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arXiv2018

Stress-dependent amplification of active forces in nonlinear elastic media

The production of mechanical stresses in living organisms largely relies on localized, force-generating active units embedded in filamentous matrices. Numerical simulations of discrete fiber networks with fixed boundaries have shown that buckling in the matrix dramatically amplifies the resulting active stresses. Here we extend this result to a bucklable continuum elastic medium subjected to an arbitrary external stress, and derive analytical expressions for the active, nonlinear constitutive relations characterizing the full active medium. Inserting these relations into popular "active gel" descriptions of living tissues and the cytoskeleton will enable investigations into nonlinear regimes previously inaccessible due to the phenomenological nature of these theories.

physics.bio-ph↗

arXiv2018

Modeling water transport processes in dialysis

Mathematical modeling is an important theoretical tool which provides researchers with quantification of the permeability of dialyzing systems in renal replacement therapy. In the paper we provide a short review of the most successful theoretical approaches and refer to the corresponding experimental methods studying these phenomena in both biological and synthetic filters in dialysis. Two levels of modeling of fluid and solute transport are considered in the review: thermodynamic and kinetic modeling of hemodialysis and peritoneal dialysis. A brief account for hindered diffusion across cake layers formed due to membrane filters fouling is given, too.

q-bio.TO↗

arXiv2018

Continuum models of collective cell migration

Collective cell migration plays a central role in tissue development, morphogenesis, wound repair and cancer progression. With the growing realization that physical forces mediate cell motility in development and physiology, a key biological question is how cells integrate molecular activities for force generation on multicellular scales. In this review we discuss recent advances in modeling collective cell migration using quantitative tools and approaches rooted in soft matter physics. We focus on theoretical models of cell aggregates as continuous active media, where the feedback between mechanical forces and regulatory biochemistry gives rise to rich collective dynamical behavior. This class of models provides a powerful predictive framework for the physiological dynamics that underlies many developmental processes, where cells need to collectively migrate like a viscous fluid to reach a target region, and then stiffen to support mechanical stresses and maintain tissue cohesion.

physics.bio-ph↗

arXiv2018

A Two-Phase Model of Early Fibrous Cap Formation in Atherosclerosis

Atherosclerotic plaque growth is characterised by chronic inflammation that promotes accumulation of cellular debris and extracellular fat in the inner artery wall. This material is highly thrombogenic, and plaque rupture can lead to the formation of blood clots that occlude major arteries and cause myocardial infarction or stroke. In advanced plaques, vascular smooth muscle cells (SMCs) migrate from deeper in the artery wall to synthesise a cap of fibrous tissue that stabilises the plaque and sequesters the thrombogenic plaque content from the bloodstream. The fibrous cap provides crucial protection against the clinical consequences of atherosclerosis, but the mechanisms of cap formation are poorly understood. In particular, it is unclear why certain plaques become stable and robust while others become fragile and vulnerable to rupture. We develop a multiphase model with non-standard boundary conditions to investigate early fibrous cap formation in the atherosclerotic plaque. The model is parameterised using a range of in vitro and in vivo data, and includes highly nonlinear mechanisms of SMC proliferation and migration in response to an endothelium-derived chemical signal. We demonstrate that the model SMC population naturally evolves towards a steady-state, and predict a rate of cap formation and a final plaque SMC content consistent with experimental observations in mice. Parameter sensitivity simulations show that SMC proliferation makes a limited contribution to cap formation, and highlight that stable cap formation relies on a critical balance between SMC recruitment to the plaque, SMC migration within the plaque and SMC loss by apoptosis. The model represents the first detailed in silico study of fibrous cap formation in atherosclerosis, and establishes a multiphase modelling framework that can be readily extended to investigate many other aspects of plaque development.

