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arXiv2014

Simulating Organogenesis in COMSOL: Image-based Modeling

Mathematical Modelling has a long history in developmental biology. Advances in experimental techniques and computational algorithms now permit the development of increasingly more realistic models of organogenesis. In particular, 3D geometries of developing organs have recently become available. In this paper, we show how to use image-based data for simulations of organogenesis in COMSOL Multiphysics. As an example, we use limb bud development, a classical model system in mouse developmental biology. We discuss how embryonic geometries with several subdomains can be read into COMSOL using the Matlab LiveLink, and how these can be used to simulate models on growing embryonic domains. The ALE method is used to solve signaling models even on strongly deforming domains.

cs.CE↗

arXiv2014

Travelling wave solutions of the reaction-diffusion mathematical model of glioblastoma growth: An Abel equation based approach

We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are characterized by extensive infiltration into the brain and are highly resistant to treatment. The second order nonlinear equation describing the glioblastoma growth through travelling waves can be reduced to a first order Abel type equation. By using the integrability conditions for the Abel equation several classes of exact travelling wave solutions of the general reaction-diffusion equation that describes glioblastoma growth are obtained, corresponding to different forms of the product of the diffusion and reaction functions. The solutions are obtained by using the Chiellini lemma and the Lemke transformation, respectively, and the corresponding equations represent generalizations of the classical Fisher--Kolmogorov equation. The biological implications of two classes of solutions are also investigated by using both numerical and semi-analytical methods for realistic values of the biological parameters.

q-bio.TO↗

arXiv2014

The giant low-density lipoproteins (LDL) accumulation in the multi-layer artery wall model

The mathematical, four-layer model of the LDL transport across the arterial wall including the sensitivity of the transport coefficients to the wall shear stress (WSS) is studied. In that model the advection-diffusion equations in porous media are used to determine the LDL concentration profiles in each layer of the arterial wall. We demonstrate the effect of the giant accumulation of the LDL in the intima layer. This property turns out to be an interplay between the layered structure of the arterial wall and WSS sensitivity of the endothelium. Interestingly, we also show that the single-layer models with the same WSS sensitivity mechanism and corresponding parameters, obscure the accumulation phenomenon, which predicts the one order of magnitude larger LDL concentration.

q-bio.TO↗

arXiv2014

Micronucleus induction by 915 MHz Radiofrequency Radiation in Vicia faba root tips

The mutagenic effect of radiofrequency electromagnetic field (RF-EMF) is evaluated by the micronucleus (MN) test in secondary roots of Vicia faba seedlings. Root exposures were carried out with 915 MHz continuous wave (CW) radiation for 72h, at power densities of 25, 38, 50 W/m$^2$. The specific absorption rate (SAR) corresponding to the experimental exposures was measured with a calorimetric method and fall in the range 0.3-1.8 W/kg. Results show a significant increase of MN frequency up to ten fold, correlated with the increasing power densities values.

q-bio.QM↗

arXiv2014

Stochastic model for computer simulation of the number of cancer cells and lymphocytes in homogeneous sections of cancer tumors

We deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into account natural birth and death rates. Other rates are also introduced to consider medical treatment: natural birth rate of lymphocytes and cancer cells; induced death rate of cancer cells due to self-competition, and other ones caused by the activated lymphocytes acting on cancer cells. Additionally, a death rate of cancer cells due to induced apoptosis is considered. Weakness due to the advance of sickness is considered by introducing a lymphocytes death rate proportional to proliferation of cancer cells. Simulation is developed considering different combinations of the parameters and its values, so that several strategies are taken into account to study the effect of anti-angiogenic drugs as well the self-competition between cancer cells. Immune response, with the presence of a kind of specialized lymphocytes, is introduced such that they appear once cancer cells are detected. Induced apoptosis of cancer cells is introduced to model the action of several drugs under development right now. Besides, the model predicts the cancer relapse even from a very small number of cells. Simulation is done by using Gillespie algorithm.

physics.med-ph↗

arXiv2014

Simulating Organogenesis: Algorithms for the Image-based Determination of Displacement Fields

Recent advances in imaging technology now provide us with 3D images of developing organs. These can be used to extract 3D geometries for simulations of organ development. To solve models on growing domains, the displacement fields between consecutive image frames need to be determined. Here we develop and evaluate different landmark-free algorithms for the determination of such displacement fields from image data. In particular, we examine minimal distance, normal distance, diffusion-based and uniform mapping algorithms and test these algorithms with both synthetic and real data in 2D and 3D. We conclude that in most cases the normal distance algorithm is the method of choice and wherever it fails, diffusion-based mapping provides a good alternative.

q-bio.QM↗

arXiv2014

TiQuant: Software for tissue analysis, quantification and surface reconstruction

Motivation: TiQuant is a modular software tool for efficient quantification of biological tissues based on volume data obtained by biomedical image modalities. It includes a number of versatile image and volume processing chains tailored to the analysis of different tissue types which have been experimentally verified. TiQuant implements a novel method for the reconstruction of three-dimensional surfaces of biological systems, data that often cannot be obtained experimentally but which is of utmost importance for tissue modelling in systems biology. Availability: TiQuant is freely available for non-commercial use at msysbio.com/tiquant. Windows, OSX and Linux are supported.

