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arXiv2016

A Mathematical Model of Mechanotransduction

This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between intracellular and extracellular displacements drive mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two dimensions. In several cases the equations are solved analytically, illustrating how displacements divide into two parts: monodomain displacements are identical in both spaces and therefore do not contribute to mechanotransduction, whereas bidomain displacements cause mechanotransduction. A new length constant depends on the intracellular and extracellular shear moduli and the integrin spring constant, and bidomain effects often occur within a few length constants of the tissue edge. Numerical methods for solving the model equations are being developed. Precursors to the model and potential applications are discussed. The bidomain model may be applicable to cardiac remodeling, blood vessel regulation, tissue engineering, stem cell differentiation, cancer biology, and development.

physics.bio-ph↗

arXiv2016

One-dimensional Arterial Network Model for Bypass Grafts Assessment

We propose an arterial network model based on 1D blood hemodynamic equations to study the behavior of different vascular surgical bypass grafts in case of an arterial occlusive pathology: an obliteration or stenosis of the iliac artery. We investigate the performances of three different bypass grafts (Aorto-Femoral, Axillo-Femoral and cross-over Femoral) depending on the degree of obliteration of the stenosis. Numerical simulations show that all bypass grafts are efficient since we retrieve in all cases the normal hemodynamics in the stenosed region while ensuring at the same time a global healthy circulation. We analyze in particular the Axillo-Femoral bypass graft by performing hundreds of simulations by varying the values of the Young's modulus [0.1--50 MPa] and the radius [0.01--5 cm] of the bypass graft. We show that the Young's modulus and radius of commercial bypass grafts are optimal in terms of hemodynamic considerations. The numerical findings prove that this approach could be used to optimize or plan surgeries for specific patients, to perform parameter's statistics and error propagation evaluations by running extensive simulations, or to characterize numerically specific bypass grafts.

physics.med-ph↗

arXiv2016

Lipidomic approach for stratification of Acute Myeloid Leukemia patients

The pathogenesis and progression of many tumors, including hematologic malignancies is highly dependent on enhanced lipogenesis. De novo fatty-acid synthesis permits accelerated proliferation of tumor cells by providing structural components to build the membranes. It may also lead to alterations of physicochemical properties of the formed membranes, which can have an impact on signaling or even increase resistance to drugs in cancer cells. Cancer type-specific lipid profiles would allow understanding the actual effects of lipid changes and therefore could potentially serve as fingerprints for individual tumors and be explored as diagnostic markers. We have used shotgun MS approach to identify lipid patterns in different types of acute myeloid leukemia (AML) patients that either show no karyotype changes or belong to t(8;21) or inv16 types. The observed differences in lipidomes of t(8;21) and inv(16) patients, as compared to AML patients without karyotype changes, concentrate mostly on substantial modulation of ceramides/sphingolipids synthesis. Also significant changes in the physicochemical properties of the membranes, between the t(8;21) and the other patients, were noted that were related to a marked alteration in the saturation levels of lipids. The revealed differences in lipid profiles of various AML types increase our understanding of the affected biochemical pathways and can potentially serve as diagnostic tools.

q-bio.TO↗

arXiv2016

Mechanisms of stochastic onset and termination of atrial fibrillation episodes: Insights using a cellular automaton model

Mathematical models of cardiac electrical excitation are increasingly complex, with multiscale models seeking to represent and bridge physiological behaviours across temporal and spatial scales. The increasing complexity of these models makes it computationally expensive to both evaluate long term (>60 seconds) behaviour and determine sensitivity of model outputs to inputs. This is particularly relevant in models of atrial fibrillation (AF), where individual episodes last from seconds to days, and inter-episode waiting times can be minutes to months. Potential mechanisms of transition between sinus rhythm and AF have been identified but are not well understood, and it is difficult to simulate AF for long periods of time using state-of-the-art models. In this study, we implemented a Moe-type cellular automaton on a novel, topologically correct surface geometry of the left atrium. We used the model to simulate stochastic initiation and spontaneous termination of AF, arising from bursts of spontaneous activation near pulmonary veins. The simplified representation of atrial electrical activity reduced computational cost, and so permitted us to investigate AF mechanisms in a probabilistic setting. We computed large numbers (~10^5) of sample paths of the model, to infer stochastic initiation and termination rates of AF episodes using different model parameters. By generating statistical distributions of model outputs, we demonstrated how to propagate uncertainties of inputs within our microscopic level model up to a macroscopic level. Lastly, we investigated spontaneous termination in the model and found a complex dependence on its past AF trajectory, the mechanism of which merits future investigation.

