Airway obstruction in respiratory viral infections due to impaired mucociliary clearance.

Respiratory viral infections, such as SARS-CoV-2 or influenza, can lead to impaired mucociliary clearance in the bronchial tree due to increased mucus viscosity and its hyper-secretion. We develop in this work a mathematical model to study the interplay between viral infection and mucus motion. The results of numerical simulations show that infection progression can be characterized by three main stages. At the first stage, infection spreads through the most part of mucus producing airways (about 90% of the length) without significant changes in mucus velocity and thickness layer. During the second stage, when it passes through the remaining generations, mucus viscosity increases, its velocity drops down, and it forms a plug. At the last stage, the thickness of the mucus layer gradually increases because mucus is still produced but not removed by the flow. After some time, the thickness of the mucus layer in the small airways becomes comparable with their diameter leading to their complete obstruction.

Pharmacokinetic/pharmacodynamic model of a methionine starvation based anti-cancer drug.

A new therapeutic approach against cancer is developed by the firm Erytech. This approach is based on starved cancer cells of an amino acid essential to their growth (the L-methionine). The depletion of plasma methionine level can be induced by an enzyme, the methionine-γ-lyase. The new therapeutic formulation is a suspension of erythrocytes encapsulating the activated enzyme. Our work reproduces a preclinical trial of a new anti-cancer drug with a mathematical model and numerical simulations in order to replace animal experiments and to have a deeper insight on the underlying processes. With a combination of a pharmacokinetic/pharmacodynamic model for the enzyme, substrate, and co-factor with a hybrid model for tumor, we develop a "global model" that can be calibrated to simulate different human cancer cell lines. The hybrid model includes a system of ordinary differential equations for the intracellular concentrations, partial differential equations for the concentrations of nutrients and drugs in the extracellular matrix, and individual based model for cancer cells. This model describes cell motion, division, differentiation, and death determined by the intracellular concentrations. The models are developed on the basis of experiments in mice carried out by Erytech. Parameters of the pharmacokinetics model were determined by fitting a part of experimental data on the concentration of methionine in blood. Remaining experimental protocols effectuated by Erytech were used to validate the model. The validated PK model allowed the investigation of pharmacodynamics of cell populations. Numerical simulations with the global model show cell synchronization and proliferation arrest due to treatment similar to the available experiments. Thus, computer modeling confirms a possible effect of treatment based on the decrease of methionine concentration. The main goal of the study is the development of an integrated pharmacokinetic/pharmacodynamic model for encapsulated methioninase and of a mathematical model of tumor growth/regression in order to determine the kinetics of L-methionine depletion after co-administration of Erymet product and Pyridoxine.

Interplay between reaction and diffusion processes in governing the dynamics of virus infections.

Spreading of viral infection in the tissues such as lymph nodes or spleen depends on virus multiplication in the host cells, their transport and on the immune response. Reaction-diffusion systems of equations with delays in cell proliferation and death by apoptosis represent an appropriate model to study this process. The properties of the cells of the immune system and the initial viral load determine the spatiotemporal regimes of infection spreading. Infection can be completely eliminated or it can persist at some level together with a certain chronic immune response in a spatially uniform or oscillatory mode. Finally, the immune cells can be completely exhausted leading to a high viral load persistence in the tissue. It has been found experimentally, that virus proteins can affect the immune cell migration. Our study shows that both the motility of immune cells and the virus infection spreading represented by the diffusion rate coefficients are relevant control parameters determining the fate of virus-host interaction.

Mathematical model of T-cell lymphoblastic lymphoma: disease, treatment, cure or relapse of a virtual cohort of patients.

T lymphoblastic lymphoma (T-LBL) is a rare type of lymphoma with a good prognosis with a remission rate of 85%. Patients can be completely cured or can relapse during or after a 2-year treatment. Relapses usually occur early after the remission of the acute phase. The median time of relapse is equal to 1 year, after the occurrence of complete remission (range 0.2-5.9 years) (Uyttebroeck et al., 2008). It can be assumed that patients may be treated longer than necessary with undue toxicity.The aim of our model was to investigate whether the duration of the maintenance therapy could be reduced without increasing the risk of relapses and to determine the minimum treatment duration that could be tested in a future clinical trial.We developed a mathematical model of virtual patients with T-LBL in order to obtain a proportion of virtual relapses close to the one observed in the real population of patients from the EuroLB database. Our simulations reproduced a 2-year follow-up required to study the onset of the disease, the treatment of the acute phase and the maintenance treatment phase.

