A biomathematical model of atherosclerosis in mice.

Atherosclerosis is one of the leading causes of death worldwide. Biomathematical modelling of the underlying disease and therapy processes might be a useful aid to develop and improve preventive and treatment concepts of atherosclerosis. We here propose a biomathematical model of murine atherosclerosis under different diet and treatment conditions including lipid modulating compound and antibiotics. The model is derived by translating known biological mechanisms into ordinary differential equations and by assuming appropriate response kinetics to the applied interventions. We explicitly describe the dynamics of relevant immune cells and lipid species in atherosclerotic lesions including the degree of blood vessel occlusion due to growing plaques. Unknown model parameters were determined by fitting the predictions of model simulations to time series data derived from mice experiments. Parameter fittings resulted in a good agreement of model and data for all 13 experimental scenarios considered. The model can be used to predict the outcome of alternative treatment schedules of combined antibiotic, immune modulating, and lipid lowering agents under high fat or normal diet. We conclude that we established a comprehensive biomathematical model of atherosclerosis in mice. We aim to validate the model on the basis of further experimental data.

A biomathematical model of immune response and barrier function in mice with pneumococcal lung infection.

Pneumonia is one of the leading causes of death worldwide. The course of the disease is often highly dynamic with unforeseen critical deterioration within hours in a relevant proportion of patients. Besides antibiotic treatment, novel adjunctive therapies are under development. Their additive value needs to be explored in preclinical and clinical studies and corresponding therapy schedules require optimization prior to introduction into clinical practice. Biomathematical modeling of the underlying disease and therapy processes might be a useful aid to support these processes. We here propose a biomathematical model of murine immune response during infection with Streptococcus pneumoniae aiming at predicting the outcome of different treatment schedules. The model consists of a number of non-linear ordinary differential equations describing the dynamics and interactions of the pulmonal pneumococcal population and relevant cells of the innate immune response, namely alveolar- and inflammatory macrophages and neutrophils. The cytokines IL-6 and IL-10 and the chemokines CCL2, CXCL1 and CXCL5 are considered as major mediators of the immune response. We also model the invasion of peripheral blood monocytes, their differentiation into macrophages and bacterial penetration through the epithelial barrier causing blood stream infections. We impose therapy effects on this system by modelling antibiotic therapy and treatment with the novel C5a-inactivator NOX-D19. All equations are derived by translating known biological mechanisms into equations and assuming appropriate response kinetics. Unknown model parameters were determined by fitting the predictions of the model to time series data derived from mice experiments with close-meshed time series of state parameters. Parameter fittings resulted in a good agreement of model and data for the experimental scenarios. The model can be used to predict the performance of alternative schedules of combined antibiotic and NOX-D19 treatment. We conclude that we established a comprehensive biomathematical model of pneumococcal lung infection, immune response and barrier function in mice allowing simulations of new treatment schedules. We aim to validate the model on the basis of further experimental data. We also plan the inclusion of further novel therapy principles and the translation of the model to the human situation in the near future.

A biomathematical model of human erythropoiesis and iron metabolism.

Anaemia therapy or perisurgical support of erythropoiesis often require both, EPO and iron medication. However, excessive iron medication can result in iron overload and it is challenging to control haemoglobin levels in a desired range. To support this task, we develop a biomathematical model to simulate EPO- and iron medication in humans. We combine our previously established model of human erythropoiesis including comprehensive pharmacokinetic models of EPO applications with a newly developed model of iron metabolism including iron supplementation. Equations were derived by translating known biological mechanisms into ordinary differential equations. Qualitative model behaviour is studied in detail considering a variety of interventions such as bleeding, iron malnutrition and medication. The model can explain time courses of erythrocytes, reticulocytes, haemoglobin, haematocrit, red blood cells, EPO, serum iron, ferritin, transferrin saturation, and transferrin under a variety of scenarios including EPO and iron application into healthy volunteers or chemotherapy patients. Unknown model parameters were determined by fitting the predictions of the model to time series data from literature. We demonstrate how the model can be used to make predictions of untested therapy options such as cytotoxic chemotherapy supported by iron and EPO. Following our ultimate goal of establishing a model of anaemia treatment in chronic kidney disease, we aim at translating our model to this pathological condition in the near future.

Alarming India-wide phenomenon of antifungal resistance in dermatophytes: A multicentre study.

