Leveraging Mathematical Modeling to Quantify Pharmacokinetic and Pharmacodynamic Pathways: Equivalent Dose Metric

Treatment response assays are often summarized by sigmoidal functions comparing cell survival at a single timepoint to applied drug concentration. This approach has a limited biophysical basis, thereby reducing the biological insight gained from such analysis. In particular, drug pharmacokinetic and pharmacodynamic (PK/PD) properties are overlooked in developing treatment response assays, and the accompanying summary statistics conflate these processes. Here, we utilize mathematical modeling to decouple and quantify PK/PD pathways. We experimentally modulate specific pathways with small molecule inhibitors and filter the results with mechanistic mathematical models to obtain quantitative measures of those pathways. Specifically, we investigate the response of cells to time-varying doxorubicin treatments, modulating doxorubicin pharmacology with small molecules that inhibit doxorubicin efflux from cells and DNA repair pathways. We highlight the practical utility of this approach through proposal of the “equivalent dose metric.” This metric, derived from a mechanistic PK/PD model, provides a biophysically-based measure of drug effect. We define equivalent dose as the functional concentration of drug that is bound to the nucleus following therapy. This metric can be used to quantify drivers of treatment response and potentially guide dosing of combination therapies. We leverage the equivalent dose metric to quantify the specific intracellular effects of these small molecule inhibitors using population-scale measurements, and to compare treatment response in cell lines differing in expression of drug efflux pumps. More generally, this approach can be leveraged to quantify the effects of various pharmaceutical and biologic perturbations on treatment response

Real-Time Compressive Sensing MRI Reconstruction Using GPU Computing and Split Bregman Methods

Compressive sensing (CS) has been shown to enable dramatic acceleration of MRI acquisition in some applications. Being an iterative reconstruction technique, CS MRI reconstructions can be more time-consuming than traditional inverse Fourier reconstruction. We have accelerated our CS MRI reconstruction by factors of up to 27 by using a split Bregman solver combined with a graphics processing unit (GPU) computing platform. The increases in speed we find are similar to those we measure for matrix multiplication on this platform, suggesting that the split Bregman methods parallelize efficiently. We demonstrate that the combination of the rapid convergence of the split Bregman algorithm and the massively parallel strategy of GPU computing can enable real-time CS reconstruction of even acquisition data matrices of dimension 40962 or more, depending on available GPU VRAM. Reconstruction of two-dimensional data matrices of dimension 10242 and smaller took ~0.3 s or less, showing that this platform also provides very fast iterative reconstruction for small-to-moderate size images

Current and Future Trends in Magnetic Resonance Imaging Assessments of the Response of Breast Tumors to Neoadjuvant Chemotherapy

The current state-of-the-art assessment of treatment response in breast cancer is based on the response evaluation criteria in solid tumors (RECIST). RECIST reports on changes in gross morphology and divides response into one of four categories. In this paper we highlight how dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) and diffusion-weighted MRI (DW-MRI) may be able to offer earlier, and more precise, information on treatment response in the neoadjuvant setting than RECIST. We then describe how longitudinal registration of breast images and the incorporation of intelligent bioinformatics approaches with imaging data have the potential to increase the sensitivity of assessing treatment response. We conclude with a discussion of the potential benefits of breast MRI at the higher field strength of 3T. For each of these areas, we provide a review, illustrative examples from clinical trials, and offer insights into future research directions

Predicting High-Grade Glioma Response to Chemoradiation via MRI-Calibrated

https://openworks.mdanderson.org/sumexp21/1085/thumbnail.jp

An untrained deep learning method for reconstructing dynamic magnetic resonance images from accelerated model-based data

The purpose of this work is to implement physics-based regularization as a stopping condition in tuning an untrained deep neural network for reconstructing MR images from accelerated data. The ConvDecoder neural network was trained with a physics-based regularization term incorporating the spoiled gradient echo equation that describes variable-flip angle (VFA) data. Fully-sampled VFA k-space data were retrospectively accelerated by factors of R={8,12,18,36} and reconstructed with ConvDecoder (CD), ConvDecoder with the proposed regularization (CD+r), locally low-rank (LR) reconstruction, and compressed sensing with L1-wavelet regularization (L1). Final images from CD+r training were evaluated at the \emph{argmin} of the regularization loss; whereas the CD, LR, and L1 reconstructions were chosen optimally based on ground truth data. The performance measures used were the normalized root-mean square error, the concordance correlation coefficient (CCC), and the structural similarity index (SSIM). The CD+r reconstructions, chosen using the stopping condition, yielded SSIMs that were similar to the CD (p=0.47) and LR SSIMs (p=0.95) across R and that were significantly higher than the L1 SSIMs (p=0.04). The CCC values for the CD+r T1 maps across all R and subjects were greater than those corresponding to the L1 (p=0.15) and LR (p=0.13) T1 maps, respectively. For R > 12 (<4.2 minutes scan time), L1 and LR T1 maps exhibit a loss of spatially refined details compared to CD+r. We conclude that the use of an untrained neural network together with a physics-based regularization loss shows promise as a measure for determining the optimal stopping point in training without relying on fully-sampled ground truth data.Comment: 45 pages, 7 figures, 2 Tables, supplementary material included (10 figures, 4 tables

