Alen Tosenberger

Modelling of thrombus growth in flow with a DPD-PDE method.

Hemostatic plug covering the injury site (or a thrombus in the pathological case) is formed due to the complex interaction of aggregating platelets with biochemical reactions in plasma that participate in blood coagulation. The mechanisms that control clot growth and which lead to growth arrest are not yet completely understood. We model them with numerical simulations based on a hybrid DPD-PDE model. Dissipative particle dynamics (DPD) is used to model plasma flow with platelets while fibrin concentration is described by a simplified reaction-diffusion-advection equation. The model takes into account consecutive stages of clot growth. First, a platelet is weakly connected to the clot and after some time this connection becomes stronger due to other surface receptors involved in platelet adhesion. At the same time, the fibrin mesh is formed inside the clot. This becomes possible because flow does not penetrate the clot and cannot wash out the reactants participating in blood coagulation. Platelets covered by the fibrin mesh cannot attach new platelets. Modelling shows that the growth of a hemostatic plug can stop as a result of its exterior part being removed by the flow thus exposing its non-adhesive core to the flow.

Modelling of platelet–fibrin clot formation in flow with a DPD–PDE method

The paper is devoted to mathematical modelling of clot growth in blood flow. Great complexity of the hemostatic system dictates the need of usage of the mathematical models to understand its functioning in the normal and especially in pathological situations. In this work we investigate the interaction of blood flow, platelet aggregation and plasma coagulation. We develop a hybrid DPD–PDE model where dissipative particle dynamics (DPD) is used to model plasma flow and platelets, while the regulatory network of plasma coagulation is described by a system of partial differential equations. Modelling results confirm the potency of the scenario of clot growth where at the first stage of clot formation platelets form an aggregate due to weak inter-platelet connections and then due to their activation. This enables the formation of the fibrin net in the centre of the platelet aggregate where the flow velocity is significantly reduced. The fibrin net reinforces the clot and allows its further growth. When the clot becomes sufficiently large, it stops growing due to the narrowed vessel and the increase of flow shear rate at the surface of the clot. Its outer part is detached by the flow revealing the inner part covered by fibrin. This fibrin cap does not allow new platelets to attach at the high shear rate, and the clot stops growing. Dependence of the final clot size on wall shear rate and on other parameters is studied.

A Conceptual Model of Morphogenesis and Regeneration

Abstract This paper is devoted to computer modelling of the development and regeneration of multicellular biological structures. Some species (e.g. planaria and salamanders) are able to regenerate parts of their body after amputation damage, but the global rules governing cooperative cell behaviour during morphogenesis are not known. Here, we consider a simplified model organism, which consists of tissues formed around special cells that can be interpreted as stem cells. We assume that stem cells communicate with each other by a set of signals, and that the values of these signals depend on the distance between cells. Thus the signal distribution characterizes location of stem cells. If the signal distribution is changed, then the difference between the initial and the current signal distribution affects the behaviour of stem cells—e.g. as a result of an amputation of a part of tissue the signal distribution changes which stimulates stem cells to migrate to new locations, appropriate for regeneration of the proper pattern. Moreover, as stem cells divide and form tissues around them, they control the form and the size of regenerating tissues. This two-level organization of the model organism, with global regulation of stem cells and local regulation of tissues, allows its reproducible development and regeneration.

On a Model of Pattern Regeneration Based on Cell Memory

We present here a new model of the cellular dynamics that enable regeneration of complex biological morphologies. Biological cell structures are considered as an ensemble of mathematical points on the plane. Each cell produces a signal which propagates in space and is received by other cells. The total signal received by each cell forms a signal distribution defined on the cell structure. This distribution characterizes the geometry of the cell structure. If a part of this structure is removed, the remaining cells have two signals. They keep the value of the signal which they had before the amputation (memory), and they receive a new signal produced after the amputation. Regeneration of the cell structure is stimulated by the difference between the old and the new signals. It is stopped when the two signals coincide. The algorithm of regeneration contains certain rules which are essential for its functioning, being the first quantitative model of cellular memory that implements regeneration of complex patterns to a specific target morphology. Correct regeneration depends on the form and the size of the cell structure, as well as on some parameters of regeneration.

Modelling of thrombus growth and growth stop in flow by the method of dissipative particle dynamics

Abstract Platelet aggregation at the site of the vascular injury leads to the formation of a hemostatic plug covering the injury site, or a thrombus in the pathological case. The mechanisms that control clot growth or lead to growth arrest are not yet completely understood. In order to study these mechanisms theoretically, we use the Dissipative Particle Dynamics method, which allows us to model individual platelets in the flow and in the clot. The model takes into account different stages of the platelet adhesion process. First, a platelet is captured reversibly by the aggregate, then it is activated and adheres firmly, becoming a part of its core.We suggest that the core of the clot is composed of platelets unable to attach new platelets from the flow due to their activation by thrombin and/or wrapping by the fibrin mesh. The simulations are in a good agreement with the experimental results [9]. Modelling shows that stopping the growth of a hemostatic plug (and thrombus) may result from its exterior part being removed by the flow and exposed its non-adhesive core to the flow.

