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The purpose of this study is to model a lymphedema following a mastectomy and its management (compression therapy). During surgery for breast cancer, an axillary node dissection can be done and cause damages to the lymphatic system leading to a secondary lymphedema located in upper limb. Limb lymphedema is an incurable disease associated with chronic and progressive limb swelling condition. The main clinical consequence of lymphedema is the limb edema, clinically resulting in pain, discomfort, strength reduction and musculoskeletal complications due to limb excessive heaviness. Some devices for lymphedema (e.g. bandaging and garments) could be more personalized, taking into account both characteristics of compressions and patients. Before the evaluation of these therapeutic strategies in humans, an ``in silico'' approach could be used to investigate the interest of gradual or intermittent compression testing in virtual patients. For that purpose, we developed a simplified model of the lymph flow through the lymphatic system in a whole upper limb including the corresponding interstitial fluid exchanges.

Multiple myeloma (MM) infiltrates bone marrow and causes anemia by disrupting erythropoiesis, but the effects of marrow infiltration on anemia are difficult to quantify. Marrow biopsies of newly diagnosed MM patients were analyzed before and after four 28-day cycles of non-erythrotoxic remission induction chemotherapy. Complete blood cell counts and serum paraprotein concentrations were measured at diagnosis and before each chemotherapy cycle. At diagnosis, marrow area infiltrated by myeloma correlated negatively with hemoglobin, erythrocytes, and marrow erythroid cells. After successful chemotherapy, patients with less than 30% myeloma infiltration at diagnosis had no change in these parameters, whereas patients with more than 30% myeloma infiltration at diagnosis increased all three parameters. Clinical data were used to develop mathematical models of the effects of myeloma infiltration on the marrow niches of terminal erythropoiesis, the erythroblastic islands (EBIs). A hybrid discrete-continuous model of erythropoiesis based on EBI structure/function was extended to sections of marrow containing multiple EBIs. In the model, myeloma cells can kill erythroid cells by physically destroying EBIs and by producing proapoptotic cytokines. Following chemotherapy, changes in serum paraproteins as measures of myeloma cells and changes in erythrocyte numbers as measures of marrow erythroid cells allowed modeling of myeloma cell death and erythroid cell recovery, respectively. Simulations of marrow infiltration by myeloma and treatment with non-erythrotoxic chemotherapy demonstrate that myeloma-mediated destruction and subsequent reestablishment of EBIs and expansion of erythroid cell populations in EBIs following chemotherapy provide explanations for anemia development and its therapy-mediated recovery in MM patients.

The functional unit of definitive mammalian erythropoiesis, the erythroblastic island, consists of a central macrophage surrounded by adherent erythroid progenitor cells at the colony-forming unit/proerythroblast (CFU-E/Pro-EB) stages of differentiation 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 through the erythroblast stages into reticulocytes that are released into the blood, c) death by apoptosis. CFU-E/Pro-EB fate is under the control of a complex intracellular molecular network that is highly dependent upon environmental conditions in the erythroblastic island. Direct examination of erythroblastic island function in vivo has been limited in mice and unfeasible in humans. In order to assess the functional role of spatial organization coupled with the complex network behavior in erythroblastic islands, we developed hybrid discrete-continuous models of erythropoiesis. A mathematical model was developed in which the cells of the erythroblastic island are considered as individual physical objects, intracellular regulatory networks are modeled with ordinary differential equations, and extracellular concentrations of cytokines or hormones are modeled by partial differential equations. The concentrations of the cytokines Fas-ligand and bone morphogenetic protein-4, which are produced locally in the erythroblastic island, and the hormones erythropoietin and glucocorticosteroid hormone, which are produced at remote locations in the body, are included in the model. We used the model in simulations that investigated the impact of an important difference between humans and mice in which mature late-stage erythroblasts produce the most Fas-ligand in humans, and 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 recovery time of hematocrits and erythrocyte numbers to their baselines following the development of acute anemia in humans as compared to mice. These simulation results with the model were consistent with the more rapid recovery to baseline in mice that were bled to about one-half of their normal hematocrit compared to two patients who had acute blood loss to about one-half of their respective baseline hematocrits and recovered without erythrocyte transfusions. Our modeling approach was also very consistent with the previously reported results of in vitro cultures, where the central macrophages in reconstituted erythroblastic islands of mice had a strong impact on the dynamics of erythroid cell proliferation. The spatial organization of cells in erythroblastic islands is important for the normal, stable functioning of mammalian erythropoiesis, both in vitro and in vivo. Our model of a simplified molecular network controlling erythroid progenitor cell decision and fate provides a realistic functional unit of mammalian erythropoiesis that integrates factors within the microenvironment of the erythroblastic island with those of circulating regulators of erythropoiesis. Our model highlights the need for proper inclusion of the spatial relationships of erythropoietic cells and allowing decisions to be made at the level of individual erythroid cells in the modeling process. Disclosures: Koury: Keryx Biopharmaceuticals, Inc.: Consultancy; TG Therapeutics, Inc.: Consultancy.