Wound Healing and Scale Modelling in Zebrafish.

We propose to study the wound healing in Zebrafish by using firstly a differential approach for modelling morphogens diffusion and cell chemotactic motion, and secondly a hybrid model of tissue regeneration, where cells are considered as individual objects and molecular concentrations are described by partial differential equations.

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.

Travelling Waves of Cell Differentiation.

The paper is devoted to modelling of cell differentiation in an initially homogeneous cell population. The mechanism which provides coexistence of two cell lineages in the initially homogeneous cell population is suggested. If cell differentiation is initiated locally in space in the population of undifferentiated cells, it can propagate as a travelling wave converting undifferentiated cells into differentiated ones. We suggest a model of this process which takes into account intracellular regulation, extracellular regulation and different cell types. They include undifferentiated cells and two types of differentiated cells. When a cell differentiates, its choice between two types of differentiated cells is determined by the concentrations of intracellular proteins. Differentiated cells can either stimulate differentiation into their own cell lineage or into another cell lineage. In the case of the positive feedback, only one lineage of differentiated cells will finally appear. In the case of negative feedback, both of them can coexist. In this case a periodic spatial pattern emerges behind the wave.

A conceptual model of morphogenesis and regeneration.

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.

Model of mucociliary clearance in cystic fibrosis lungs.

Mucus clearance is a primary innate defense mechanism in the human airways. Cystic fibrosis (CF) is a genetic disease caused by mutations in the gene encoding the cystic fibrosis transmembrane conductance regulator (CFTR) protein. CF is characterized by dehydration of airway surface liquid and impaired mucociliary clearance. As a result, microorganisms are not efficiently removed from the airways, and patients experience chronic pulmonary infections and inflammation. We propose a new physiologically based mathematical model of muco-ciliary transport consisting of the two major components of the mucociliary clearance system: (i) periciliary liquid layer (PCL) and (ii) mucus layer. We study mucus clearance under normal conditions and in CF patients. Restoring impaired clearance of airway secretions in one of the major goals of therapy in patients with CF. We consider the action of the aerosolized and inhaled medication dornase alfa, which reduces the viscosity of cystic fibrosis mucus, by selectively cleaving the long DNA strands it contains. The results of the model simulations stress the potential relevance of the location of the drug deposition in the central or peripheral airways. Mucus clearance was increased in case the drug was primarily deposited peripherally, i.e. in the small airways.

The role of spatial organization of cells in erythropoiesis.

Erythropoiesis, the process of red blood cell production, occurs mainly in the bone marrow. The functional unit of mammalian erythropoiesis, the erythroblastic island, consists of a central macrophage surrounded by adherent erythroid progenitor cells (CFU-E/Pro-EBs) and their differentiating progeny, the erythroblasts. Central macrophages display on their surface or secrete various growth or inhibitory factors that influence the fate of the surrounding erythroid cells. CFU-E/Pro-EBs have three possible fates: (a) expansion of their numbers without differentiation, (b) differentiation into reticulocytes that are released into the blood, (c) death by apoptosis. CFU-E/Pro-EB fate is under the control of a complex molecular network, that is highly dependent upon environmental conditions in the erythroblastic island. In order to assess the functional role of space coupled with the complex network behavior in erythroblastic islands, we developed hybrid discrete-continuous models of erythropoiesis. A model was developed in which cells are considered as individual physical objects, intracellular regulatory networks are modeled with ordinary differential equations and extracellular concentrations by partial differential equations. We used the model to investigate the impact of an important difference between humans and mice in which mature late-stage erythroblasts produce the most Fas-ligand in humans, whereas early-stage erythroblasts produce the most Fas-ligand in mice. Although the global behaviors of the erythroblastic islands in both species were similar, differences were found, including a relatively slower response time to acute anemia in humans. Also, our modeling approach was very consistent with in vitro culture data, where the central macrophage in reconstituted erythroblastic islands has a strong impact on the dynamics of red blood cell production. The specific spatial organization of erythroblastic islands is key to the normal, stable functioning of mammalian erythropoiesis, both in vitro and in vivo. Our model of a simplified molecular network controlling cell decision provides a realistic functional unit of mammalian erythropoiesis that integrates multiple microenvironmental influences within the erythroblastic island with those of circulating regulators of erythropoiesis, such as EPO and glucocorticosteroids, that are produced at remote sites.