On the regimes of blood coagulation

Abstract Reaction–diffusion system of equations describing blood clotting is studied. Different regimes of clot growth are identified in a quiescent plasma and in blood flow depending on the relative strength of initiation, propagation and inhibition of the thrombin production.

Numerical simulation of blood flows with non-uniform distribution of erythrocytes and platelets

Abstract Blood cell interactions present an important mechanism in many processes occurring in blood. Due to different blood cell properties, cells of different types behave differently in the flow. Among the observed phenomena is segregation of erythrocytes, which group near the flow axis, from platelets, which migrate towards the blood vessel wall. In this work, a three dimensional model based on the Dissipative Particle Dynamics method is used to study the interaction of erythrocytes and platelets in a flow inside a cylindrical channel. Erythrocytes are modelled as elastic highly deformable membranes, while platelets are modelled as elastic spherical membranes which tend to preserve their spherical shape. As the result of the modelling, the separation of erythrocytes and platelets in a cylindrical vessel flow is shown for vessels of different diameters. Erythrocyte and platelet distribution profiles in the vessel cross-section are in good agreement with the existing experimental results. The described 3-D model can be used for further modelling of blood flow-related problems.

The inconvenience of data of convenience: Computational research beyond post-mortem analyses

The inconvenience of data of convenience: computational research beyond post-mortem analyses

A multiscale model of early cell lineage specification including cell division

Embryonic development is a self-organised process during which cells divide, interact, change fate according to a complex gene regulatory network and organise themselves in a three-dimensional space. Here, we model this complex dynamic phenomenon in the context of the acquisition of epiblast and primitive endoderm identities within the inner cell mass of the preimplantation embryo in the mouse. The multiscale model describes cell division and interactions between cells, as well as biochemical reactions inside each individual cell and in the extracellular matrix. The computational results first confirm that the previously proposed mechanism by which extra-cellular signalling allows cells to select the appropriate fate in a tristable regulatory network is robust when considering a realistic framework involving cell division and three-dimensional interactions. The simulations recapitulate a variety of in vivo observations on wild-type and mutant embryos and suggest that the gene regulatory network confers differential plasticity to the different cell fates. A detailed analysis of the specification process emphasizes that developmental transitions and the salt-and-pepper patterning of epiblast and primitive endoderm cells from a homogenous population of inner cell mass cells arise from the interplay between the internal gene regulatory network and extracellular signalling by Fgf4. Importantly, noise is necessary to create some initial heterogeneity in the specification process. The simulations suggest that initial cell-to-cell differences originating from slight inhomogeneities in extracellular Fgf4 signalling, in possible combination with slightly different concentrations of the key transcription factors between daughter cells, are able to break the original symmetry and are amplified in a flexible and self-regulated manner until the blastocyst stage.Author summaryThe early development of the mammalian embryo involves cell divisions and highly regulated lineage specification events. Cell fates are determined by gene regulatory networks exhibiting multiple steady states. The question arises as to how these networks interact with extracellular signalling, cell division and cell movement. Here, we investigate this question in the context of establishment of the salt-and-pepper pattern of epiblast (Epi) and primitive endoderm (PrE) cells within the inner cell mass (ICM) of the preimplantation embryo in the mouse, using a multi-scale computational model. The three cell fates correspond to three stable steady states of the gene regulatory network, which coexist in the salt-and-pepper pattern. The specification process is self-regulated through extracellular signalling and is robust towards cell division and cell movement.

Target morphology and cell memory: a model of regenerative pattern formation

Despite the growing body of work on molecular components required for regenerative repair, we still lack a deep understanding of the ability of some animal species to regenerate their appropriate complex anatomical structure following damage. A key question is how regenerating systems know when to stop growth and remodeling - what mechanisms implement recognition of correct morphology that signals a stop condition? In this work, we review two conceptual models of pattern regeneration that implement a kind of pattern memory. In the first one, all cells communicate with each other and keep the value of the total signal received from the other cells. If a part of the pattern is amputated, the signal distribution changes. The difference fromthe original signal distribution stimulates cell proliferation and leads to pattern regeneration, in effect implementing an error minimization process that uses signaling memory to achieve pattern correction. In the second model, we consider a more complex pattern organization with different cell types. Each tissue contains a central (coordinator) cell that controls the tissue and communicates with the other central cells. Each of them keeps memory about the signals received from other central cells. The values of these signals depend on the mutual cell location, and the memory allows regeneration of the structure when it is modified. The purpose of these models is to suggest possible mechanisms of pattern regeneration operating on the basis of cell memory which are compatible with diverse molecular implementation mechanisms within specific organisms.