Multiple myeloma (MM) infiltrates bone marrow and causes anemia by disrupting erythropoiesis, but the effects of marrow infiltration on anemia are difficult to quantify. Marrow biopsies of newly diagnosed MM patients were analyzed before and after four 28-day cycles of non-erythrotoxic remission induction chemotherapy. Complete blood cell counts and serum paraprotein concentrations were measured at diagnosis and before each chemotherapy cycle. At diagnosis, marrow area infiltrated by myeloma correlated negatively with hemoglobin, erythrocytes, and marrow erythroid cells. After successful chemotherapy, patients with less than 30% myeloma infiltration at diagnosis had no change in these parameters, whereas patients with more than 30% myeloma infiltration at diagnosis increased all three parameters. Clinical data were used to develop mathematical models of the effects of myeloma infiltration on the marrow niches of terminal erythropoiesis, the erythroblastic islands (EBIs). A hybrid discrete-continuous model of erythropoiesis based on EBI structure/function was extended to sections of marrow containing multiple EBIs. In the model, myeloma cells can kill erythroid cells by physically destroying EBIs and by producing proapoptotic cytokines. Following chemotherapy, changes in serum paraproteins as measures of myeloma cells and changes in erythrocyte numbers as measures of marrow erythroid cells allowed modeling of myeloma cell death and erythroid cell recovery, respectively. Simulations of marrow infiltration by myeloma and treatment with non-erythrotoxic chemotherapy demonstrate that myeloma-mediated destruction and subsequent reestablishment of EBIs and expansion of erythroid cell populations in EBIs following chemotherapy provide explanations for anemia development and its therapy-mediated recovery in MM patients.

International audience; Reaction-diffusion equations with a space dependent nonlinearity are considered on the whole axis. Existence of pulses, stationary solutions which vanish at infinity, is studied by the Leray-Schauder method. It is based on the topological degree for Fredholm and proper operators with the zero index in some special weighted spaces and on a priori estimates of solutions in these spaces. Existence of solutions is related to the speed of travelling wave solutions for the corresponding autonomous equations with the limiting nonlinearity.

Introduction Developing orphan drugs is challenging because of their severity and the requisite for effective drugs. The small number of patients does not allow conducting adequately powered randomized controlled trials (RCTs). There is a need to develop high quality, ethically investigated, and appropriately authorized medicines, without subjecting patients to unnecessary trials. Aims and Objectives The main aim is to develop generalizable framework for choosing the best-performing drug/endpoint/design combinations in orphan drug development using an in silico modeling and trial simulation approach. The two main objectives were (i) to provide a global strategy for each disease to identify the most relevant drugs to be evaluated in specific patients during phase III RCTs, (ii) and select the best design for each drug to be used in future RCTs. Methodological approach In silico phase III RCT simulation will be used to find the optimal trial design and was carried out in two steps: (i) statistical analysis of available clinical databases and (ii) integrative modeling that combines mathematical models for diseases with pharmacokinetic-pharmacodynamics models for the selected drug candidates. Conclusion There is a need to speed up the process of orphan drug development, develop new methods for translational research and personalized medicine, and contribute to European Medicines Agency guidelines. The approach presented here offers many perspectives in clinical trial conception.