BACKGROUND: An alarming increase in recalcitrant dermatophytosis has been witnessed in India over the past decade. Drug resistance may play a major role in this scenario. OBJECTIVES: The aim of the present study was to determine the prevalence of in vitro resistance to terbinafine, itraconazole and voriconazole in dermatophytes, and to identify underlying mutations in the fungal squalene epoxidase (SQLE) gene. PATIENTS/METHODS: We analysed skin samples from 402 patients originating from eight locations in India. Fungi were identified by microbiological and molecular methods, tested for antifungal susceptibility (terbinafine, itraconazole, voriconazole), and investigated for missense mutations in SQLE. RESULTS: Trichophyton (T.) mentagrophytes internal transcribed spacer (ITS) Type VIII was found in 314 (78%) samples. Eighteen (5%) samples harboured species identified up to the T interdigitale/mentagrophytes complex, and T rubrum was detected in 19 (5%) samples. 71% of isolates were resistant to terbinafine. The amino acid substitution Phe397Leu in the squalene epoxidase of resistant T mentagrophytes was highly prevalent (91%). Two novel substitutions in resistant Trichophyton strains, Ser395Pro and Ser443Pro, were discovered. The substitution Ala448Thr was found in terbinafine-sensitive and terbinafine-resistant isolates but was associated with increased MICs of itraconazole and voriconazole. CONCLUSIONS: The high frequencies of terbinafine resistance in dermatophytes are worrisome and demand monitoring and further research. Squalene epoxidase substitutions between Leu393 and Ser443 could serve as markers of resistance in the future.

Integration of mathematical model predictions into routine workflows to support clinical decision making in haematology.

BACKGROUND: Individualization and patient-specific optimization of treatment is a major goal of modern health care. One way to achieve this goal is the application of high-resolution diagnostics together with the application of targeted therapies. However, the rising number of different treatment modalities also induces new challenges: Whereas randomized clinical trials focus on proving average treatment effects in specific groups of patients, direct conclusions at the individual patient level are problematic. Thus, the identification of the best patient-specific treatment options remains an open question. Systems medicine, specifically mechanistic mathematical models, can substantially support individual treatment optimization. In addition to providing a better general understanding of disease mechanisms and treatment effects, these models allow for an identification of patient-specific parameterizations and, therefore, provide individualized predictions for the effect of different treatment modalities. RESULTS: In the following we describe a software framework that facilitates the integration of mathematical models and computer simulations into routine clinical processes to support decision-making. This is achieved by combining standard data management and data exploration tools, with the generation and visualization of mathematical model predictions for treatment options at an individual patient level. CONCLUSIONS: By integrating model results in an audit trail compatible manner into established clinical workflows, our framework has the potential to foster the use of systems-medical approaches in clinical practice. We illustrate the framework application by two use cases from the field of haematological oncology.

Model-based optimization of G-CSF treatment during cytotoxic chemotherapy.

PURPOSE: Although G-CSF is widely used to prevent or ameliorate leukopenia during cytotoxic chemotherapies, its optimal use is still under debate and depends on many therapy parameters such as dosing and timing of cytotoxic drugs and G-CSF, G-CSF pharmaceuticals used and individual risk factors of patients. METHODS: We integrate available biological knowledge and clinical data regarding cell kinetics of bone marrow granulopoiesis, the cytotoxic effects of chemotherapy and pharmacokinetics and pharmacodynamics of G-CSF applications (filgrastim or pegfilgrastim) into a comprehensive model. The model explains leukocyte time courses of more than 70 therapy scenarios comprising 10 different cytotoxic drugs. It is applied to develop optimized G-CSF schedules for a variety of clinical scenarios. RESULTS: Clinical trial results showed validity of model predictions regarding alternative G-CSF schedules. We propose modifications of G-CSF treatment for the chemotherapies 'BEACOPP escalated' (Hodgkin's disease), 'ETC' (breast cancer), and risk-adapted schedules for 'CHOP-14' (aggressive non-Hodgkin's lymphoma in elderly patients). CONCLUSIONS: We conclude that we established a model of human granulopoiesis under chemotherapy which allows predictions of yet untested G-CSF schedules, comparisons between them, and optimization of filgrastim and pegfilgrastim treatment. As a general rule of thumb, G-CSF treatment should not be started too early and patients could profit from filgrastim treatment continued until the end of the chemotherapy cycle.

A Biomathematical Model of Pneumococcal Lung Infection and Antibiotic Treatment in Mice.

Pneumonia is considered to be one of the leading causes of death worldwide. The outcome depends on both, proper antibiotic treatment and the effectivity of the immune response of the host. However, due to the complexity of the immunologic cascade initiated during infection, the latter cannot be predicted easily. We construct a biomathematical model of the murine immune response during infection with pneumococcus aiming at predicting the outcome of antibiotic treatment. The model consists of a number of non-linear ordinary differential equations describing dynamics of pneumococcal population, the inflammatory cytokine IL-6, neutrophils and macrophages fighting the infection and destruction of alveolar tissue due to pneumococcus. Equations were derived by translating known biological mechanisms and assuming certain response kinetics. Antibiotic therapy is modelled by a transient depletion of bacteria. Unknown model parameters were determined by fitting the predictions of the model to data sets derived from mice experiments of pneumococcal lung infection with and without antibiotic treatment. Time series of pneumococcal population, debris, neutrophils, activated epithelial cells, macrophages, monocytes and IL-6 serum concentrations were available for this purpose. The antibiotics Ampicillin and Moxifloxacin were considered. Parameter fittings resulted in a good agreement of model and data for all experimental scenarios. Identifiability of parameters is also estimated. The model can be used to predict the performance of alternative schedules of antibiotic treatment. We conclude that we established a biomathematical model of pneumococcal lung infection in mice allowing predictions regarding the outcome of different schedules of antibiotic treatment. We aim at translating the model to the human situation in the near future.

