinical trials for patients who are not average

The heterogeneity inherent in cancer means that even a successful clinical trial merely results in a therapeutic regimen that achieves, on average, a positive result only in a subset of patients. The only way to optimize an intervention for an individual patient is to reframe their treatment as their own, personalized trial. Toward this goal, we formulate a computational framework for performing personalized trials that rely on four mathematical techniques. First, mathematical models that can be calibrated with patient-specific data to make accurate predictions of response. Second, digital twins built on these models capable of simulating the effects of interventions. Third, optimal control theory applied to the digital twins to optimize outcomes. Fourth, data assimilation to continually update and refine predictions in response to therapeutic interventions. In this perspective, we describe each of these techniques, quantify their "state of readiness", and identify use cases for personalized clinical trials.

Ensemble Inversion for Brain Tumor Growth Models With Mass Effect

We propose a method for extracting physics-based biomarkers from a single multiparametric Magnetic Resonance Imaging (mpMRI) scan bearing a glioma tumor. We account for mass effect, the deformation of brain parenchyma due to the growing tumor, which on its own is an important radiographic feature but its automatic quantification remains an open problem. In particular, we calibrate a partial differential equation (PDE) tumor growth model that captures mass effect, parameterized by a single scalar parameter, tumor proliferation, migration, while localizing the tumor initiation site. The single-scan calibration problem is severely ill-posed because the precancerous, healthy, brain anatomy is unknown. To address the ill-posedness, we introduce an ensemble inversion scheme that uses a number of normal subject brain templates as proxies for the healthy precancer subject anatomy. We verify our solver on a synthetic dataset and perform a retrospective analysis on a clinical dataset of 216 glioblastoma (GBM) patients. We analyze the reconstructions using our calibrated biophysical model and demonstrate that our solver provides both global and local quantitative measures of tumor biophysics and mass effect. We further highlight the improved performance in model calibration through the inclusion of mass effect in tumor growth models-including mass effect in the model leads to 10% increase in average dice coefficients for patients with significant mass effect. We further evaluate our model by introducing novel biophysics-based features and using them for survival analysis. Our preliminary analysis suggests that including such features can improve patient stratification and survival prediction.

Modeling of glioma growth using modified reaction-diffusion equation on brain MR images

BACKGROUND AND OBJECTIVE

Modeling of glioma growth and evolution is of key importance for cancer diagnosis, predicting clinical progression and improving treatment outcomes of neurosurgery. However, existing models are unable to characterize spatial variations of the proliferation and infiltration of tumor cells, making it difficult to achieve accurate prediction of tumor growth.

METHODS

In this paper, a new growth model of brain tumor using a reaction-diffusion equation on brain magnetic resonance images is proposed. Both the heterogeneity of brain tissue and the density of tumor cells are used to estimate the proliferation and diffusion coefficients of brain tumor cells. The diffusion coefficient that characterizes tumor diffusion and infiltration is calculated based on the ratio of tissues (white and gray matter), while the proliferation coefficient is evaluated using the spatial gradient of tumor cells. In addition, a parameter space is constructed using inverse distance weighted interpolation to describe the spatial distribution of proliferation coefficient.

RESULTS

The glioma growth predicted by the proposed model were tested by comparing with the real magnetic resonance images of the patients. Experiments and simulation results show that the proposed method achieves accurate modeling of glioma growth. The interpolation-based growth model has higher average dice score of 0.0647 and 0.0545, and higher average Jaccard index of 0.0673 and 0.0573, respectively, compared to the uniform- and gradient-based growth models.

CONCLUSIONS

The experimental results demonstrate the feasibility of calculating the proliferation and diffusion coefficients of the growth model based on patient-specific anatomy. The parameter space that characterizes spatial distribution of proliferation and diffusion coefficients is established and incorporated into the simulation of glioma growth. It enables to obtain patient-specific models about glioma growth by estimating and calibrating only a few model parameters.

