Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth.

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue. This work introduces a Bayesian framework to calibrate the two-/three-dimensional spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model-predicted tumor shape.

Realistic computer modelling of stent retriever thrombectomy: a hybrid finite-element analysis-smoothed particle hydrodynamics model.

Stent retriever thrombectomy is a pre-eminent treatment modality for large vessel ischaemic stroke. Simulation of thrombectomy could help understand stent and clot mechanics in failed cases and provide a digital testbed for the development of new, safer devices. Here, we present a novel, in silico thrombectomy method using a hybrid finite-element analysis (FEA) and smoothed particle hydrodynamics (SPH). Inspired by its biological structure and components, the blood clot was modelled with the hybrid FEA-SPH method. The Solitaire self-expanding stent was parametrically reconstructed from micro-CT imaging and was modelled as three-dimensional finite beam elements. Our simulation encompassed all steps of mechanical thrombectomy, including stent packaging, delivery and self-expansion into the clot, and clot extraction. To test the feasibility of our method, we simulated clot extraction in simple straight vessels. This was compared against in vitro thrombectomies using the same stent, vessel geometry, and clot size and composition. Comparisons with benchtop tests indicated that our model was able to accurately simulate clot deflection and penetration of stent wires into the clot, the relative movement of the clot and stent during extraction, and clot fragmentation/embolus formation. In this study, we demonstrated that coupling FEA and SPH techniques could realistically model stent retriever thrombectomy.

Bayesian calibration of a stochastic, multiscale agent-based model for predicting in vitro tumor growth.

Hybrid multiscale agent-based models (ABMs) are unique in their ability to simulate individual cell interactions and microenvironmental dynamics. Unfortunately, the high computational cost of modeling individual cells, the inherent stochasticity of cell dynamics, and numerous model parameters are fundamental limitations of applying such models to predict tumor dynamics. To overcome these challenges, we have developed a coarse-grained two-scale ABM (cgABM) with a reduced parameter space that allows for an accurate and efficient calibration using a set of time-resolved microscopy measurements of cancer cells grown with different initial conditions. The multiscale model consists of a reaction-diffusion type model capturing the spatio-temporal evolution of glucose and growth factors in the tumor microenvironment (at tissue scale), coupled with a lattice-free ABM to simulate individual cell dynamics (at cellular scale). The experimental data consists of BT474 human breast carcinoma cells initialized with different glucose concentrations and tumor cell confluences. The confluence of live and dead cells was measured every three hours over four days. Given this model, we perform a time-dependent global sensitivity analysis to identify the relative importance of the model parameters. The subsequent cgABM is calibrated within a Bayesian framework to the experimental data to estimate model parameters, which are then used to predict the temporal evolution of the living and dead cell populations. To this end, a moment-based Bayesian inference is proposed to account for the stochasticity of the cgABM while quantifying uncertainties due to limited temporal observational data. The cgABM reduces the computational time of ABM simulations by 93% to 97% while staying within a 3% difference in prediction compared to ABM. Additionally, the cgABM can reliably predict the temporal evolution of breast cancer cells observed by the microscopy data with an average error and standard deviation for live and dead cells being 7.61±2.01 and 5.78±1.13, respectively.

Solution-shearing of dielectric polymer with high thermal conductivity and electric insulation.

Polymer dielectrics, an insulating material ubiquitous in electrical power systems, must be ultralight, mechanically and dielectrically strong, and very thermally conductive. However, electric and thermal transport parameters are intercorrelated in a way that works against the occurrence of thermally conductive polymer electric insulators. Here, we describe how solution gel-shearing­strained polyethylene yields an electric insulating material with an outstanding in-plane thermal conductivity of 10.74 W m−1 K−1 and an average dielectric constant of 4.1. The dielectric constant and loss of such sheared polymer electric insulators are nearly independent of the frequency and a wide temperature range. The gel-shearing aligns ultrahigh­molecular weight polymer crystalline chains for the formation of separated and aligned nanoscale fibrous arrays. Together with lattice strains and the presence of boron nitride nanosheets, the dielectric polymer shows high current density carrying and high operating temperature, which is attributed to greatly enhanced heat conduction.

Hierarchical Structural Engineering of Ultrahigh-Molecular-Weight Polyethylene.

Nature has inspired the design of next-generation lightweight architectured structural materials, for example, nacre-bearing extreme impact and paw-pad absorbing energy. Here, a bioinspired functional gradient structure, consisting of an impact-resistant hard layer and an energy-absorbing ductile layer, is applied to additively manufacture ultrahigh-molecular-weight polyethylene (UHMWPE). Its crystalline graded and directionally solidified structure enables superior impact resistance. In addition, we demonstrate nonequilibrium processing, ultrahigh strain rate pulsed laser shock wave peening, which could trigger surface hardening for enhanced crystallinity and polymer phase transformation. Moreover, we demonstrate the paw-pad-inspired soft- and hard-fiber-reinforced composite structure to absorb the impact energy. The bioinspired design and nonequilibrium processing of graded UHMWPE shed light on lightweight engineering polymer materials for impact-resistant and threat-protection applications.

A Coupled Mass Transport and Deformation Theory of Multi-constituent Tumor Growth.

We develop a general class of thermodynamically consistent, continuum models based on mixture theory with phase effects that describe the behavior of a mass of multiple interacting constituents. The constituents consist of solid species undergoing large elastic deformations and compressible viscous fluids. The fundamental building blocks framing the mixture theories consist of the mass balance law of diffusing species and microscopic (cellular scale) and macroscopic (tissue scale) force balances, as well as energy balance and the entropy production inequality derived from the first and second laws of thermodynamics. A general phase-field framework is developed by closing the system through postulating constitutive equations (i.e., specific forms of free energy and rate of dissipation potentials) to depict the growth of tumors in a microenvironment. A notable feature of this theory is that it contains a unified continuum mechanics framework for addressing the interactions of multiple species evolving in both space and time and involved in biological growth of soft tissues (e.g., tumor cells and nutrients). The formulation also accounts for the regulating roles of the mechanical deformation on the growth of tumors, through a physically and mathematically consistent coupled diffusion and deformation framework. A new algorithm for numerical approximation of the proposed model using mixed finite elements is presented. The results of numerical experiments indicate that the proposed theory captures critical features of avascular tumor growth in the various microenvironment of living tissue, in agreement with the experimental studies in the literature.

Optimal Control Theory for Personalized Therapeutic Regimens in Oncology: Background, History, Challenges, and Opportunities.

Optimal control theory is branch of mathematics that aims to optimize a solution to a dynamical system. While the concept of using optimal control theory to improve treatment regimens in oncology is not novel, many of the early applications of this mathematical technique were not designed to work with routinely available data or produce results that can eventually be translated to the clinical setting. The purpose of this review is to discuss clinically relevant considerations for formulating and solving optimal control problems for treating cancer patients. Our review focuses on two of the most widely used cancer treatments, radiation therapy and systemic therapy, as they naturally lend themselves to optimal control theory as a means to personalize therapeutic plans in a rigorous fashion. To provide context for optimal control theory to address either of these two modalities, we first discuss the major limitations and difficulties oncologists face when considering alternate regimens for their patients. We then provide a brief introduction to optimal control theory before formulating the optimal control problem in the context of radiation and systemic therapy. We also summarize examples from the literature that illustrate these concepts. Finally, we present both challenges and opportunities for dramatically improving patient outcomes via the integration of clinically relevant, patient-specific, mathematical models and optimal control theory.