Regulation of platelet production: the normal response to perturbation and cyclical platelet disease

The highs and lows of cyclic thrombocytopenia

Cyclic thrombocytopenia (CTP) is characterized by periodic platelet oscillation with substantial amplitude. Most CTP cases have a thrombocytopenic background and are often misdiagnosed as immune thrombocytopenia with erratically effective treatment choices. CTP also occurs during hydroxyurea treatment in patients with myeloproliferative diseases. While the aetiology of CTP remains uncertain, here we evaluate historical, theoretical and clinical findings to provide a framework for understanding CTP pathophysiology. CTP retains the intrinsic oscillatory factors defined by the homeostatic regulation of platelet count, presenting as reciprocal platelet/thrombopoietin oscillations and stable oscillation periodicity. Moreover, CTP patients possess pathogenic factors destabilizing the platelet homeostatic system thereby creating opportunities for external perturbations to initiate and sustain the exaggerated platelet oscillations. Beyond humoral and cell-mediated autoimmunity, we propose recently uncovered germline and somatic genetic variants, such as those of MPL, STAT3 or DNMT3A, as pathogenic factors in thrombocytopenia-related CTP. Likewise, the JAK2 V617F or BCR::ABL1 translocation that drives underlying myeloproliferative diseases may also play a pathogenic role in hydroxyurea-induced CTP, where hydroxyurea treatment can serve as both a trigger and a pathogenic factor of platelet oscillation. Elucidating the pathogenic landscape of CTP provides an opportunity for targeted therapeutic approaches in the future.

A Blueprint for Identifying Phenotypes and Drug Targets in Complex Disorders with Empirical Dynamics

A central challenge in medicine is translating from observational understanding to mechanistic understanding, where some observations are recognized as causes for the others. This can lead not only to new treatments and understanding, but also to recognition of novel phenotypes. Here, we apply a collection of mathematical techniques (empirical dynamics), which infer mechanistic networks in a model-free manner from longitudinal data, to hematopoiesis. Our study consists of three subjects with markers for cyclic thrombocytopenia, in which multiple cells and proteins undergo abnormal oscillations. One subject has atypical markers and may represent a rare phenotype. Our analyses support this contention, and also lend new evidence to a theory for the cause of this disorder. Simulations of an intervention yield encouraging results, even when applied to patient data outside our three subjects. These successes suggest that this blueprint has broader applicability in understanding and treating complex disorders.

Periodic hematological disorders: Quintessential examples of dynamical diseases

This paper summarizes the evidence supporting the classification of cyclic neutropenia as a dynamical disease and periodic chronic myelogenous leukemia is also considered. The unsatisfactory state of knowledge concerning the genesis of cyclic thrombocytopenia and periodic autoimmune hemolytic anemia is detailed.

Evaluating the Role of Janus Kinase Pathways in Platelet Homeostasis Using a Systems Modeling Approach

Maintaining platelet homeostasis is important to avoid spontaneous bleeding and organ damage. Thrombopoietin, the primary regulator of platelet production, is affected by and acts in part via Janus kinase (JAK)‐signal transducer and activator of transcription (STAT)–mediated mechanisms. Interleukin‐6 is also partly responsible for inducing thrombopoietin production via the JAK‐STAT pathway. Although current understanding suggests that JAK2 is a primary mediator of platelet regulation, the emerging data show that a JAK1‐specific inhibitor resulted in the modulation of platelet numbers following dosing. To gain a mechanistic understanding, a model describing platelet regulation based on known physiology and JAK‐STAT pathways was built. The model provides a tool to coalesce biological understanding of platelet physiology and an in silico experimental platform to explore drug effects on platelet homeostasis. In this article, we explain the model construction and demonstrate the use of JAK‐inhibitor programs as informing probes of the physiology, gaining insights on dosing paradigms that avoid platelet‐related safety concerns.

Modeling individual time courses of thrombopoiesis during multi-cyclic chemotherapy

Background

Thrombocytopenia is a major side-effect of cytotoxic cancer therapies. The aim of precision medicine is to develop therapy modifications accounting for the individual’s risk.

