Quantitative Biology - Tissues and Organs Publications (50)


Quantitative Biology - Tissues and Organs Publications

By means of a recently-proposed metric or structural derivative, called scale-q-derivative approach, we formulate differential equation that models the cell death by a radiation exposure in tumor treatments. The considered independent variable here is the absorbed radiation dose D instead of usual time. The survival factor, Fs, for radiation damaged cell obtained here is in agreement with the literature on the maximum entropy principle, as it was recently shown and also exhibits an excellent agreement with the experimental data. Read More

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. Read More

The aims of the current study were to establish a system of culture for induction of paralysed chondrocytes and to investigate if these cells are really dying. Chondrocytes were isolated from the growth cartilage of fetal equines, centrifuged and cultured as pellets in either 10% fetal calf serum or 10% horse serum for 28 days and processed for light and electron microscopy. Different cell types were counted and expressed as a percentage to the total cell number. Read More

The Zika virus has been found in individual cases but has not been confirmed as the cause of in the large number of cases of microcephaly in Brazil in 2015-6. Indeed, disparities between the incidence of Zika and microcephaly across geographic locations has led to questions about the virus's role. Here we consider whether the insecticide pyriproxyfen used in Brazilian drinking water might be the primary cause or a cofactor. Read More

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. Read More

The spirally arranged stems of the spikemoss Selaginella lepidophylla, an ancient resurrection plant, compactly curl into a nest-ball shape upon dehydration. Due to its spiral phyllotaxy, older outer stems on the plant interlace and envelope the younger inner stems forming the plant centre. Stem curling is a morphological mechanism that limits photoinhibitory and thermal damages the plant might experience in arid environments. Read More

In the context of tissue engineering, we recently proposed a lattice model for a bioactive porous tissue scaffold in order to understand the role of an active pore network in tissue growth [Lattice and Continuum Modelling of a Bioactive Porous Tissue Scaffold, preprint, 2017]. This model considered the scaffold as an evolving lattice of pores, with coupling between local cell growth in the pores, and fluid flow through the medium. Here we consider a variant of this lattice model as well as a spatially continuous analogue. Read More

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 in an averaged way through parameters in these models, either phenomenologically or through techniques like mathematical homogenization. Read More

Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype of each cell determines its success. Selection in this process is imposed by both the microenvironment (neighboring cells, extracellular matrix, and diffusing substances), and the whole of the organism through for example the blood supply. Read More

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. Read More

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). Read More

The temporal and spatial development of Parkinson's disease has been characterised as the progressive formation of {\alpha}-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 {\alpha}-synuclein and neurotoxic levels of oxidative species. Read More

Osteocytes and their cell processes reside in a large, interconnected network of voids pervading the mineralized bone matrix of most vertebrates. This osteocyte lacuno-canalicular network (OLCN) is believed to play important roles in mechanosensing, mineral homeostasis, and for the mechanical properties of bone. While the extracellular matrix structure of bone is extensively studied on ultrastructural and macroscopic scales, there is a lack of quantitative knowledge on how the cellular network is organized. Read More

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. Read More

We consider evolving networks in which each node can have various associated properties (a state) in addition to those that arise from network structure. For example, each node can have a spatial location and a velocity, or some more abstract internal property that describes something like social trait. Edges between nodes are created and destroyed, and new nodes enter the system. Read More

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. Read More

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. Read More

We present a continuum model for the mechanical behavior of the skeletal muscle tissue when its functionality is reduced due to aging. The loss of ability of activating is typical of the geriatric syndrome called sarcopenia. The material is described by a hyperelastic, polyconvex, transverse isotropic strain energy function. Read More

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. Read More

We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of the microenvironment for aberrant growth. Accounting for cellular metabolic activity, competition for nutrients, spatial diffusion and their feedbacks on aberrant replication and death rates, we obtain a phase portrait where distinct asymptotic whole-tissue states are found upon varying the tissue-blood turnover rate and the level of blood-borne primary nutrient. Over a broad range of parameters, the spreading dynamics is bistable as random fluctuations can impact the final state of the tissue. Read More