q-bio.CB↗

arXiv2018

Early Cancer Detection in Blood Vessels Using Mobile Nanosensors

In this paper, we propose using mobile nanosensors (MNSs) for early stage anomaly detection. For concreteness, we focus on the detection of cancer cells located in a particular region of a blood vessel. These cancer cells produce and emit special molecules, so-called biomarkers, which are symptomatic for the presence of anomaly, into the cardiovascular system. Detection of cancer biomarkers with conventional blood tests is difficult in the early stages of a cancer due to the very low concentration of the biomarkers in the samples taken. However, close to the cancer cells, the concentration of the cancer biomarkers is high. Hence, detection is possible if a sensor with the ability to detect these biomarkers is placed in the vicinity of the cancer cells. Therefore, in this paper, we study the use of MNSs that are injected at a suitable injection site and can move through the blood vessels of the cardiovascular system, which potentially contain cancer cells. These MNSs can be activated by the biomarkers close to the cancer cells, where the biomarker concentration is sufficiently high. Eventually, the MNSs are collected by a fusion center (FC) where their activation levels are read and exploited to declare the presence of anomaly. We analytically derive the biomarker concentration as well as the probability mass function of the MNSs' activation levels and validate the obtained results via particle-based simulations. Then, we derive the optimal decision rule for the FC regarding the presence of anomaly assuming that the entire network is known at the FC. Finally, for the FC, we propose a simple sum detector that does not require knowledge of the network topology. Our simulations reveal that while the optimal detector achieves a higher performance than the sum detector, both proposed detectors significantly outperform a benchmark scheme that used fixed nanosensors at the FC.

q-bio.TO↗

arXiv2018

Comments on the National Toxicology Program Report on Cancer, Rats and Cell Phone Radiation

With the National Toxicology Program issuing its final report on cancer, rats and cell phone radiation, one can draw the following conclusions from their data. There is a roughly linear relationship between gliomas (brain cancers) and schwannomas (cancers of the nerve sheaths around the heart) with increased absorption of 900 MHz radiofrequency radiation for male rats. The rate of these cancers in female rats is about one third the rate in male rats; the rate of gliomas in female humans is about two thirds the rate in male humans. Both of these observations can be explained by a decrease in sensitivity to chemical carcinogenesis in both female rats and female humans. The increase in male rat life spans with increased radiofrequency absorption is due to a reduction in kidney failure from a decrease in food intake. No such similar increase in the life span of humans who use cell phones is expected.

q-bio.TO↗

arXiv2018

A Numerical Study of the Relationship Between Erectile Pressure and Shear Wave Speed of Corpus Cavernosa in Ultrasound Vibro-elastography

The objective of this study was to investigate the relationship between erectile pressure (EP) and shear wave speed of the corpus cavernosa obtained via a specific ultrasound vibro-elastography (UVE) technique. This study builds upon our prior investigation, in which UVE was used to evaluate the viscoelastic properties of the corpus cavernosa in the flaccid and erect states. A two-dimensional poroviscoelastic finite element model (FEM) was developed to simulate wave propagation in the penile tissue according to our experimental setup. Various levels of EP were applied to the corpus cavernosa, and the relationship between shear wave speed in the corpus cavernosa and EP was investigated. Results demonstrated non-linear, positive correlations between shear wave speeds in the corpus cavernosa and increasing EP at different vibration frequencies (100-200 Hz). These findings represent the first report of the impact of EP on shear wave speed and validates the use of UVE in the evaluation of men with erectile dysfunction. Further evaluations are warranted to determine the clinical utility of this instrument in the diagnosis and treatment of men with erectile dysfunction.

q-bio.TO↗

arXiv2018

Holographic Neural Architectures

Representation learning is at the heart of what makes deep learning effective. In this work, we introduce a new framework for representation learning that we call "Holographic Neural Architectures" (HNAs). In the same way that an observer can experience the 3D structure of a holographed object by looking at its hologram from several angles, HNAs derive Holographic Representations from the training set. These representations can then be explored by moving along a continuous bounded single dimension. We show that HNAs can be used to make generative networks, state-of-the-art regression models and that they are inherently highly resistant to noise. Finally, we argue that because of their denoising abilities and their capacity to generalize well from very few examples, models based upon HNAs are particularly well suited for biological applications where training examples are rare or noisy.

stat.ML↗

arXiv2018

Experimental and Numerical Evaluations of the Viscoelastic Mechanical Behavior of Arterial Tissue

The viscoelastic properties of arterial tissue dictate vessel behavior in certain disease states, injury modalities, and during some endovascular procedures. In this study, we characterized the viscoelastic mechanical response of porcine abdominal aortic tissue via uniaxial mechanical experiments on vascular tissue samples coupled with full-field surface strain measurements using the 2-D digital image correlation (DIC) technique. The measured stress relaxation response and intimal surface strain field were used to identify material parameters for a proposed viscoelastic anisotropic (VA) constitutive model of the passive arterial wall. The obtained results show that the VA constitutive model is able to capture the viscoelastic mechanical behavior of the arterial tissue over clinically-relevant time scales. The identified material model and numerical simulations provide a comprehensive description of the passive viscoelastic tissue properties of the arterial wall, and a quantitative understanding of the spatial and directional variability underlying arterial tissue mechanical behavior.