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.

Modeling erythroblastic islands: using a hybrid model to assess the function of central macrophage.

The production and regulation of red blood cells, erythropoiesis, occurs in the bone marrow where erythroid cells proliferate and differentiate within particular structures, called erythroblastic islands. A typical structure of these islands consists of a macrophage (white cell) surrounded by immature erythroid cells (progenitors), with more mature cells on the periphery of the island, ready to leave the bone marrow and enter the bloodstream. A hybrid model, coupling a continuous model (ordinary differential equations) describing intracellular regulation through competition of two key proteins, to a discrete spatial model describing cell-cell interactions, with growth factor diffusion in the medium described by a continuous model (partial differential equations), is proposed to investigate the role of the central macrophage in normal erythropoiesis. Intracellular competition of the two proteins leads the erythroid cell to either proliferation, differentiation, or death by apoptosis. This approach allows considering spatial aspects of erythropoiesis, involved for instance in the occurrence of cellular interactions or the access to external factors, as well as dynamics of intracellular and extracellular scales of this complex cellular process, accounting for stochasticity in cell cycle durations and orientation of the mitotic spindle. The analysis of the model shows a strong effect of the central macrophage on the stability of an erythroblastic island, when assuming the macrophage releases pro-survival cytokines. Even though it is not clear whether or not erythroblastic island stability must be required, investigation of the model concludes that stability improves responsiveness of the model, hence stressing out the potential relevance of the central macrophage in normal erythropoiesis.

Modeling of branching patterns in plants.

A major determinant of plant architecture is the arrangement of branches around the stem, known as phyllotaxis. However, the specific form of branching conditions is not known. Here we discuss this question and suggest a branching model which seems to be in agreement with biological observations.Recently, a number of models connected with the genetic network or molecular biology regulation of the processes of pattern formation appeared. Most of these models consider the plant hormone, auxin, transport and distribution in the apical meristem as the main factors for pattern formation and phyllotaxis. However, all these models do not take into consideration the whole plant morphogenesis, concentrating on the events in the shoot or root apex. On the other hand, other approaches for modeling phyllotaxis, where the whole plant is considered, usually are mostly phenomenological, and due to it, do not describe the details of plant growth and branching mechanism. In this work, we develop a mathematical model and study pattern formation of the whole, though simplified, plant organism where the main physiological factors of plant growth and development are taken into consideration. We model a growing plant as a system of intervals, which we will consider as branches. We assume that the number and location of the branches are not given a priori, but appear and grow according to certain rules, elucidated by the application of mathematical modeling. Four variables are included in our model: concentrations of the plant hormones auxin and cytokinin, proliferation and growth factor, and nutrients-we observe a wide variety of plant forms and study more specifically the involvement of each variable in the branching process. Analysis of the numerical simulations shows that the process of pattern formation in plants depends on the interaction of all these variables. While concentrations of auxin and cytokinin determine the appearance of a new bud, its growth is determined by the concentrations of nutrients and proliferation factors. Possible mechanisms of apical domination in the frame of our model are discussed.

[The Central Scientific Research Roentgenoradiology Institute of the USSR Ministry of Public Health--70th anniversary (on the history of the Institute)]. / Tsentral'nomu nauchno-issledovatel'skomu rentgenoradiologicheskomu institutu Minzdrava SSSR--70 let (k istorii instituta)

The paper is devoted to the history of the organization of the Central Research Roentgenoradiology Institute, USSR Ministry of Health and its 70th anniversary. The great role of the Institute in the organization of Soviet and world roentgenoradiology is emphasized; the main stages of its investigations are described; qualified personnel has been trained over this period. The authors briefly describe the on-going investigations and prospects of their development.

[History and future of the scientific activities of the Division of Radiation Pathology of the Central Scientific Research Roentgenoradiology Institute of the USSR Ministry of Public Health]. / Istoriia i perspektivy nauchnoi deiatel'nosti otdeleniia radiatsionnoi patologii Tsentral'nogo nauchno-issledovatel'skogo rentgenoradiologicheskogo instituta Minzdrava SSSR.

One of the main lines of research pursued in the Department is concerned with the assessment of the contribution of small doses of ionizing radiation to the development of some features of a number of somatic and infectious diseases in persons exposed to ionizing radiation. For this purpose, combined clinicolaboratory investigation of this group of patients and some organizational and methodological measures are proposed for the optimization of their follow-up.