Structural and practical identifiability of contrast transport models for DCE-MRI.

Contrast transport models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

The effects of intravoxel contrast agent diffusion on the analysis of DCE-MRI data in realistic tissue domains.

PURPOSE: Quantitative evaluation of dynamic contrast enhanced MRI (DCE-MRI) allows for estimating perfusion, vessel permeability, and tissue volume fractions by fitting signal intensity curves to pharmacokinetic models. These compart mental models assume rapid equilibration of contrast agent within each voxel. However, there is increasing evidence that this assumption is violated for small molecular weight gadolinium chelates. To evaluate the error introduced by this invalid assumption, we simulated DCE-MRI experiments with volume fractions computed from entire histological tumor cross-sections obtained from murine studies. METHODS: A 2D finite element model of a diffusion-compensated Tofts-Kety model was developed to simulate dynamic T1 signal intensity data. Digitized histology slices were segmented into vascular (vp ), cellular and extravascular extracellular (ve ) volume fractions. Within this domain, Ktrans (the volume transfer constant) was assigned values from 0 to 0.5 min-1 . A representative signal enhancement curve was then calculated for each imaging voxel and the resulting simulated DCE-MRI data analyzed by the extended Tofts-Kety model. RESULTS: Results indicated parameterization errors of -19.1% ± 10.6% in Ktrans , -4.92% ± 3.86% in ve , and 79.5% ± 16.8% in vp for use of Gd-DTPA over 4 tumor domains. CONCLUSION: These results indicate a need for revising the standard model of DCE-MRI to incorporate a correction for slow diffusion of contrast agent. Magn Reson Med 80:330-340, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Image-guided patient-specific optimization of catheter placement for convection-enhanced nanoparticle delivery in recurrent glioblastoma.

BACKGROUND: Proper catheter placement for convection-enhanced delivery (CED) is required to maximize tumor coverage and minimize exposure to healthy tissue. We developed an image-based model to patient-specifically optimize the catheter placement for rhenium-186 (186Re)-nanoliposomes (RNL) delivery to treat recurrent glioblastoma (rGBM). METHODS: The model consists of the 1) fluid fields generated via catheter infusion, 2) dynamic transport of RNL, and 3) transforming RNL concentration to the SPECT signal. Patient-specific tissue geometries were assigned from pre-delivery MRIs. Model parameters were personalized with either 1) individual-based calibration with longitudinal SPECT images, or 2) population-based assignment via leave-one-out cross-validation. The concordance correlation coefficient (CCC) was used to quantify the agreement between the predicted and measured SPECT signals. The model was then used to simulate RNL distributions from a range of catheter placements, resulting in a ratio of the cumulative RNL dose outside versus inside the tumor, the "off-target ratio" (OTR). Optimal catheter placement) was identified by minimizing OTR. RESULTS: Fifteen patients with rGBM from a Phase I/II clinical trial (NCT01906385) were recruited to the study. Our model, with either individual-calibrated or population-assigned parameters, achieved high accuracy (CCC > 0.80) for predicting RNL distributions up to 24 h after delivery. The optimal catheter placements identified using this model achieved a median (range) of 34.56 % (14.70 %-61.12 %) reduction on OTR at the 24 h post-delivery in comparison to the original placements. CONCLUSIONS: Our image-guided model achieved high accuracy for predicting patient-specific RNL distributions and indicates value for optimizing catheter placement for CED of radiolabeled liposomes.

Model discovery approach enables noninvasive measurement of intra-tumoral fluid transport in dynamic MRI.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a routine method to noninvasively quantify perfusion dynamics in tissues. The standard practice for analyzing DCE-MRI data is to fit an ordinary differential equation to each voxel. Recent advances in data science provide an opportunity to move beyond existing methods to obtain more accurate measurements of fluid properties. Here, we developed a localized convolutional function regression that enables simultaneous measurement of interstitial fluid velocity, diffusion, and perfusion in 3D. We validated the method computationally and experimentally, demonstrating accurate measurement of fluid dynamics in situ and in vivo. Applying the method to human MRIs, we observed tissue-specific differences in fluid dynamics, with an increased fluid velocity in breast cancer as compared to brain cancer. Overall, our method represents an improved strategy for studying interstitial flows and interstitial transport in tumors and patients. We expect that our method will contribute to the better understanding of cancer progression and therapeutic response.

Data driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables.

In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.

Structural and practical identifiability of contrast transport models for DCE-MRI.