physics.med-ph↗

arXiv2020

Parameter estimation and treatment optimization in a stochastic model for immunotherapy of cancer

Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. in 2015 for modeling immunotherapy against melanoma skin cancer. First, we estimate the parameters of the deterministic limit of the model based on biological data of tumor growth in mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic Approximation Expectation Maximization algorithm. With the estimated parameters, we head back to the stochastic model and calculate the probability that the T cells all get exhausted during the treatment. We show that for some relevant parameter values, an early relapse is due to stochastic fluctuations (complete T cells exhaustion) with a non negligible probability. Then, focusing on the relapse related to the T cell exhaustion, we propose to optimize the treatment plan (treatment doses and restimulation times) by minimizing the T cell exhaustion probability in the parameter estimation ranges.

q-bio.PE↗

arXiv2018

Use of mathematical modeling to study pressure regimes in normal and Fontan blood flow circulations

We develop two mathematical lumped parameter models for blood pressure distribution in the Fontan blood flow circulation: an ODE based spatially homogeneous model and a PDE based spatially inhomogeneous model. We present numerical simulations of the cardiac pressure-volume cycle and study the effect of pulmonary resistance on cardiac output. We analyze solutions of two initial-boundary value problems for a non-linear parabolic partial differential equation (PDE models) with switching in the time dynamic boundary conditions which model blood pressure distribution in the cardiovascular system with and without Fontan surgery. We also obtain necessary conditions for parameter values of the PDE models for existence and uniqueness of non-negative bounded periodic solutions.

math.AP↗

arXiv2018

Quantitative Histopathology of Stained Tissues using Color Spatial Light Interference Microscopy (cSLIM)

Tissue biopsy evaluation in the clinic is in need of quantitative disease markers for diagnosis and, most importantly, prognosis. Among the new technologies, quantitative phase imaging (QPI) has demonstrated promise for histopathology because it reveals intrinsic tissue nanoarchitecture through the refractive index. However, a vast majority of past QPI investigations have relied on imaging unstained tissues, which disrupts the established specimen processing. Here we present color spatial light interference microscopy (cSLIM) as a new whole slide imaging modality that performs interferometric imaging with a color detector array. As a result, cSLIM yields in a single scan both the intrinsic tissue phase map and the standard color bright-field image, familiar to the pathologist. Our results on 196 breast cancer patients indicate that cSLIM can provide not only diagnostic but also prognostic information from the alignment of collagen fibers in the tumor microenvironment. The effects of staining on the tissue phase maps were corrected by a simple mathematical normalization. These characteristics are likely to reduce barriers to clinical translation for the new cSLIM technology.

physics.med-ph↗

arXiv2018

Simulation of morphogen and tissue dynamics

Morphogenesis, the process by which an adult organism emerges from a single cell, has fascinated humans for a long time. Modelling this process can provide novel insights into development and the principles that orchestrate the developmental processes. This chapter focusses on the mathematical description and numerical simulation of developmental processes. In particular, we discuss the mathematical representation of morphogen and tissue dynamics on static and grow- ing domains, as well as the corresponding tissue mechanics. In addition, we give an overview of numerical methods that are routinely used to solve the resulting systems of partial differential equations. These include the finite element method and the Lattice Boltzmann method for the discretisation as well as the arbitrary Lagrangian-Eulerian method and the Diffuse-Domain method to numerically treat deforming domains.

q-bio.TO↗

arXiv2018

Measures of Tractography Convergence

In the present work, we use information theory to understand the empirical convergence rate of tractography, a widely-used approach to reconstruct anatomical fiber pathways in the living brain. Based on diffusion MRI data, tractography is the starting point for many methods to study brain connectivity. Of the available methods to perform tractography, most reconstruct a finite set of streamlines, or 3D curves, representing probable connections between anatomical regions, yet relatively little is known about how the sampling of this set of streamlines affects downstream results, and how exhaustive the sampling should be. Here we provide a method to measure the information theoretic surprise (self-cross entropy) for tract sampling schema. We then empirically assess four streamline methods. We demonstrate that the relative information gain is very low after a moderate number of streamlines have been generated for each tested method. The results give rise to several guidelines for optimal sampling in brain connectivity analyses.