Modelling chemotherapy effects on granulopoiesis.

BACKGROUND: Although the growth-factor G-CSF is widely used to prevent granulotoxic side effects of cytotoxic chemotherapies, its optimal use is still unknown since treatment outcome depends on many parameters such as dosing and timing of chemotherapies, pharmaceutical derivative of G-CSF used and individual risk factors. We showed in the past that a pharmacokinetic and -dynamic model of G-CSF and human granulopoiesis can be used to predict the performance of yet untested G-CSF schedules. However, only a single chemotherapy was considered so far. RESULTS: Model assumptions proved to be feasible in explaining granulotoxicity of 10 different chemotherapeutic drugs or drug-combinations applied in 33 different schedules with and without G-CSF. Risk groups of granulotoxicity were traced back to differences in toxicity parameters. CONCLUSION: We established a comprehensive model of combined G-CSF and chemotherapy action in humans which allows us to predict and compare the outcome of alternative G-CSF schedules. We aim to apply the model in different clinical contexts to optimize and individualize G-CSF treatment.

A combined model of human erythropoiesis and granulopoiesis under growth factor and chemotherapy treatment.

BACKGROUND: Haematotoxicity of conventional chemotherapies often results in delays of treatment or reduction of chemotherapy dose. To ameliorate these side-effects, patients are routinely treated with blood transfusions or haematopoietic growth factors such as erythropoietin (EPO) or granulocyte colony-stimulating factor (G-CSF). For the latter ones, pharmaceutical derivatives are available, which differ in absorption kinetics, pharmacokinetic and -dynamic properties. Due to the complex interaction of cytotoxic effects of chemotherapy and the stimulating effects of different growth factor derivatives, optimal treatment is a non-trivial task. In the past, we developed mathematical models of thrombopoiesis, granulopoiesis and erythropoiesis under chemotherapy and growth-factor applications which can be used to perform clinically relevant predictions regarding the feasibility of chemotherapy schedules and cytopenia prophylaxis with haematopoietic growth factors. However, interactions of lineages and growth-factors were ignored so far. RESULTS: To close this gap, we constructed a hybrid model of human granulopoiesis and erythropoiesis under conventional chemotherapy, G-CSF and EPO applications. This was achieved by combining our single lineage models of human erythropoiesis and granulopoiesis with a common stem cell model. G-CSF effects on erythropoiesis were also implemented. Pharmacodynamic models are based on ordinary differential equations describing proliferation and maturation of haematopoietic cells. The system is regulated by feedback loops partly mediated by endogenous and exogenous EPO and G-CSF. Chemotherapy is modelled by depletion of cells. Unknown model parameters were determined by fitting the model predictions to time series data of blood counts and cytokine profiles. Data were extracted from literature or received from cooperating clinical study groups. Our model explains dynamics of mature blood cells and cytokines after growth-factor applications in healthy volunteers. Moreover, we modelled 15 different chemotherapeutic drugs by estimating their bone marrow toxicity. Taking into account different growth-factor schedules, this adds up to 33 different chemotherapy regimens explained by the model. CONCLUSIONS: We conclude that we established a comprehensive biomathematical model to explain the dynamics of granulopoiesis and erythropoiesis under combined chemotherapy, G-CSF, and EPO applications. We demonstrate how it can be used to make predictions regarding haematotoxicity of yet untested chemotherapy and growth-factor schedules.

Ycasd - a tool for capturing and scaling data from graphical representations.