Compartment models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

Model discovery approach enables non-invasive measurement of intra-tumoral fluid transport in dynamic MRI.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a routine method to non-invasively quantify perfusion dynamics in tissues. The standard practice for analyzing DCE-MRI data is to fit an ordinary differential equation to each voxel. Recent advances in data science provide an opportunity to move beyond existing methods to obtain more accurate measurements of fluid properties. Here, we developed a localized convolutional function regression that enables simultaneous measurement of interstitial fluid velocity, diffusion, and perfusion in 3D. We validated the method computationally and experimentally, demonstrating accurate measurement of fluid dynamics in situ and in vivo. Applying the method to human MRIs, we observed tissue-specific differences in fluid dynamics, with an increased fluid velocity in breast cancer as compared to brain cancer. Overall, our method represents an improved strategy for studying interstitial flows and interstitial transport in tumors and patients. We expect that it will contribute to the better understanding of cancer progression and therapeutic response.

Delivery strategies for cell-based therapies in the brain: overcoming multiple barriers.

Cell-based therapies to the brain are promising for the treatment of multiple brain disorders including neurodegeneration and cancers. In order to access the brain parenchyma, there are multiple physiological barriers that must be overcome depending on the route of delivery. Specifically, the blood-brain barrier has been a major difficulty in drug delivery for decades, and it still presents a challenge for the delivery of therapeutic cells. Other barriers, including the blood-cerebrospinal fluid barrier and lymphatic-brain barrier, are less explored, but may offer specific challenges or opportunities for therapeutic delivery. Here we discuss the barriers to the brain and the strategies currently in place to deliver cell-based therapies, including engineered T cells, dendritic cells, and stem cells, to treat diseases. With a particular focus on cancers, we also highlight the current ongoing clinical trials that use cell-based therapies to treat disease, many of which show promise at treating some of the deadliest illnesses.

Repeatability of tumor perfusion kinetics from dynamic contrast-enhanced MRI in glioblastoma.

BACKGROUND: Dynamic contrast-enhanced MRI (DCE-MRI) parameters have been shown to be biomarkers for treatment response in glioblastoma (GBM). However, variations in analysis and measurement methodology complicate determination of biological changes measured via DCE. The aim of this study is to quantify DCE-MRI variations attributable to analysis methodology and image quality in GBM patients. METHODS: The Extended Tofts model (eTM) and Leaky Tracer Kinetic Model (LTKM), with manually and automatically segmented vascular input functions (VIFs), were used to calculate perfusion kinetic parameters from 29 GBM patients with double-baseline DCE-MRI data. DCE-MRI images were acquired 2-5 days apart with no change in treatment. Repeatability of kinetic parameters was quantified with Bland-Altman and percent repeatability coefficient (%RC) analysis. RESULTS: The perfusion parameter with the least RC was the plasma volume fraction (v p ), with a %RC of 53%. The extra-cellular extra-vascular volume fraction (v e ) %RC was 82% and 81%, for extended Tofts-Kety Model (eTM) and LTKM respectively. The %RC of the volume transfer rate constant (K trans ) was 72% for the eTM, and 82% for the LTKM, respectively. Using an automatic VIF resulted in smaller %RCs for all model parameters, as compared to manual VIF. CONCLUSIONS: As much as 72% change in K trans (eTM, autoVIF) can be attributable to non-biological changes in the 2-5 days between double-baseline imaging. Poor K trans repeatability may result from inferior temporal resolution and short image acquisition time. This variation suggests DCE-MRI repeatability studies should be performed institutionally, using an automatic VIF method and following quantitative imaging biomarkers alliance guidelines.

Patient specific, imaging-informed modeling of rhenium-186 nanoliposome delivery via convection-enhanced delivery in glioblastoma multiforme.

