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arXiv2015

A model of fractional-order diffusion in the glial scar

Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, which is thought to be detrimental for the neurons surrounding the electrode. Mechanisms of this type of neuroinflammation are still not understood well. Recent experimental and theoretical results point out possible role of the diffusion species in this process. The paper considers a model of anomalous diffusion occurring in the glial scar around a chronic implant in two simple geometries -- a separable rectilinear electrode and a cylindrical electrode, which are solvable exactly. We describe a hypothetical extended source of diffusing species and study its concentration profile in steady-state conditions. Diffusion transport is assumed to obey a fractional-order Fick law, which is derived from physically realistic assumptions using a fractional calculus approach. The derived fractional-order distribution morphs into regular order diffusion in the case of integer fractional exponents. The model presented here demonstrates that accumulation of diffusing species can occur and the scar properties (i.e. tortuosity, fractional order, scar thickness) can influence such accumulation. The observed shape of the concentration profile corresponds qualitatively with GFAP profiles reported in the literature. The main difference with respect to the previous studies is the explicit incorporation of the apparatus of fractional calculus without assumption of an ad hoc tortuosity parameter. Intended application of the approach is the study of diffusing substances in the glial scar after implantation of neural prostheses, although the approach can be adapted to other studies of diffusion in biological tissues, for example of biomolecules or small drug molecules.

q-bio.TO↗

arXiv2015

Mathematical model of the interaction between baroreflex and cerebral autoregulation

Baroreflex (BR) and cerebral autoregulation (CA) are two important mechanisms regulating blood pressure and flow. However, the functional relationship between BR and CA in humans is unknown. Since BR impairment is an adverse prognostic indicator for both cardiac and cerebrovascular diseases it would be of clinical interest to better understand the relationship between BR and CA. Motivated by this observation we develop a simple mathematical framework aiming to simulate the effects of BR on the cerebral blood flow dynamics.

q-bio.TO↗

arXiv2015

Localisation of antifreeze proteins in Rhagium mordax using immunofluorescence

Larvae of the blackspotted pliers support beetle, Rhagium mordax, express antifreeze proteins in their haemolymph during temperate climate winter. It is believed that they also express antifreeze proteins in their cuticle as a means of preventing inoculative freezing. Larvae of Rhagium mordax were collected during winter (March) and summer (May) of 2011. Larvae were fixated, embedded in paraffin wax, sectioned on a microtome, incubated with custom made anti-AFP antibodies and isualised on a fluorescence microscope. The larvae of both winter and summer showed AFP activity in their cuticle, gut lumen and -epithelium. Due to the long synthesis process of AFPs, the larvae contain them all year round. The distribution of these AFPs change during summer, possibly relocating to vesicles in the cuticle and gut lumen/epithelium.

q-bio.TO↗

arXiv2015

Left ventricular myocardium of heart as a 3D scheme

In this paper it will be shown that according to the scheme theory in algebraic geometry, human heart as an elastic body can be represented as a 3D scheme, on account of algebraic equations of the myocardial fibers as the local parts of the global scheme. It is possible that the fiber movements to be discussed here are identical with the so-called "myocardial fiber transactions"; however the information available to me regarding the latter is lacking in precision, that I can from no judgment in the matter. It is hoped that some enquirer may succeed shortly in this introduced scheme suggested here, which is so important in connection with the theory of schemes.

q-bio.TO↗

arXiv2016

Towards a cell-based mechanostat theory of bone: the need to account for osteocyte desensitisation and osteocyte replacement

Bone's mechanostat theory describes the adaptation of bone tissues to their mechanical environment. Many experiments have investigated and observed such structural adaptation. However, there is still much uncertainty about how to define the reference mechanical state at which bone structure is adapted and stable. Clinical and experimental observations show that this reference state varies both in space and in time, over a wide range of timescales. We propose an osteocyte-based mechanostat theory that links various timescales of structural adaptation with various dynamic features of the osteocyte network in bone. This theory assumes that osteocytes are formed adapted to their current local mechanical environment through modulation of morphological and genotypic osteocyte properties involved in mechanical sensitivity. We distinguish two main types of physiological responses by which osteocytes subsequently modify the reference mechanical state. One is the replacement of osteocytes during bone remodelling, which occurs over the long timescales of bone turnover. The other is cell desensitisation responses, which occur more rapidly and reversibly during an osteocyte's lifetime. The novelty of this theory is to propose that long-lasting morphological and genotypic osteocyte properties provide a material basis for a long-term mechanical memory of bone that is gradually reset by bone remodelling. We test this theory by simulating long-term mechanical disuse (modelling spinal cord injury), and short-term mechanical loadings (modelling daily exercises) with a mathematical model. The consideration of osteocyte desensitisation and of osteocyte replacement by remodelling is able to capture the different phenomena and timescales observed during the mechanical adaptation of bone tissues, lending support to this theory.