cs.CE↗

arXiv2014

A Multidomain Model for Ionic Electrodiffusion and Osmosis with an Application to Cortical Spreading Depression

Ionic electrodiffusion and osmotic water flow are central processes in many physiological systems. We formulate a system of partial differential equations that governs ion movement and water flow in biological tissue. A salient feature of this model is that it satisfies a free energy identity, ensuring the thermodynamic consistency of the model. A numerical scheme is developed for the model in one spatial dimension and is applied to a model of cortical spreading depression, a propagating breakdown of ionic and cell volume homeostasis in the brain.

q-bio.TO↗

arXiv2014

Modeling Age-Dependent Radiation-Induced Second Cancer Risks and Estimation of Mutation Rate: An Evolutionary Approach

Although the survival rate of cancer patients has significantly increased due to advances in anti-cancer therapeutics, one of the major side effects of these therapies, particularly radiotherapy, is the potential manifestation of radiation-induced secondary malignancies. In this work, a novel evolutionary stochastic model is introduced that couples short-term formalism (during radiotherapy) and long-term formalism (post treatment). This framework is used to estimate the risks of second cancer as a function of spontaneous background and radiation-induced mutation rates of normal and pre-malignant cells. By fitting the model to available clinical data for spontaneous background risk together with data of Hodgkins lymphoma survivors (for various organs), the second cancer mutation rate is estimated. The model predicts a significant increase in mutation rate for some cancer types, which may be a sign of genomic instability. Finally, it is shown that the model results are in agreement with the measured results for excess relative risk (ERR) as a function of exposure age, and that the model predicts a negative correlation of ERR with increase in attained age. This novel approach can be used to analyze several radiotherapy protocols in current clinical practice, and to forecast the second cancer risks over time for individual patients.

q-bio.QM↗

arXiv2015

A poroelastic model coupled to a fluid network with applications in lung modelling

Here we develop a lung ventilation model, based a continuum poroelastic representation of lung parenchyma and a 0D airway tree flow model. For the poroelastic approximation we design and implement a lowest order stabilised finite element method. This component is strongly coupled to the 0D airway tree model. The framework is applied to a realistic lung anatomical model derived from computed tomography data and an artificially generated airway tree to model the conducting airway region. Numerical simulations produce physiologically realistic solutions, and demonstrate the effect of airway constriction and reduced tissue elasticity on ventilation, tissue stress and alveolar pressure distribution. The key advantage of the model is the ability to provide insight into the mutual dependence between ventilation and deformation. This is essential when studying lung diseases, such as chronic obstructive pulmonary disease and pulmonary fibrosis. Thus the model can be used to form a better understanding of integrated lung mechanics in both the healthy and diseased states.

physics.comp-ph↗

arXiv2014

Connecting local active forces to macroscopic stress in elastic media

In contrast with ordinary materials, living matter drives its own motion by generating active, out-of-equilibrium internal stresses. These stresses typically originate from localized active elements embedded in an elastic medium, such as molecular motors inside the cell or contractile cells in a tissue. While many large-scale phenomenological theories of such active media have been developed, a systematic understanding of the emergence of stress from the local force-generating elements is lacking. In this paper, we present a rigorous theoretical framework to study this relationship. We show that the medium's macroscopic active stress tensor is equal to the active elements' force dipole tensor per unit volume in both continuum and discrete linear homogeneous media of arbitrary geometries. This relationship is conserved on average in the presence of disorder, but can be violated in nonlinear elastic media. Such effects can lead to either a reinforcement or an attenuation of the active stresses, giving us a glimpse of the ways in which nature might harness microscopic forces to create active materials.

cond-mat.soft↗

arXiv2014

Exact Modeling of Cardiovascular System Using Lumped Method

Electrical analogy (Lumped method) is an easy way to model human cardiovascular system. In this paper Lumped method is used for simulating a complete model. It describes a 36-vessel model and cardiac system of human body with details that could show hydrodynamic parameters of cardiovascular system. Also this paper includes modeling of pulmonary, atrium, left and right ventricles with their equivalent circuits. Exact modeling of right and left ventricles pressure increases the accuracy of our simulation. In this paper we show that a calculated pressure for aorta from our complex circuit is near to measured pressure by using advanced medical instruments.

physics.med-ph↗

arXiv2014

High-throughput screening for modulators of cellular contractile force

When cellular contractile forces are central to pathophysiology, these forces comprise a logical target of therapy. Nevertheless, existing high-throughput screens are limited to upstream signaling intermediates with poorly defined relationship to such a physiological endpoint. Using cellular force as the target, here we screened libraries to identify novel drug candidates in the case of human airway smooth muscle cells in the context of asthma, and also in the case of Schlemm's canal endothelial cells in the context of glaucoma. This approach identified several drug candidates for both asthma and glaucoma. We attained rates of 1000 compounds per screening day, thus establishing a force-based cellular platform for high-throughput drug discovery.