q-bio.TO↗

arXiv2016

Structure, Function, and Control of the Musculoskeletal Network

The human body is a complex organism whose gross mechanical properties are enabled by an interconnected musculoskeletal network controlled by the nervous system. The nature of musculoskeletal interconnection facilitates stability, voluntary movement, and robustness to injury. However, a fundamental understanding of this network and its control by neural systems has remained elusive. Here we utilize medical databases and mathematical modeling to reveal the organizational structure, predicted function, and neural control of the musculoskeletal system. We construct a whole-body musculoskeletal network in which single muscles connect to multiple bones via both origin and insertion points. We demonstrate that a muscle's role in this network predicts susceptibility of surrounding components to secondary injury. Finally, we illustrate that sets of muscles cluster into network communities that mimic the organization of motor cortex control modules. This novel formalism for describing interactions between the muscular and skeletal systems serves as a foundation to develop and test therapeutic responses to injury, inspiring future advances in clinical treatments.

q-bio.TO↗

arXiv2016

Automatic labeling of molecular biomarkers of whole slide immunohistochemistry images using fully convolutional networks

This paper addresses the problem of quantifying biomarkers in multi-stained tissues, based on color and spatial information. A deep learning based method that can automatically localize and quantify the cells expressing biomarker(s) in a whole slide image is proposed. The deep learning network is a fully convolutional network (FCN) whose input is the true RGB color image of a tissue and output is a map of the different biomarkers. The FCN relies on a convolutional neural network (CNN) that classifies each cell separately according to the biomarker it expresses. In this study, images of immunohistochemistry (IHC) stained slides were collected and used. More than 4,500 RGB images of cells were manually labeled based on the expressing biomarkers. The labeled cell images were used to train the CNN (obtaining an accuracy of 92% in a test set). The trained CNN is then extended to an FCN that generates a map of all biomarkers in the whole slide image acquired by the scanner (instead of classifying every cell image). To evaluate our method, we manually labeled all nuclei expressing different biomarkers in two whole slide images and used theses as the ground truth. Our proposed method for immunohistochemical analysis compares well with the manual labeling by humans (average F-score of 0.96).

q-bio.TO↗

arXiv2016

Effects of non-physiological blood pressure artefacts on measures of cerebral autoregulation

Cerebral autoregulation refers to regulation mechanisms that aim to maintain cerebral blood flow approximately constant. It is often assessed by autoregulation index (ARI), which uses arterial blood pressure and cerebral blood flow velocity time series to produce a ten-scale index of autoregulation performance (0 denoting the absence of and 9 the strongest autoregulation). Unfortunately, data are rarely free from various artefacts. Here, we consider four of the most common non-physiological blood pressure artefacts (saturation, square wave, reduced pulse pressure and impulse) and study their effects on ARI for a range of different artefact sizes. We show that a sufficiently large saturation and square wave always result in ARI reaching the maximum value of 9. The pulse pressure reduction and impulse artefact lead to a more diverse behaviour. Finally, we characterised the critical size of artefacts, defined as the minimum artefact size that, on average, leads to a 10\% deviation of ARI

q-bio.TO↗

arXiv2017

Rhombic Tilings and Primordia Fronts of Phyllotaxis

We introduce and study properties of phyllotactic and rhombic tilings on the cylin- der. These are discrete sets of points that generalize cylindrical lattices. Rhombic tilings appear as periodic orbits of a discrete dynamical system S that models plant pattern formation by stacking disks of equal radius on the cylinder. This system has the advantage of allowing several disks at the same level, and thus multi-jugate config- urations. We provide partial results toward proving that the attractor for S is entirely composed of rhombic tilings and is a strongly normally attracting branched manifold and conjecture that this attractor persists topologically in nearby systems. A key tool in understanding the geometry of tilings and the dynamics of S is the concept of pri- mordia front, which is a closed ring of tangent disks around the cylinder. We show how fronts determine the dynamics, including transitions of parastichy numbers, and might explain the Fibonacci number of petals often encountered in compositae.

q-bio.TO↗

arXiv2017

Quantification of myosin distribution predicts global morphogenetic flow in the fly embryo