Integrating mechanism-based modeling with biomedical imaging to build practical digital twins for clinical oncology

Digital twins employ mathematical and computational models to virtually represent a physical object (e.g., planes and human organs), predict the behavior of the object, and enable decision-making to optimize the future behavior of the object. While digital twins have been widely used in engineering for decades, their applications to oncology are only just emerging. Due to advances in experimental techniques quantitatively characterizing cancer, as well as advances in the mathematical and computational sciences, the notion of building and applying digital twins to understand tumor dynamics and personalize the care of cancer patients has been increasingly appreciated. In this review, we present the opportunities and challenges of applying digital twins in clinical oncology, with a particular focus on integrating medical imaging with mechanism-based, tissue-scale mathematical modeling. Specifically, we first introduce the general digital twin framework and then illustrate existing applications of image-guided digital twins in healthcare. Next, we detail both the imaging and modeling techniques that provide practical opportunities to build patient-specific digital twins for oncology. We then describe the current challenges and limitations in developing image-guided, mechanism-based digital twins for oncology along with potential solutions. We conclude by outlining five fundamental questions that can serve as a roadmap when designing and building a practical digital twin for oncology and attempt to provide answers for a specific application to brain cancer. We hope that this contribution provides motivation for the imaging science, oncology, and computational communities to develop practical digital twin technologies to improve the care of patients battling cancer.

Deep Learning for Reaction-Diffusion Glioma Growth Modeling: Towards a Fully Personalized Model?

Simple Summary

Mathematical tumor growth models have been proposed for decades to capture the growth of gliomas, an aggressive form of brain tumor. However, the estimation of the tumor cell-density distribution at diagnosis and model parameters from partial observations provided by magnetic resonance imaging are ill-posed problems. In this work, we propose a deep learning-based approach to address these problems. 1200 synthetic tumors are first generated using the mathematical model over brain geometries of 6 volunteers. Two deep convolutional neural networks are then trained to (i) reconstruct a whole tumor cell-density distribution and (ii) evaluate the model parameters from partial observations provided in the form of threshold-like imaging contours, with state-of-the-art results. From the estimated cell-density distribution and parameter values, the spatio-temporal evolution of the tumor can ultimately be accurately captured by the mathematical model. Such an approach could be of great interest for glioma characterization and therapy planning.

Abstract

Reaction-diffusion models have been proposed for decades to capture the growth of gliomas, the most common primary brain tumors. However, ill-posedness of the initialization at diagnosis time and parameter estimation of such models have restrained their clinical use as a personalized predictive tool. In this work, we investigate the ability of deep convolutional neural networks (DCNNs) to address commonly encountered pitfalls in the field. Based on 1200 synthetic tumors grown over real brain geometries derived from magnetic resonance (MR) data of six healthy subjects, we demonstrate the ability of DCNNs to reconstruct a whole tumor cell-density distribution from only two imaging contours at a single time point. With an additional imaging contour extracted at a prior time point, we also demonstrate the ability of DCNNs to accurately estimate the individual diffusivity and proliferation parameters of the model. From this knowledge, the spatio-temporal evolution of the tumor cell-density distribution at later time points can ultimately be precisely captured using the model. We finally show the applicability of our approach to MR data of a real glioblastoma patient. This approach may open the perspective of a clinical application of reaction-diffusion growth models for tumor prognosis and treatment planning.

CLAIRE: Constrained Large Deformation Diffeomorphic Image Registration on Parallel Computing Architectures

CLAIRE (Mang & Biros, 2019) is a computational framework for Constrained LArge deformation diffeomorphic Image REgistration (Mang et al., 2019). It supports highly-optimized, parallel computational kernels for (multi-node) CPU (Gholami et al., 2017; Mang et al., 2019; Mang & Biros, 2016) and (multi-node multi-)GPU architectures (Brunn et al., 2020, 2021). CLAIRE uses MPI for distributed-memory parallelism and can be scaled up to thousands of cores (Mang et al., 2019; Mang & Biros, 2016) and GPU devices (Brunn et al., 2020). The multi-GPU implementation uses device direct communication. The computational kernels are interpolation for semi-Lagrangian time integration, and a mixture of high-order finite difference operators and Fast-Fourier-Transforms (FFTs) for differentiation. CLAIRE uses a Newton-Krylov solver for numerical optimization (Mang & Biros, 2015, 2017). It features various schemes for regularization of the control problem (Mang & Biros, 2016) and different similarity measures. CLAIRE implements different preconditioners for the reduced space Hessian (Brunn et al., 2020; Mang et al., 2019) to optimize computational throughput and enable fast convergence. It uses PETSc (Balay et al., n.d.) for scalable and efficient linear algebra operations and solvers and TAO (Balay et al., n.d.; Munson et al., 2015) for numerical optimization. CLAIRE can be downloaded at https://github.com/andreasmang/claire.