Methodology/Principle findings

To solve this task, we develop an individualized bio-mechanistic model of the dynamics of bone marrow thrombopoiesis, circulating platelets and therapy effects thereon. Comprehensive biological knowledge regarding cell differentiation, amplification, apoptosis rates, transition times and corresponding regulations are translated into ordinary differential equations. A model of osteoblast/osteoclast interactions was incorporated to mechanistically describe bone marrow support of quiescent cell stages. Thrombopoietin (TPO) as a major regulator is explicitly modelled including pharmacokinetics and–dynamics of TPO injections. Effects of cytotoxic drugs are modelled by transient depletions of proliferating cells.

To calibrate the model, we used population data from the literature and close-meshed individual data of N = 135 high-grade non-Hodgkin’s lymphoma patients treated with CHOP-like chemotherapies. To limit the number of free parameters, several parsimony assumptions were derived from biological data and tested via Likelihood methods. Heterogeneity of patients was explained by a few model parameters. The over-fitting issue of individual parameter estimation was successfully dealt with a virtual participation of each patient in population-based experiments.

The model qualitatively and quantitatively explains a number of biological observations such as the role of osteoblasts in explaining long-term toxic effects, megakaryocyte-mediated feedback on stem cells, bi-phasic stimulation of thrombopoiesis by TPO, dynamics of megakaryocyte ploidies and non-exponential platelet degradation. Almost all individual time series could be described with high precision. We demonstrated how the model can be used to provide predictions regarding individual therapy adaptations.

Conclusions

We propose a mechanistic thrombopoiesis model of unprecedented comprehensiveness in both, biological mechanisms considered and experimental data sets explained. Our innovative method of parameter estimation allows robust determinations of individual parameter settings facilitating the development of individual treatment adaptations during chemotherapy.

Chemotherapy is ubiquitously used to treat cancer diseases. Due to general toxicity of the drugs, chemotherapy results in a number of side effects especially with respect to blood formation. Here we study the loss of platelets during chemotherapy which is dose limiting in many situations. However, this side-effect greatly varies between patients with respect to both, severity and necessity of clinical countermeasures.We therefore developed a mathematical model to predict the time course of platelets of patients under chemotherapy and to propose possible treatment adaptations in cases of intolerable toxicity. The model is based on available biological knowledge and data of platelet formation and therapeutic effects thereon. As a major result, we could describe individual time series data of 135 patients under chemotherapy. Conversely, the model can be used to make predictions regarding alternative therapy schedules such as postponement of therapy or chemotherapy dose reductions. Our model is intended to support clinical decision making on an individual patient level.

Cyclic thrombocytopenia with statistically significant neutrophil oscillations

Cyclic thrombocytopenia is often misdiagnosed as immune thrombocytopenia due to similar clinical features, a fact of significance because cyclic thrombocytopenia generally responds poorly to treatments used successfully in immune thrombocytopenia. A precise diagnosis must establish the statistical significance of periodicity of the platelet counts using statistical methods (eg, Lomb-Scargle periodogram).

Oscillatory haematopoiesis in adults with sickle cell disease treated with hydroxycarbamide

Hydroxycarbamide therapy has been associated with significant oscillations in peripheral blood counts from myeloid, lymphoid and erythroid lineages in patients with polycythaemia vera and chronic myeloid leukaemia. We retrospectively evaluated serial blood counts over an 8-year period from 44 adult patients with sickle cell disease receiving hydroxycarbamide. Platelet counts, leucocyte counts, haemoglobin values and reticulocyte counts, apportioned by hydroxycarbamide status, were analysed using a Lomb-Scargle periodogram algorithm. Significant periodicities were present in one or more counts in 38 patients receiving hydroxycarbamide for a mean duration of 4·81 years. Platelet and leucocyte counts oscillated in 56·8% and 52·3% of patients, respectively. These oscillations generally became detectable within days of initiating therapy. During hydroxycarbamide therapy, the predominant periods of oscillation were 27 ± 1 d for platelet counts and 15 ± 1 d for leucocyte counts. Despite an absolute decrease in leucocyte and platelet counts during hydroxycarbamide treatment, the amplitudes between nadirs and zeniths remained similar regardless of exposure. Our observations appear consistent with previously proposed models of cyclic haematopoiesis, and document that hydroxycarbamide-induced oscillations in blood counts are innocuous phenomena not limited to myeloproliferative disorders as described previously. We speculate the known cell cycle inhibitory properties of hydroxycarbamide may accentuate otherwise latent constitutive oscillatory haematopoiesis.