During embryogenesis tissue layers continuously rearrange and fold into specific shapes. Developmental biology identified patterns of gene expression and cytoskeletal regulation underlying local tissue dynamics, but how actions of multiple domains of distinct cell types coordinate to remodel tissues at the organ scale remains unclear. We use in toto light-sheet microscopy, automated image analysis, and physical modeling to quantitatively investigate the link between kinetics of global tissue transformations and force generation patterns during Drosophila gastrulation. We find embryo-scale shape changes are represented by a temporal sequence of three simple flow field configurations. Each phase is accompanied by a characteristic spatial myosin distribution, quantified in terms of a coarse-grained 'myosin tensor' that captures both concentration and anisotropy. Our model assumes tissue flow is driven by stress proportional to the myosin tensor, and is effectively visco-elastic with two parameters that control 'irrotational' and 'divergence-less' components of the flow. With just three global parameters, this model achieves up to 90% agreement between predicted and measured flow. The analysis uncovers importance of a) spatial modulation of myosin distribution and b) long-range spreading of its effect due to mechanical interaction of cells. In particular, we find germband extension phase is associated with the onset of effective areal incompressibility of the epithelium, which makes the relation of flow and myosin forcing strongly non-local. Our analysis also revealed a new function for basal myosin in generating a dorsally directed flow and, combined with mutant analysis, identified an unconventional control mechanism through twist dependent reduction of basal myosin levels on the ventral side. We conclude that understanding morphogenetic flow requires a fundamentally global perspective.

q-bio.TO↗

arXiv2016

Fractional Calculus and the ESR test

We consider a partial differential equation associated with a mathematical model describing the concentration of nutrients in blood which interferes directly on the erythrocyte sedimentation rate in the case of an average fluid velocity equal to zero. Introducing the fractional derivative in the Caputo sense, we propose a time-fractional mathematical model which contains, as a particular case, the model proposed by Sharma et al. Our main purpose is to obtain an analytic solution of this time-fractional partial differential equation in terms of the Mittag-Leffler function and Wright function.

q-bio.TO↗

arXiv2017

The Biological Consequences of the Computational World: Mathematical Reflections on Cancer Biology

The role of continua has been clear since antiquity in the mathematical approaches to physics, while discrete manifolds were brought to the limelight mostly by Quantum and Information Theories, in the XX century. We first recall how theorizing and measuring radically change in physics when using discrete vs. continuous mathematical manifolds. It will follow that the reference to discrete structures and digital information is far from neutral in knowledge construction. In biology, in particular, the introduction of information as a new observable on discrete data types has been promoting a dramatic reorganization of the tools for knowledge. We briefly analyze the origin and the nature, then some consequences of the bias thus induced in life sciences, with particular emphasis on research on cancer. We finally summarize new theoretical frames that propose different directions as for the organizing principles for biological thinking and experimenting, including in cancer research. Cancer is now viewed as an organismal, tissue based issue, according to the perspective proposed in (Sonnenschein, Soto, 1999; Baker, 2015).

q-bio.TO↗

arXiv2017

Energy from food

Expressing the energy content of food as the heat energy released by its combustion is potentially misleading. Food is used to produce adenosine triphosphate (ATP). The free energy of conversion of ATP into adenosine diphosphate is used directly for processes such as muscular contraction, without the need for intermediate heat production. The number of ATP molecules produced depends on the task being performed and the fitness level of the person performing the task, since both affect the extent to which aerobic and anaerobic respiration are involved. The digestion and metabolism of soluble carbohydrates, complex carbohydrates and fats requires production of different enzymes. The information required to assess whether this affects the net ATP production by these different types of food does not appear to be available.

physics.bio-ph↗

arXiv2017

Categorical Description Of Plant Morphogenesis

This article presents formalistic tool for description of structural and biochemical relations between cells in the course of development of the body of plants. This is flexible formalistic space, based on the Category theory and the Petri Net approach, which embeds and mutually supplements biological data from methodically different sources. Relation between functional and morphological ways of plant description was mathematically realized with help of the adjoint functors. It was shown that histology and proliferative activity of the formative tissues give a template for the gene interaction networks.