q-bio.CB↗

arXiv2015

Modelling the Role of Nitric Oxide in Cerebral Autoregulation

Malfunction of the system which regulates the bloodflow in the brain is a major cause of stroke and dementia, costing many lives and many billions of pounds each year in the UK alone. This regulatory system, known as cerebral autoregulation, has been the subject of much experimental and mathematical investigation yet our understanding of it is still quite limited. One area in which our understanding is particularly lacking is that of the role of nitric oxide, understood to be a potent vasodilator. The interactions of nitric oxide with the better understood myogenic response remain un-modelled and poorly understood. In this thesis we present a novel model of the arteriolar control mechanism, comprising a mixture of well-established and new models of individual processes, brought together for the first time. We show that this model is capable of reproducing experimentally observed behaviour very closely and go on to investigate its stability in the context of the vasculature of the whole brain. In conclusion we find that nitric oxide, although it plays a central role in determining equilibrium vessel radius, is unimportant to the dynamics of the system and its responses to variation in arterial blood pressure. We also find that the stability of the system is very sensitive to the dynamics of Ca$^{2+}$ within the muscle cell, and that self-sustaining Ca$^{2+}$ waves are not necessary to cause whole-vessel radius oscillations consistent with vasomotion.

q-bio.TO↗

arXiv2016

Fracture toughness of leaves: Overview and observations

One might ask why is it important to know the mechanism of fracture in leaves when Mother Nature is doing her job perfectly. I could list the following reasons to address that question: (a) Leaves are natural composite structures, during millions of years of evolution, they have adapted themselves to their surrounding environment and their design is optimized, one can apply the knowledge gained from studying the fracture mechanism of leaves to the development of new composite materials; (b) Other soft tissues like skin and blood vessel have similar structure at some scales and may possess the same fracture mechanism. The gained knowledge can also be applied to these materials; (c) Global need for food is skyrocketing. There are few countries, including the United States, that have all the potentials (i.e. water, soil, sunlight, and manpower) to play a major role in the future world food supplying market. If we can increase the output of our farms and forests, by means of protecting them against herbivores [Beck 1965], pathogens [Campbell et al. 1980], and other physical damages, our share of the future market will be higher. It will also enforce our national food security because we will not be dependent on food import. We do not yet know how much of our farms and forests output can be saved if we can genetically design tougher materials, but the whole idea does worth to be studied.

q-bio.TO↗

arXiv2016

The effects of fibroblasts on wave dynamics in a mathematical model for human ventricular tissue

We present systematic numerical studies of electrical-wave propagation in two-dimensional (2D) and three-dimensional (3D) mathematical models, for human, ventricular tissue with myocyte cells that are attached (a) regularly and (b) randomly to distributed fibroblasts. In both these cases we show that there is a parameter regime in which single rotating spiral- and scroll-wave states (RS) retain their integrity and do not evolve to a state ST that displays spatiotemporal chaos and turbulence. However, in another range of parameters, we observe a transition from ST to RS states in both 2D or 3D domains and for both cases (a) and (b). Our studies show that the ST-RS transition and rotation period of a spiral or scroll wave in the RS state depends on (i) the coupling strength between myocytes and fibroblasts and (ii) the number of fibroblasts attached to myocytes. We conclude that myocyte-fibroblast coupling strength and the number of fibroblasts are more important for the ST-RS transition than the precise way in which fibroblasts are distributed over myocyte tissue.

q-bio.TO↗

arXiv2016

The fallacy of tumor immunology: Evolutionary pressures, viruses as nature's genetic engineering tools and T cell surveillance emergence for purging nascent selfish cells