q-bio.QM↗

arXiv2018

An inverse analysis of cohesive zone model parameter values for human fibrous cap mode I tearing

Atherosclerotic plaque failure results from various pathophysiological events, with the existence of fibrous cap mode I tearing in the arterial wall, having the potential to block the aortic lumen and correspondingly induce serious clinical conditions.The aim of this study was to quantify the interfacial strength and critical energy release rate of the fibrous tissue across the thickness. in this study, an inverse analysis method via finite element modeling and simulation approach was presented. A cohesive zone model (CZM) was applied to simulate the tearing of the fibrous cap tissue under uniaxial tensile tests along the circumferential direction. A fiber-reinforced hyperelastic model (Holzapfel-Gasser-Ogden) was implemented for characterizing the mechanical properties of bulk material. With the material parameter values of HGO model from inverse analysis process as the input for the bulk material, the interfacial strength and critical energy release rate along the tearing path or failure zones are obtained through the same method as material identification process of HGO model. Results of this study demonstrate the fibrous cap tissue tearing failure processes.

q-bio.TO↗

arXiv2018

A Comparative Study of Cohesive Zone Models for Predicting Delamination Behaviors of Arterial Wall

Arterial tissue delamination, manifested as the failure between arterial layers, is a critical process in the rupture of atherosclerotic plaque, leading to potential life-threatening clinical consequences. Numerous models have been used to characterize the arterial tissue delamination. Few has investigated the effect of Cohesive Zone Model (CZM) shapes on predicting the delamination behavior of the arterial wall. In this study, four types of cohesive zone models (triangular, trapezoidal, linear-exponential and exponential-linear) were investigated to compare their predictability of the arterial wall failure. The Holzapfel-Gasser-Ogden (HGO) model was adopted for modelling the mechanical behavior of the aortic bulk material. The simulation results using CZM on the aortic media delamination were also compared with the results on mouse plaque delamination and human fibrous cap delamination. The results show that: 1) the simulation results based on the four shapes of CZMs match well with the experimental results, 2) the triangular and exponential-linear CZMs are in good agreement with the experimental force-displacement curves of mouse plaque delamination, 3) considering the viscoelastic effect of the arterial tissue, the triangular and exponential-linear CZMs match well with the experimental force-displacement curves of human fibrous cap delamination. Thus, triangular and exponential-linear CZMs can capture the arterial tissue failure response well.

q-bio.TO↗

arXiv2018

A mathematical model for chemoimmunotherapy of chronic lymphocytic leukemia

Immunotherapy is currently regarded as the most promising treatment to fight against cancer. This is particularly true in the treatment of chronic lymphocytic leukemia, an indolent neoplastic disease of B-lymphocytes which eventually causes the immune system's failure. In this and other areas of cancer research, mathematical modeling is pointed out as a prominent tool to analyze theoretical and practical issues. Its lack in studies of chemoimmunotherapy of chronic lymphocytic leukemia is what motivates us to come up with a simple ordinary differential equation model. It is based on ideas of de Pillis & Radunskaya and on standard pharmacokinetics-pharmacodynamics assumptions. In order to check the positivity of the state variables, we first establish an invariant region where these time-dependent variables remain positive. Afterwards, the action of the immune system, as well as the chemoimmunotherapeutic role in promoting cancer cure are investigated by means of numerical simulations and the classical linear stability analysis. The role of adoptive cellular immunotherapy is also addressed. Our overall conclusion is that chemoimmunotherapeutic protocols can be effective in treating chronic lymphocytic leukemia provided that chemotherapy is not a limiting factor to the immunotherapy efficacy.

q-bio.TO↗

arXiv2018

Pulsing dynamics in randomly wired glider cellular automata

Sustained rhythmic oscillations, pulsing dynamics, emerge spontaneously when the local connection scheme is randomised in 3-value cellular automata that feature"glider" dynamics. Time-plots of pulsing measures maintain a distinct waveform for each glider rule, and scatter plots of entropy/density and the density return-map show unique signatures, which have the characteristics of chaotic strange attractors. We present case studies, possible mechanisms, and implications for oscillatory networks in biology.

nlin.CG↗