Objectives The main objective of our work was to compare different randomized clinical trial (RCT) experimental designs in terms of power, accuracy of the estimation of treatment effect, and number of patients receiving active treatment using in silico simulations. Study Design and Setting A virtual population of patients was simulated and randomized in potential clinical trials. Treatment effect was modeled using a dose–effect relation for quantitative or qualitative outcomes. Different experimental designs were considered, and performances between designs were compared. One thousand clinical trials were simulated for each design based on an example of modeled disease. Results According to simulation results, the number of patients needed to reach 80% power was 50 for crossover, 60 for parallel or randomized withdrawal, 65 for drop the loser (DL), and 70 for early escape or play the winner (PW). For a given sample size, each design had its own advantage: low duration (parallel, early escape), high statistical power and precision (crossover), and higher number of patients receiving the active treatment (PW and DL). Conclusion Our approach can help to identify the best experimental design, population, and outcome for future RCTs. This may be particularly useful for drug development in rare diseases, theragnostic approaches, or personalized medicine.

International audience; Erythropoiesis is the process of red blood cell production in the bone marrow. Terminal stages of human erythropoiesis occur in multicellular structures called erythroblastic islands (EBIs). EBIs contain up to several dozen erythroid cells of varying maturities organized around a central macrophage. Immature erythroid cells, burst forming units (BFU-E) circulate in blood and home to bone marrow, where they can have limited but random movement. When BFU-Es approach a macrophage, they divide producing colony forming units-erythroid (CFU-E), which are the next stage of erythroid differentiation. CFU-Es and their immediate progeny, proerythroblasts, can self-renew, differentiate into more mature cells or die by apoptosis. The BFU-E, CFU-E, and the subsequent erythroblast stages provide normal functioning of erythropoiesis. In this work we develop a hybrid discrete-continuous model in order to describe normal erythropoiesis in the bone marrow. Cells are represented as individual objects that move, divide, differentiate, die and interact with each other. We show how BFU-E cells initiate EBIs.

A hybrid model of cell dynamics is presented. It is illustrated by model examples and applied to study erythropoiesis (red blood cell production). In this approach, cells are considered as discrete objects while intra-cellular proteins and extra-cellular biochemical substances are described with continuous models. Spatial organization of erythropoiesis occurring in specific structures of the bone marrow, called erythroblastic island, is investigated.