We derive a Cahn-Hilliard-Darcy model to describe multiphase tumour growth taking interactions with multiple chemical species into account as well as the simultaneous occurrence of proliferating, quiescent and necrotic regions. Via a coupling of the Cahn-Hilliard-Darcy equations to a system of reaction-diffusion equations a multitude of phenomena such as nutrient diffusion and consumption, angiogenesis, hypoxia, blood vessel growth, and inhibition by toxic agents, which are released for example by the necrotic cells, can be included. A new feature of the modelling approach is that a volume-averaged velocity is used, which dramatically simplifies the resulting equations. Read More

Although redistribution of red blood cells at bifurcated vessels is highly dependent on flow rate, it is still challenging to quantitatively express the dependency of flow rate in plasma skimming due to nonlinear cellular interactions. We suggest a plasma skimming model that can involve the effect of fractional blood flow at each bifurcation point. For validating the new model, it is compared with \textit{in vivo} data at single bifurcation points, as well as microvascular network systems. Read More

In this paper we investigate the extent to which variable porosity drug-eluting coatings can provide better control over drug release than coatings where the porosity is constant throughout. In particular, we aim to establish the potential benefits of replacing a single-layer with a two-layer coating of identical total thickness and initial drug mass. In our study, what distinguishes the layers (other than their individual thickness and initial drug loading) is the underlying microstructure, and in particular the effective porosity and the tortuosity of the material. Read More

Aims. Clinical data indicating a heart rate (HR) target during rate control therapy for permanent atrial fibrillation (AF) and assessing its eventual relationship with reduced exercise tolerance are lacking. The present study aims at investigating the impact of resting HR on the hemodynamic response to exercise in permanent AF patients by means of a computational cardiovascular model. Read More

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. Read More

How can tissues generate large numbers of cells, yet keep the divisional load (the number of divisions along cell lineages) low in order to curtail the accumulation of somatic mutations and reduce the risk of cancer? To answer the question we consider a general model of hierarchically organized self-renewing tissues and show that the lifetime divisional load of such a tissue is independent of the details of the cell differentiation processes, and depends only on two structural and two dynamical parameters. Our results demonstrate that a strict analytical relationship exists between two seemingly disparate characteristics of self-renewing tissues: divisional load and tissue organization. Most remarkably, we find that a sufficient number of progressively slower dividing cell types can be almost as efficient in minimizing the divisional load, as non-renewing tissues. Read More

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. Read More

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. Read More

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. Read More

Cells in tissues can organize into a broad spectrum of structures according to their function. Drastic changes of organization, such as epithelial-mesenchymal transitions or the formation of spheroidal aggregates, are often associated either to tissue morphogenesis or to cancer progression. Here, we study the organization of cell colonies by means of simulations of self-propelled particles with generic cell-like interactions. Read More

The understanding of the macroscopic phenomenological models of the population growth at a microscopic level is important to predict the population behaviors emerged from the interactions between the individuals. In this work we consider the influence of the cell-cell interaction on the population growth rate $R$ in a tumor system, and show that, in most cases especially small proliferative probabilities, the regulative role of the interaction will be strengthened with the decline of the intrinsic proliferative probabilities. For the high replication rates of an individual and the cooperative interactions, the proliferative probability almost has no effect. Read More

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. Read More

Mounting evidence for the role of oxidative stress in the degeneration of articular cartilage after an injurious impact requires our modeling & simulation efforts to temporarily shift from just describing the effect of mechanical stress and inflammation on osteoarthritis (OA). The hypothesis that the injurious impact causes irreversible damage to chondrocyte mitochondria, which in turn increase their production of free radicals, affecting their energy production and their ability to rebuild the extracellular matrix, has to be modeled and the processes quantified in order to further the understanding of OA, its causes, and viable treatment options. The current article presents a calibrated model that captures the damage oxidative stress incurs on the cell viability, ATP production, and cartilage stability in a cartilage explant after a drop-tower impact. Read More