Understanding, treating and avoiding hematological disease: better medicine through mathematics?

This paper traces the experimental, clinical and mathematical modeling efforts to understand a periodic hematological disease-cyclical neutropenia. It is primarily a highly personal account by two scientists from quite different backgrounds of their interactions over almost 40 years and their attempts to understand this intriguing disease. It's also a story of their efforts to offer effective treatments for the patients who suffer from cyclic neutropenia and other conditions causing neutropenia and infections.

A biomathematical model of human thrombopoiesis under chemotherapy

Intensification of cytotoxic chemotherapy enhances the outcome of several malignancies but is limited by haematotoxicity. While neutropenia and anaemia can be treated with supportive growth factor applications, thrombocytopenia remains a dose-limiting side effect due to the lack of clinically approved pharmaceutical growth factors. Hence, it is necessary to assess the degree of thrombocytopenia of newly designed intensified regimens in the planning phase of a clinical trial. We present a simple ordinary differential equations model of thrombopoiesis under chemotherapy which maps the dynamics of stem cells, CFU-Mk, megakaryocytes and platelets in spleen and circulation. Major regulatory cytokine of thrombopoiesis is thrombopoietin (TPO) whose production and consumption is explicitly modelled. TPO acts by increasing the number of mitoses of CFU-Mk and increasing the mass and maturation of megakaryocytes. Chemotherapy is modelled by a drug-dose and cell-stage specific acute cell loss. Most of the cell kinetic parameters of the model were taken from literature. Parameters regarding TPO regulation and chemotherapy toxicity were estimated by fitting the predictions of the model to time series data of platelets received from large clinical data sets of patients under seven different chemotherapies. We obtained a good agreement between model and data for all scenarios. Parameter estimates were biologically plausible throughout. For validation, the model also explains data of TPO and platelet dynamics after thrombopheresis taken from literature. We used the model to make clinically relevant predictions. Regarding thrombocytopenia we estimated that the CHOP regimen for the treatment of high-grade non-Hodgkin's lymphoma can be time-intensified to a cycle duration of 12 days while the time-intensified CHOEP regimen would result in severe cumulative toxicity. We conclude that our proposed model proved validity for both, different chemotherapeutic regimens and thrombopheresis as well. It is useful to assess the thrombocytopenic risk in the planning phase of a clinical trial.

G-CSF treatment of canine cyclical neutropenia: A comprehensive mathematical model

OBJECTIVE

To study the effects of different G-CSF temporal treatment schemes using a comprehensive mathematical model of the mammalian hematopoietic system that couples the pharmacokinetics of granulocyte colony-stimulating factor (G-CSF) to the hematopoietic stem cell, neutrophil, platelet, and erythrocyte dynamics.

MATERIALS AND METHODS

Data from cyclical neutropenic (CN) grey collies are used to build an extended model that reproduces the dynamics of circulating blood cells found in laboratory data from the dogs with and without daily G-CSF therapy. The effects of varying the treatment initiation time, and whether injections are given daily, every other day, or every three days, are examined.

RESULTS

The mathematical model is able to reproduce the large variation in data that occurs from one dog to another. Different drug delivery times, with no other changes in the model parameters, can have significant long-term effects on neutrophil numbers. The frequency of drug delivery also has long-term effects on the oscillations.

CONCLUSION

Using a realistic representation of the effects of G-CSF on the tissue-level hematopoietic system, the model matches a wide range of laboratory data. This implies that it would be possible to generate individualized predictions for specific dogs if data were available in real time. The proposed interventions are practical and may reduce the amount of G-CSF required while potentially maintaining or even improving the treatment effects.

A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate

We develop a quasilinear structured model that describes the regulation of erythropoiesis, the process in which red blood cells are developed. In our model, the maturation velocity of precursor cells is assumed to be a function of the erythropoietin hormone, and the decay rate of this hormone is assumed to be a function of the number of precursor cells, unlike other models which assume these parameters to be constants. Existence-uniqueness results are established and convergence of a finite difference approximation to the unique solution of the model is obtained. The finite difference scheme is then used to investigate the effects of these nonlinear parameters on the model dynamics. Our results show that a velocity of precursor cells maturation rate which is an increasing function of the hormone level and a decay rate of the hormone which is an increasing function of the number of precursor cells have a stabilizing effect on the dynamics of the model. While assuming that one parameter is a function and letting the other be a constant stabilizes the oscillations in the mature cells level, the effect is more significant when both parameters are taken to be functions. A study of robustness with respect to the forms of these functions and parameter sensitivity is also carried out.