The US and Hungarian statistical records of the years 1900 and 1896, respectively, before the dramatic medical advances, show 32% and 27% deaths attributable to infections, whereas only 5% and 2% due to cancer. These data can be interpreted to mean that (i) the immune system evolved for purging nascent selfish cells, which establish natural chimerism littering the soma and the germline by conspecific alien cells and (ii) defense against pathogens that represent xenogeneic aliens appeared later in evolution. `Liberating' T cells from the semantic trap of immunity and the shackles of the `two-signal' model of T cell activation, we point out theoretical grounds that the immune response to cancer is conceptually different from the immune response to infection. We argue for a one-signal model (with stochastic influences) as the explanation for T cell activation in preference to the widely accepted two-signal model of co-stimulation. Convincing evidence for our one-signal model emerged from the widespread autoimmune adverse events in 64.2% of advanced melanoma patients treated with the anti-CTLA-4 antibody (ipilimumab) that blocks an immune checkpoint. Harnessing the unleashed autoimmune power of T cells could be rewarding to defeat cancer. Assuming that immunization against isogeneic tumors also would be effective is a fallacy.

q-bio.MN↗

arXiv2016

Limiting the Development of Anti-Cancer Drug Resistance in a Spatial Model of Micrometastases

While chemoresistance in primary tumors is well-studied, much less is known about the influence of systemic chemotherapy on the development of drug resistance at metastatic sites. In this work, we use a hybrid spatial model of tumor response to a DNA damaging drug to study how the development of chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider cell populations that harbor pre-existing resistance to the drug, and those that acquire resistance during the course of treatment. For each of these independent scenarios, we consider one hypothetical cell line that is responsive to metronomic chemotherapy, and another that with high probability cannot be eradicated by a metronomic protocol. Motivated by experimental work on ovarian cancer xenografts, we consider all possible combinations of a one week treatment protocol, repeated for three weeks, and constrained by the total weekly drug dose. Simulations reveal a small number of fractionated-dose protocols that are at least as effective as metronomic therapy in eradicating micrometastases with acquired resistance (weak or strong), while also being at least as effective on those that harbor weakly pre-existing resistant cells. Given the responsiveness of very different theoretical cell lines to these few fractionated-dose protocols, these may represent more effective ways to schedule chemotherapy with the goal of limiting metastatic tumor progression.

q-bio.TO↗

arXiv2016

Dipole density instead of potentials in electrocardiology

We discuss the forward and inverse problems between the potential V(x) measured in a heart chamber and its sources represented by a dipole density d(y) located on the heart wall. We show that the mapping from d(y) to V(x) is a compact integral operator. Its inverse is unbounded which makes the inverse problem ill-posed in the mathematical sense. We investigate methods to solve the inverse problem approximately in view of the mapping of complicated cardiac arrhythmias. We point out an analogy between phase mapping and 2-dimensional hydrodynamics.

q-bio.TO↗

arXiv2019

Modeling Oral Glucose Tolerance Test (OGTT) data and its Bayesian Inverse Problem

One common way to test for diabetes is the Oral Glucose Tolerance Test or OGTT. Most common methods for the analysis of the data on this test are wasteful of much of the information contained therein. We propose to model blood glucose during an OGTT using a compartmental dynamic model with a system of ODEs. Our model works well in describing most scenarios that occur during an OGTT considering only 4 parameters. Fitting the model to data is an inverse problem, which is suitable for Bayesian inference. Priors are specified and posterior inference results are shown using real data.

stat.AP↗

arXiv2016

A novel computational modelling to describe the anisotropic, remodelling and reorientation behaviour of collagen fibrres in articular cartilage

In articular cartilage the orientation of collagen fibres is not uniform, varying mostly with the depth on the tissue. Besides, the biomechanical response of each layer of the articular cartilage differs from the neighbouring ones, evolving through thickness as a function of the distribution, density and orientation of the collagen fibres. Based on a finite element implementation, a new continuum formulation is proposed to describe the remodelling and reorientation of the collagen fibres under arbitrary mechanical loads: the cartilaginous tissue is modelled based on a hyperelastic formulation, being the ground isotropic matrix described by a neo-Hookean law and the fibrillar anisotropic part modelled by a new anisotropic formulation introduced for the first time in the present work, in which both reorientation and remodelling are taken into account. To characterize the orientation of fibres, a structure tensor is defined to represent the expected distribution and orientation of fibres around a reference direction. The isotropic and anisotropic constitutive parameters were determined by the good validation of the numerical models with the experimental data available from the literature. Considering the effect of realistic collagen fibre reorientation in the cartilage tissue, the remodelling algorithm associated with a distribution of fibres model showed accurate results with few numerical calculations.

