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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.

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.

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.