physics.bio-ph↗

arXiv2014

Emergence of Anti-Cancer Drug Resistance: Exploring the Importance of the Microenvironmental Niche via a Spatial Model

Practically, all chemotherapeutic agents lead to drug resistance. Clinically, it is a challenge to determine whether resistance arises prior to, or as a result of, cancer therapy. Further, a number of different intracellular and microenvironmental factors have been correlated with the emergence of drug resistance. With the goal of better understanding drug resistance and its connection with the tumor microenvironment, we have developed a hybrid discrete-continuous mathematical model. In this model, cancer cells described through a particle-spring approach respond to dynamically changing oxygen and DNA damaging drug concentrations described through partial differential equations. We thoroughly explored the behavior of our self-calibrated model under the following common conditions: a fixed layout of the vasculature, an identical initial configuration of cancer cells, the same mechanism of drug action, and one mechanism of cellular response to the drug. We considered one set of simulations in which drug resistance existed prior to the start of treatment, and another set in which drug resistance is acquired in response to treatment. This allows us to compare how both kinds of resistance influence the spatial and temporal dynamics of the developing tumor, and its clonal diversity. We show that both pre-existing and acquired resistance can give rise to three biologically distinct parameter regimes: successful tumor eradication, reduced effectiveness of drug during the course of treatment (resistance), and complete treatment failure.

q-bio.PE↗

arXiv2014

Gastric Slow Wave Modelling Based on Stomach Morphology and Neuronal Firings

Gastric content's mass and pH commonly assessed invasively using endoscopic biopsy, or semi-invasively using swallowable transducer. EGG (electrogastrography) is a technique for observing gastric myoelectrical activity non-invasively, that could be designed as mobile device. In this research, 72 EGG recordings were obtained from 13 local white rabbit (Oryctolagus cuniculus). Recorded EGG processed using SCILAB 5.5.1 package. Signal processing consists of waveform identification altogether with recognition of resting, depolarization, ECA plateau, and repolarization segments of each EGG in the time domain based on amplitude and temporal filter. All rabbits were sacrificed after the recording in order to obtain its stomach content's mass and pH data. EGG waveform generator based on gastric morphological neuron assembly modeled using those data. If this model proved to be accurate, the mass and pH from rabbit (Oryctolagus cuniculus)'s stomach content could be assessed non-invasively, and could be a basis for human (Homo sapiens) trial.

q-bio.TO↗

arXiv2014

A Stochastic Model for the Normal Tissue Complication Probability (NTCP) in Radiation Treatment of Cancer

The normal tissue complication probability (NTCP) is a measure for the estimated side effects of a given radiation treatment schedule. Here we use a stochastic logistic birth death process to define an organ specific and patient specific NTCP. We emphasise an asymptotic simplification which relates the NTCP to the solution of a logistic differential equation. This framework allows for a direct use of the NTCP model in clinical practice. We formulate, but do not solve, related optimization problems.

q-bio.TO↗

arXiv2014

Correlations between Chondroitin Sulfate Physicochemical Properties and its in-vitro Absorption and Anti-inflammatory Activity

Here, we investigated the influence of physicochemical characteristics of chondroitin sulfate (CS) on its in vitro absorption and anti-inflammatory activity. We used eight different synthetic and natural CS samples with a range of molecular weights (7-35 kDa) and sulfation patterns. Our studies indicate that the absorption of CS is moderately correlated to percentage of chondroitin-6-sulfate while the anti-inflammatory activity may be weakly related to the molecular weight and the amount of total sulfation in the samples. Our in vitro studies could provide helpful screening tools for quick and effective evaluation of CS samples as a preliminary step towards in vivo studies.

q-bio.TO↗

arXiv2014

Mathematical modeling of type 1 diabetes in the NOD mouse: separating incidence and age of onset

Type 1 diabetes (T1D) is an autoimmune disease of the beta cells of the pancreas. The nonobese diabetic (NOD) mouse is a commonly used animal model, with roughly an 80% incidence rate of T1D among females. In 100% of NOD mice, macrophages and T-cells invade the islets in a process called insulitis. It can be several weeks between insulitis and T1D, and some mice do not progress at all. It is thought that this delay is mediated by regulatory T-cells (Tregs) and that a gradual loss of effectiveness in this population leads to T1D. However, this does not explain why some mice progress and others do not. We propose a simple mathematical model of the interaction between beta cells and the immune populations, including regulatory T-cells. We find that individual mice may enter one of two stable steady states: a `mild' insulitis state that does not progress to T1D and a `severe' insulitis state that does. We then run a sensitivity analysis to identify which parameters affect incidence of T1D versus those that affect age of onset. We also test the model by simulating several experimental manipulations found in the literature that modify insulitis severity and/or Treg activity. Notably, we are able to match a reproduce a large number of phenomena using a relatively small number of equations. We finish by proposing experiments that could help validate or refine the model.

q-bio.TO↗