physics.bio-ph↗

arXiv2016

Fast Vascular Ultrasound Imaging with Enhanced Spatial Resolution and Background Rejection

Ultrasound super-localization microscopy techniques presented in the last few years enable non-invasive imaging of vascular structures at the capillary level by tracking the flow of ultrasound contrast agents (gas microbubbles). However, these techniques are currently limited by low temporal resolution and long acquisition times. Super-resolution optical fluctuation imaging (SOFI) is a fluorescence microscopy technique enabling sub-diffraction limit imaging with high temporal resolution by calculating high order statistics of the fluctuating optical signal. The aim of this work is to achieve fast acoustic imaging with enhanced resolution by applying the tools used in SOFI to contrast-enhance ultrasound (CEUS) plane-wave scans. The proposed method was tested using numerical simulations and evaluated using two in-vivo rabbit models: scans of healthy kidneys and VX-2 tumor xenografts. Improved spatial resolution was observed with a reduction of up to 50% in the full width half max of the point spread function. In addition, substantial reduction in the background level was achieved compared to standard mean amplitude persistence images, revealing small vascular structures within tumors. The scan duration of the proposed method is less than a second while current superlocalization techniques require acquisition duration of several minutes. As a result, the proposed technique may be used to obtain scans with enhanced spatial resolution and high temporal resolution, facilitating flow-dynamics monitoring. Our method can also be applied during a breath-hold, reducing the sensitivity to motion artifacts.

q-bio.TO↗

arXiv2016

Wound pH depends on actual wound size

Wound healing is an intricate process that involves many types of cells, reaction pathways as well as chemical, physical and electrical cues. Since biochemical reactions and physiological events are pH-dependent we study here pH as an important major characteristic of the wound healing process in the presence of endogenous and exogenous electric fields. Our model gives the spatial pH distribution in a wound. In particular we isolate a number of dimensionless quantities which sets the length, energy and time scales governing the wound healing process and which can be experimentally tested. Most interesting finding is that wound pH depends on actual wound size.

physics.med-ph↗

arXiv2016

A Two-Layer Mathematical Modelling of Drug Delivery to Biological Tissues

Local drug delivery has received much recognition in recent years, yet it is still unpredictable how drug efficacy depends on physicochemical properties and delivery kinetics. The purpose of the current study is to provide a useful mathematical model for drug release from a drug delivery device and consecutive drug transport in biological tissue, thereby aiding the development of new therapeutic drug by a systemic approach. In order to study the complete process, a two-layer spatio-temporal model depicting drug transport between the coupled media is presented. Drug release is described by considering solubilisation dynamics of drug particle, diffusion of the solubilised drug through porous matrix and also some other processes like reversible dissociation / recrystallization, drug particle-receptor binding and internalization phenomena. The model has led to a system of partial differential equations describing the important properties of drug kinetics. This model contributes towards the perception of the roles played by diffusion, mass-transfer, particle binding and internalization parameters.

math.DS↗

arXiv2016

Multi-Constituent Simulation of Thrombus Deposition

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5mm x 1.6mm x 0.1mm) with small crevices (125μm x 75μm and 125μm x 137μm). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices.

physics.bio-ph↗

arXiv2016

On the fractional cell kill law governing the lysis of solid tumors

We present in silico simulations and mathematical analyses supporting several hypotheses that explain the saturation expressed in the fractional cell kill law that governs the lysis of tumor cells by cytotoxic CD8 + T cells (CTLs). In order to give insight into the significance of the parameters appearing in such law, a hybrid cellular automaton model describing the spatio-temporal evolution of tumor growth and its interaction with the cell-mediated immune response is used. When the CTLs eradicate efficiently the tumor cells, the model predicts a correlation between the morphology of the tumors and the rate at which they are lysed. As the effectiveness of the effector cells is decreased, the saturation gradually disappears. This limit is thoroughly discussed and a new fractional cell kill is proposed.

q-bio.TO↗