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. Read More

Understanding active electrolocation in weakly electric fish remains a challenging issue. In this article we propose a mathematical formulation of this problem, in terms of partial differential equations. This allows us to detail two algorithms: one for localizing a target using the multi-frequency aspect of the signal, and antoher one for identifying the shape of this target. Read More

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. Read More

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. Read More

Chitosan (CT) is an antibacterial polysaccharide that has been investigated for drug carriers, haemostats and wound dressings. For these applications, customised CT devices can often be obtained with specific experimental conditions, which can irreversibly alter native biopolymer properties and functions and lead to unreliable material behaviour. In order to investigate the structure-function relationships in CT covalent networks, monosodium 5-sulfoisophthalate (PhS) was selected as heparin-mimicking, growth factor-binding crosslinking segment, whilst 1,4-phenylenediacetic acid (4Ph) and poly(ethylene glycol) bis(carboxymethyl) ether (PEG) were employed as sulfonic acid-free diacids of low and high crosslinker length respectively. Read More

How do the topology and geometry of a tubular network affect the spread of particles within fluid flows? We investigate patterns of effective dispersion in the hierarchical, biological transport network formed by Physarum polycephalum. We demonstrate that a change in topology - pruning in the foraging state - causes a large increase in effective dispersion throughout the network. By comparison, changes in the hierarchy of tube radii result in smaller and more localized differences. Read More

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. Read More

Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a later stage. Read More

A continuum model for epithelial tissue mechanics is formulated from cell level mechanical ingredients and morphogenetic cell dynamics, including cell shape changes and cell rearrangements. The model is capable of dealing with finite deformation, and uses stress and deformation tensors that can be compared with experimental data. Using the model, we uncover the dynamical behaviour that underlies passive relaxation and active contraction-elongation of a tissue. Read More

Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue. Read More

The extent of renal scarring in chronic kidney disease (CKD) can only be ascertained by highly invasive, painful and sometimes risky tissue biopsy. Interestingly, CKD-related abnormalities in kidney size can often be visualized using ultrasound. Nevertheless, not only does the ellipsoid formula used today underestimate true renal size but also the relation governing renal size and collagen content remains unclear. Read More

Magnetic hyperthermia is a new type of cancer treatment designed for overcoming resistance to chemotherapy during the treatment of solid, inaccessible human tumors. The main challenge of this technology is increasing the local tumoral temperature with minimal side effects on the surrounding healthy tissue. This work consists of an in vitro study that compared the effect of hyperthermia in response to the application of exogenous heating (EHT) sources with the corresponding effect produced by magnetic hyperthermia (MHT) at the same target temperatures. Read More

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn--Hilliard--Darcy system coupled with an elliptic reaction-diffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn--Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered for the pressure variable, which allows for the source terms to be dependent on the solution variables. Read More

Physical therapy is the first line of treatment for adults with symptoms from degenerative spondylolisthesis. Surgical management is offered when nonoperative options have not adequately relieved symptoms. We performed PubMed literature search with the word 'spondylolisthesis', and updated till September 18, 2016. Read More

Purpose: To explore the usability and normal T1rho value of liver parenchyma with a novel single breathhold black blood single shot fast spin echo acquisition based liver imaging sequence. Materials and Methods: In total 19 health subjects (10 males, 9 females; mean age: 37.4 yrs; range: 23-54 yrs) participated in the study. Read More

Recent \emph{in vivo} experiments have illustrated the importance of understanding the hemodynamics of heart morphogenesis. In particular, ventricular trabeculation is governed by a delicate interaction between hemodynamic forces, myocardial activity, and morphogen gradients, all of which are coupled to genetic regulatory networks. The underlying hemodynamics at the stage of development in which the trabeculae form is particularly complex, given the balance between inertial and viscous forces. Read More