q-bio.TO↗

arXiv2017

A reaction-diffusion model for the progression of Parkinson's disease

The temporal and spatial development of Parkinson's disease has been characterised as the progressive formation of α-synuclein aggregations through susceptible neuronal pathways. This article describes a new model for this progression mechanism in which Parkinsonian damage moves over time through the nervous system by the combined effect of the reaction kinetics of pathogenesis and molecular diffusion. In the reaction-diffusion model, the change from a healthy state to the disease state advances through the nervous system as a wave front of Parkinsonian damage, marking its path by accumulations of damaged α-synuclein and neurotoxic levels of oxidative species. Progression according to this model follows the most vulnerable routes through the nervous system as described by Braak's staging theory and predicts that damage will advance at differing speeds depending upon the level and number of risk factors, in a manner that gives new insights into the variations with which Parkinson's disease develops.

q-bio.NC↗

arXiv2017

A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh-Nagumo model for action potentials. The one-dimensional model for a compliant lymphatic vessel is a set of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (stretch of the lymphatic wall and wall shear stress) and the mechanical variation of the lymphatic wall properties (contractions). The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a complete mathematical analysis of the stability of the stationary state of the EFMC model. Overall, the EFMC model allows imitating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled using a well-established lumped-parameter model which allows simulating stenotic and regurgitant valves. We analysed several lymphodynamical indexes of a single lymphangion for a wide range of upstream and downstream pressure combinations. Stenotic and regurgitant valves were modelled, and their effects are here quantified. Results for stenotic valves showed in the downstream lymphangion that for low frequencies of contractions the Calculated Pump Flow (CPF) index remained almost unaltered, while for high frequencies the CPF dramatically decreased depending on the severity of the stenosis (up to 93% for a severe stenosis). Results for incompetent valves showed that the net flow during a lymphatic cycle tends to zero as the degree of incompetence increases.

math.NA↗

arXiv2017

Are tumor cell lineages solely shaped by mechanical forces?

This paper investigates cells proliferation dynamics in small tumor cell aggregates using an individual based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM model is based on the hypothesis that cells are incompressible objects that grow in size and divide once a threshold size is reached, and that newly born cell adhere to the existing cell cluster. We performed comparisons between the simulation model and experimental data by using several statistical indicators. The results suggest that the emergence of particular morphologies can be explained by simple mechanical interactions.

q-bio.CB↗

arXiv2018

Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold

A contemporary procedure to grow artificial tissue is to seed cells onto a porous biomaterial scaffold and culture it within a perfusion bioreactor to facilitate the transport of nutrients to growing cells. Typical models of cell growth for tissue engineering applications make use of spatially homogeneous or spatially continuous equations to model cell growth, flow of culture medium, nutrient transport, and their interactions. The network structure of the physical porous scaffold is often incorporated through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. We derive a model on a square grid lattice to demonstrate the importance of explicitly modelling the network structure of the porous scaffold, and compare results from this model with those from a modified continuum model from the literature. We capture two-way coupling between cell growth and fluid flow by allowing cells to block pores, and by allowing the shear stress of the fluid to affect cell growth and death. We explore a range of parameters for both models, and demonstrate quantitative and qualitative differences between predictions from each of these approaches, including spatial pattern formation and local oscillations in cell density present only in the lattice model. These differences suggest that for some parameter regimes, corresponding to specific cell types and scaffold geometries, the lattice model gives qualitatively different model predictions than typical continuum models. Our results inform model selection for bioactive porous tissue scaffolds, aiding in the development of successful tissue engineering experiments and eventually clinically successful technologies.

q-bio.TO↗

arXiv2017

An intracardiac electrogram model to bridge virtual hearts and implantable cardiac devices

Virtual heart models have been proposed to enhance the safety of implantable cardiac devices through closed loop validation. To communicate with a virtual heart, devices have been driven by cardiac signals at specific sites. As a result, only the action potentials of these sites are sensed. However, the real device implanted in the heart will sense a complex combination of near and far-field extracellular potential signals. Therefore many device functions, such as blanking periods and refractory periods, are designed to handle these unexpected signals. To represent these signals, we develop an intracardiac electrogram (IEGM) model as an interface between the virtual heart and the device. The model can capture not only the local excitation but also far-field signals and pacing afterpotentials. Moreover, the sensing controller can specify unipolar or bipolar electrogram (EGM) sensing configurations and introduce various oversensing and undersensing modes. The simulation results show that the model is able to reproduce clinically observed sensing problems, which significantly extends the capabilities of the virtual heart model in the context of device validation.

eess.SY↗