BACKGROUND: Mathematical modelling of biological processes often requires a large variety of different data sets for parameter estimation and validation. It is common practice that clinical data are not available in raw formats but are provided as graphical representations. Hence, in order to include these data into environments used for model simulations and statistical analyses, it is necessary to extract them from their presentations in the literature. For this purpose, we developed the freely available open source tool ycasd. After establishing a coordinate system by simple axes definitions, it supports convenient retrieval of data points from arbitrary figures. RESULTS: After describing the general functionality and providing an overview of the programme interface, we demonstrate on an example how to use ycasd. A major advantage of ycasd is that it does not require a certain input file format to open and process figures. All options of ycasd are accessible through a single window which eases handling and speeds up data extraction. For subsequent processing of extracted data points, results can be formatted as a Matlab or an R matrix. We extensively compare the functionality and other features of ycasd with other publically available tools. Finally, we provide a short summary of our experiences with ycasd in the context of modelling. CONCLUSIONS: We conclude that our tool is suitable for convenient and accurate data retrievals from graphical representations such as papers. Comparison of tools reveals that ycasd is a good compromise between easy and quick capturing of scientific data from publications and complexity. Our tool is routinely applied in the context of biological modelling, where numerous time series data are required to develop models. The software can also be useful for other kinds of analyses for which published data are required but are not available in raw formats such as systematic reviews and meta-analyses.

A biomathematical model of human erythropoiesis under erythropoietin and chemotherapy administration.

Anaemia is a common haematologic side effect of dose-dense multi-cycle cytotoxic polychemotherapy requiring erythrocyte transfusions or erythropoietin (EPO) administration. To simulate the effectiveness of different EPO application schedules, we performed both modelling of erythropoiesis under chemotherapy and pharmacokinetic and dynamic modelling of EPO applications in the framework of a single comprehensive biomathematical model. For this purpose, a cell kinetic model of bone marrow erythropoiesis was developed that is based on a set of differential compartment equations describing proliferation and maturation of erythropoietic cell stages. The system is regulated by several feedback loops comprising those mediated by EPO. We added a model of EPO absorption after injection at different sites and a pharmacokinetic model of EPO derivatives to account for the effects of external EPO applications. Chemotherapy is modelled by a transient depletion of bone marrow cell stages. Unknown model parameters were determined by fitting the predictions of the model to data sets of circulating erythrocytes, haemoglobin, haematocrit, percentage of reticulocytes or EPO serum concentrations derived from the literature or cooperating clinical study groups. Parameter fittings resulted in a good agreement of model and data. Depending on site of injection and derivative (Alfa, Beta, Delta, Darbepoetin), nine groups of EPO applications were distinguished differing in either absorption kinetics or pharmacokinetics. Finally, eight different chemotherapy protocols were modelled. The model was validated on the basis of scenarios not used for parameter fitting. Simulations were performed to analyze the impact of EPO applications on the risk of anaemia during chemotherapy. We conclude that we established a model of erythropoiesis under chemotherapy that explains a large set of time series data under EPO and chemotherapy applications. It allows predictions regarding yet untested EPO schedules. Prospective clinical studies are needed to validate model predictions and to explore the feasibility and effectiveness of the proposed schedules.

Pharmacokinetic and -dynamic modelling of G-CSF derivatives in humans.

BACKGROUND: The human granulocyte colony-stimulating factor (G-CSF) is routinely applied to support recovery of granulopoiesis during the course of cytotoxic chemotherapies. However, optimal use of the drug is largely unknown. We showed in the past that a biomathematical compartment model of human granulopoiesis can be used to make clinically relevant predictions regarding new, yet untested chemotherapy regimen. In the present paper, we aim to extend this model by a detailed pharmacokinetic and -dynamic modelling of two commonly used G-CSF derivatives Filgrastim and Pegfilgrastim. RESULTS: Model equations are based on our physiological understanding of the drugs which are delayed absorption of G-CSF when applied to the subcutaneous tissue, dose-dependent bioavailability, unspecific first order elimination, specific elimination in dependence on granulocyte counts and reversible protein binding. Pharmacokinetic differences between Filgrastim and Pegfilgrastim were modelled as different parameter sets. Our former cell-kinetic model of granulopoiesis was essentially preserved, except for a few additional assumptions and simplifications. We assumed a delayed action of G-CSF on the bone marrow, a delayed action of chemotherapy and differences between Filgrastim and Pegfilgrastim with respect to stimulation potency of the bone marrow. Additionally, we incorporated a model of combined action of Pegfilgrastim and Filgrastim or endogenous G-CSF which interact via concurrent receptor binding. Unknown pharmacokinetic or cell-kinetic parameters were determined by fitting the predictions of the model to available datasets of G-CSF applications, chemotherapy applications or combinations of it. Data were either extracted from the literature or were received from cooperating clinical study groups. Model predictions fitted well to both, datasets used for parameter estimation and validation scenarios as well. A unique set of parameters was identified which is valid for all scenarios considered. Differences in pharmacokinetic parameter estimates between Filgrastim and Pegfilgrastim were biologically plausible throughout. CONCLUSION: We conclude that we established a comprehensive biomathematical model to explain the dynamics of granulopoiesis under chemotherapy and applications of two different G-CSF derivatives. We aim to apply the model to a large variety of chemotherapy regimen in the future in order to optimize corresponding G-CSF schedules or to individualize G-CSF treatment according to the granulotoxic risk of a patient.