Convection-enhanced delivery of rhenium-186 (186Re)-nanoliposomes is a promising approach to provide precise delivery of large localized doses of radiation for patients with recurrent glioblastoma multiforme. Current approaches for treatment planning utilizing convection-enhanced delivery are designed for small molecule drugs and not for larger particles such as186Re-nanoliposomes. To enable the treatment planning for186Re-nanoliposomes delivery, we have developed a computational fluid dynamics approach to predict the distribution of nanoliposomes for individual patients. In this work, we construct, calibrate, and validate a family of computational fluid dynamics models to predict the spatio-temporal distribution of186Re-nanoliposomes within the brain, utilizing patient-specific pre-operative magnetic resonance imaging (MRI) to assign material properties for an advection-diffusion transport model. The model family is calibrated to single photon emission computed tomography (SPECT) images acquired during and after the infusion of186Re-nanoliposomes for five patients enrolled in a Phase I/II trial (NCT Number NCT01906385), and is validated using a leave-one-out bootstrapping methodology for predicting the final distribution of the particles. After calibration, our models are capable of predicting the mid-delivery and final spatial distribution of186Re-nanoliposomes with a Dice value of 0.69 ± 0.18 and a concordance correlation coefficient of 0.88 ± 0.12 (mean ± 95% confidence interval), using only the patient-specific, pre-operative MRI data, and calibrated model parameters from prior patients. These results demonstrate a proof-of-concept for a patient-specific modeling framework, which predicts the spatial distribution of nanoparticles. Further development of this approach could enable optimizing catheter placement for future studies employing convection-enhanced delivery.

A hybrid model of tumor growth and angiogenesis: In silico experiments.

Tumor associated angiogenesis is the development of new blood vessels in response to proteins secreted by tumor cells. These new blood vessels allow tumors to continue to grow beyond what the pre-existing vasculature could support. Here, we construct a mathematical model to simulate tumor angiogenesis by considering each endothelial cell as an agent, and allowing the vascular endothelial growth factor (VEGF) and nutrient fields to impact the dynamics and phenotypic transitions of each tumor and endothelial cell. The phenotypes of the endothelial cells (i.e., tip, stalk, and phalanx cells) are selected by the local VEGF field, and govern the migration and growth of vessel sprouts at the cellular level. Over time, these vessels grow and migrate to the tumor, forming anastomotic loops to supply nutrients, while interacting with the tumor through mechanical forces and the consumption of VEGF. The model is able to capture collapsing and breaking of vessels caused by tumor-endothelial cell interactions. This is accomplished through modeling the physical interaction between the vasculature and the tumor, resulting in vessel occlusion and tumor heterogeneity over time due to the stages of response in angiogenesis. Key parameters are identified through a sensitivity analysis based on the Sobol method, establishing which parameters should be the focus of subsequent experimental efforts. During the avascular phase (i.e., before angiogenesis is triggered), the nutrient consumption rate, followed by the rate of nutrient diffusion, yield the greatest influence on the number and distribution of tumor cells. Similarly, the consumption and diffusion of VEGF yield the greatest influence on the endothelial and tumor cell numbers during angiogenesis. In summary, we present a hybrid mathematical approach that characterizes vascular changes via an agent-based model, while treating nutrient and VEGF changes through a continuum model. The model describes the physical interaction between a tumor and the surrounding blood vessels, explicitly allowing the forces of the growing tumor to influence the nutrient delivery of the vasculature.

Characterizing Trastuzumab-Induced Alterations in Intratumoral Heterogeneity with Quantitative Imaging and Immunohistochemistry in HER2+ Breast Cancer.

The purpose of this study is to investigate imaging and histology-based measurements of intratumoral heterogeneity to evaluate early treatment response to targeted therapy in a murine model of HER2+ breast cancer. BT474 tumor-bearing mice (N = 30) were treated with trastuzumab or saline and imaged longitudinally with either dynamic contrast-enhanced (DCE) magnetic resonance imaging (MRI) or 18F-fluoromisonidazole (FMISO) positron emission tomography (PET). At the imaging study end point (day 4 for MRI or 7 for PET), each tumor was excised for immunohistochemistry analysis. Voxel-based histogram analysis was performed on imaging-derived parametric maps (i.e., Ktrans and ve from DCE-MRI, SUV from 18F-FMISO-PET) of the tumor region of interest to measure heterogeneity. Image processing and histogram analysis of whole tumor slice immunohistochemistry data were performed to validate the in vivo imaging findings. Trastuzumab-treated tumors had increased heterogeneity in quantitative imaging measures of cellularity (ve), with a mean Kolmogorov-Smirnov (K-S) distance of 0.32 (P = .05) between baseline and end point distributions. Trastuzumab-treated tumors had increased vascular heterogeneity (Ktrans) and decreased hypoxic heterogeneity (SUV), with a mean K-S distance of 0.42 (P < .01) and 0.46 (P = .047), respectively, between baseline and study end points. These observations were validated by whole-slice immunohistochemistry analysis with mean interquartile range of CD31 distributions of 1.72 for treated and 0.95 for control groups (P = .02). Quantitative longitudinal changes in tumor cellular and vascular heterogeneity in response to therapy may provide evidence for early prediction of response and guide therapy for patients with HER2+ breast cancer.