Diseases that infiltrate the bone marrow disrupt erythropoiesis leading to anemia. In multiple myeloma (MM), anemia severity can be correlated with degree of marrow infiltration by myeloma cells. Infiltrating MM may impair the function and structure of erythroblastic islands (EBIs), the marrow erythropoietic niches. An EBI consists of a central macrophage surrounded by colony-forming units-erythroid/proerythroblasts (CFU-E/pro-EBs) and their progeny, the differentiating erythroblasts. Cytokines produced by MM cells, such as Fas ligand (FL), tumor necrosis factor (TNF), and TNF-related apoptosis-inducing ligand (TRAIL), can induce erythroid cell apoptosis. Physical displacement of the erythroid cells away from central macrophages by MM can destroy the EBIs. Non-erythrotoxic therapies that kill MM cells while sparing erythropoietic cells allow quantification of erythropoiesis and marrow MM infiltration before and after treatment of newly diagnosed MM patients. Marrow biopsies from 15 newly diagnosed MM patients were obtained before and after 4 courses of non-erythrotoxic induction therapy with bortezomib, dexamethasone, and lenalidomide (Richardson et al, Blood 2010). CBCs and serum MM paraprotein quantifications were obtained with the marrow biopsies and before each course of therapy. No patient had renal insufficiency, iron or cobalamin deficiency, erythropoietin (EPO) therapy, or RBC transfusion. At diagnosis, percentages of marrow space occupied by MM and erythroid cells were negatively correlated. Percentages of marrow space infiltrated by MM (range = 2.3 - 72.3%) were also negatively correlated with hemoglobin (Hb), hematocrit (Hct) and RBCs. One patient had a partial response: marrow myeloma decreasing from 27.5% to 5.3%. All other patients had reductions in marrow myeloma to < 2.2%. The 8 patients with < 30% MM infiltration at diagnosis had no change (-1.4% to 1.8%) in marrow space occupied by erythroid cells following therapy, whereas 7 patients with > 35% MM infiltration at diagnosis increased marrow space occupied by erythroid cells following therapy (3.4 to 19.2%). Hb, Hct, and RBCs did not change during therapy in patients with < 30% MM infiltration, but those with > 35% myeloma infiltration at diagnosis had progressive increases in Hb, Hct, and RBCs during therapy. These clinical data were used to study the relationship between marrow infiltration by MM and erythropoiesis. Mathematical models of MM infiltration effects on marrow EBI structure/function were developed and tested in simulations. A previously developed hybrid discrete-continuous model of erythropoiesis based on EBI (Eymard et al, J Math Biol 2015) was extended to a larger area of marrow containing multiple EBIs. In the model, CFU-E/proEBs have 3 fates-- self-renewal, differentiation, and apoptosis--that depend upon factors produced systemically, such as glucocorticoids and EPO, and locally, such as stem cell factor and bone morphogenetic protein 4 by central macrophages and FL by mature erythroblasts. Intracellular regulatory networks were modeled with ordinary differential equations and extracellular concentrations by partial differential equations. Under normal conditions, EBIs achieve a steady-state that produces new RBCs at rates which maintain normal Hb, Hct and RBCs. At early times after the section of bone marrow is infiltrated by small foci of proliferating MM cells, EBI function is not affected. With further proliferation, infiltrating MM cells occupy more marrow space, inducing erythroid cell apoptosis by producing FL, TNF or TRAIL and by displacing erythroid cells from central macrophages, thereby destroying EBIs. However, central macrophages of destroyed islands persist or are replaced by differentiation of monocyte-macrophage precursors. After MM cells are killed by therapy, the residual macrophages can interact with burst-forming units-erythroid (BFU-E), thereby reestablishing EBIs. If the MM infiltrate is not sufficiently reduced after a course of therapy, it can physically interfere with the macrophage-BFU-E interaction, preventing the reestablishment of an EBI and full recovery of RBC production until a subsequent therapy reduces the infiltrate sufficiently that the EBI is reestablished. The model is consistent with the clinical data and may apply to other marrow infiltrative diseases including myelofibrosis, systemic infections, or other malignancies. Disclosures No relevant conflicts of interest to declare.

Abnormal reemergence of depolarizing GABAA current during postnatal brain maturation may play a major role in paediatric epilepsies, Dravet syndrome (DS) being among the most severe. To study the impact of depolarizing GABA onto distinct patterns of EEG activity, we extended a neural mass model as follows: one sub-population of pyramidal cells was added as well as two sub-populations of interacting interneurons, perisomatic-projecting interneurons (basket-like) with fast synaptic kinetics GABAA (fast, I1) and dendritic-projecting interneurons with slow synaptic kinetics GABAA (slow, I2). Basket-like cells were interconnected to reproduce mutual inhibition mechanisms (I1➔I1). The firing rate of interneurons was adapted to mimic the genetic alteration of voltage gated sodium channels found in DS patients, SCN1A(+/-). We implemented the "dynamic depolarizing GABAA" mediated post-synaptic potential in the model, as some studies reported that the chloride reversal potential can switch from negative to more positive value depending on interneuron activity. The "shunting inhibition" promoted by GABAA receptor activation was also implemented. We found that increasing the proportion of depolarizing GABAA mediated IPSP (I1➔I1 and I1➔P) only (i.e., other parameters left unchanged) was sufficient to sequentially switch the EEG activity from background to (1) interictal isolated polymorphic epileptic spikes, (2) fast onset activity, (3) seizure like activity and (4) seizure termination. The interictal and ictal EEG patterns observed in 4 DS patients were reproduced by the model via tuning the amount of depolarizing GABAA postsynaptic potential. Finally, we implemented the modes of action of benzodiazepines and stiripentol, two drugs recommended in DS. Both drugs blocked seizure-like activity, partially and dose-dependently when applied separately, completely and with a synergic effect when combined, as has been observed in DS patients. This computational modeling study constitutes an innovative approach to better define the role of depolarizing GABA in infantile onset epilepsy and opens the way for new therapeutic hypotheses, especially in Dravet syndrome.