Patient-specific, mechanistic models of tumor growth incorporating artificial intelligence and big data

Despite the remarkable advances in cancer diagnosis, treatment, and management that have occurred over the past decade, malignant tumors remain a major public health problem. Further progress in combating cancer may be enabled by personalizing the delivery of therapies according to the predicted response for each individual patient. The design of personalized therapies requires patient-specific information integrated into an appropriate mathematical model of tumor response. A fundamental barrier to realizing this paradigm is the current lack of a rigorous, yet practical, mathematical theory of tumor initiation, development, invasion, and response to therapy. In this review, we begin by providing an overview of different approaches to modeling tumor growth and treatment, including mechanistic as well as data-driven models based on ``big data" and artificial intelligence. Next, we present illustrative examples of mathematical models manifesting their utility and discussing the limitations of stand-alone mechanistic and data-driven models. We further discuss the potential of mechanistic models for not only predicting, but also optimizing response to therapy on a patient-specific basis. We then discuss current efforts and future possibilities to integrate mechanistic and data-driven models. We conclude by proposing five fundamental challenges that must be addressed to fully realize personalized care for cancer patients driven by computational models

Using Dynamic Contrast-Enhanced Magnetic Resonance Imaging Data to Constrain a Positron Emission Tomography Kinetic Model: Theory and Simulations

We show how dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data can constrain a compartmental model for analyzing dynamic positron emission tomography (PET) data. We first develop the theory that enables the use of DCE-MRI data to separate whole tissue time activity curves (TACs) available from dynamic PET data into individual TACs associated with the blood space, the extravascular-extracellular space (EES), and the extravascular-intracellular space (EIS). Then we simulate whole tissue TACs over a range of physiologically relevant kinetic parameter values and show that using appropriate DCE-MRI data can separate the PET TAC into the three components with accuracy that is noise dependent. The simulations show that accurate blood, EES, and EIS TACs can be obtained as evidenced by concordance correlation coefficients >0.9 between the true and estimated TACs. Additionally, provided that the estimated DCE-MRI parameters are within 10% of their true values, the errors in the PET kinetic parameters are within approximately 20% of their true values. The parameters returned by this approach may provide new information on the transport of a tracer in a variety of dynamic PET studies

Predicting response to combination evofosfamide and immunotherapy under hypoxic conditions in murine models of colon cancer

The goal of this study is to develop a mathematical model that captures the interaction between evofosfamide, immunotherapy, and the hypoxic landscape of the tumor in the treatment of tumors. Recently, we showed that evofosfamide, a hypoxia-activated prodrug, can synergistically improve treatment outcomes when combined with immunotherapy, while evofosfamide alone showed no effects in an in vivo syngeneic model of colorectal cancer. However, the mechanisms behind the interaction between the tumor microenvironment in the context of oxygenation (hypoxic, normoxic), immunotherapy, and tumor cells are not fully understood. To begin to understand this issue, we develop a system of ordinary differential equations to simulate the growth and decline of tumors and their vascularization (oxygenation) in response to treatment with evofosfamide and immunotherapy (6 combinations of scenarios). The model is calibrated to data from in vivo experiments on mice implanted with colon adenocarcinoma cells and longitudinally imaged with [18F]-fluoromisonidazole ([18F]FMISO) positron emission tomography (PET) to quantify hypoxia. The results show that evofosfamide is able to rescue the immune response and sensitize hypoxic tumors to immunotherapy. In the hypoxic scenario, evofosfamide reduces tumor burden by $45.07 \pm 2.55$%, compared to immunotherapy alone, as measured by tumor volume. The model accurately predicts the temporal evolution of five different treatment scenarios, including control, hypoxic tumors that received immunotherapy, normoxic tumors that received immunotherapy, evofosfamide alone, and hypoxic tumors that received combination immunotherapy and evofosfamide. The average concordance correlation coefficient (CCC) between predicted and observed tumor volume is $0.86 \pm 0.05$. Interestingly, the model values to fit those five treatment arms was unable to accurately predict the response of normoxic tumors to combination evofosfamide and immunotherapy (CCC = $-0.064 \pm 0.003$). However, guided by the sensitivity analysis to rank the most influential parameters on the tumor volume, we found that increasing the tumor death rate due to immunotherapy by a factor of $18.6 \pm 9.3$ increases CCC of $0.981 \pm 0.001$. To the best of our knowledge, this is the first study to mathematically predict and describe the increased efficacy of immunotherapy following evofosfamide