Modelling Hematopoiesis Mediated by Growth Factors With Applications to Periodic Hematological Diseases

Hematopoiesis is a complex biological process that leads to the production and regulation of blood cells. It is based upon differentiation of stem cells under the action of growth factors. A mathematical approach of this process is proposed to understand some blood diseases characterized by very long period oscillations in circulating blood cells. A system of three differential equations with delay, corresponding to the cell cycle duration, is proposed and analyzed. The existence of a Hopf bifurcation at a positive steady-state is obtained through the study of an exponential polynomial characteristic equation with delay-dependent coefficients. Numerical simulations show that long-period oscillations can be obtained in this model, corresponding to a destabilization of the feedback regulation between blood cells and growth factors, for reasonable cell cycle durations. These oscillations can be related to observations on some periodic hematological diseases (such as chronic myelogenous leukemia, for example).

A mathematical model of hematopoiesis: II. Cyclical neutropenia

Cyclical neutropenia is a dynamical disease of the hematopoietic system marked by an oscillation in circulating leukocyte (e.g. neutrophil) numbers to near zero levels and then back to normal. This oscillation is also mirrored in the platelets and reticulocytes which oscillate with the same period. Cyclical neutropenia has an animal counterpart in the grey collie. Using the mathematical model of the hematopoietic system of Colijn and Mackey [A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia. Companion paper to the present paper.] we have determined what parameters are necessary to mimic laboratory and clinical data on untreated grey collies and humans, and also what changes in these parameters are necessary to fit data during treatment with granulocyte colony stimulating factor (G-CSF). Compared to the normal steady-state values, we found that the major parameter changes that mimic untreated cyclical neutropenia correspond to a decreased amplification (increased apoptosis) within the proliferating neutrophil precursor compartment, and a decrease in the maximal rate of re-entry into the proliferative phase of the stem cell compartment. For the data obtained during G-CSF treatment, good fits were obtained only when parameters were altered that would imply that G-CSF led to higher amplification (lower rate of apoptosis) in the proliferating neutrophil precursors, and a elevated rate of differentiation into the neutrophil line.

A mathematical model of hematopoiesis—I. Periodic chronic myelogenous leukemia

Periodic chronic myelogenous leukemia (PCML) is an interesting dynamical disease of the hematopoietic system in which oscillating levels of circulating leukocytes, platelets and/or reticulocytes are observed. Typically all of these three differentiated cell types have the same oscillation period, but the relation of the oscillation mean and amplitude to the normal levels is variable. Given the appearance of the abnormal Philadelphia chromosome in all of the nucleated progeny of the hematopoietic stem cells (HSCs), the most parsimonious conclusion is that chronic myelogenous leukemia, and its periodic variant, arise from derangements partially involving the dynamics of the stem cells. Here, we have synthesized several previous mathematical models of HSC dynamics, and models for the regulation of neutrophils, platelets and erythrocytes into a comprehensive model for the regulation of the hematopoietic system. Based on estimates of parameters for a typical normal human, we have systematically explored the changes in some of these parameters necessary to account for the quantitative data on leukocyte, platelet and reticulocyte cycling in 11 patients with PCML. Our results indicate that the critical model parameter changes required to simulate the PCML patient data are an increase in the amplification in the leukocyte line, an increase in the differentiation rate from the stem cell compartment into the leukocyte line, and the rate of apoptosis in the stem cell compartment. Our model system is particularly sensitive to changes in stem cell apoptosis rates, suggesting that changes in the numbers of proliferating stem cells may be important in generating PCML.

A mathematical model of haemopoiesis as exemplified by CD34 cell mobilization into the peripheral blood

A mathematical model for the kinetics of haemopoietic cells, including CD34+cells, is proposed. This minimal model reflects the known kinetics of haemopoietic progenitor cells, including peripheral blood CD34+ cells, white blood cells and platelets, in the presence of granulocyte colony-stimulating factor. Reproducing known perturbations within this system, subjected to granulocyte colony-stimulating factor treatment and apheresis of peripheral blood progenitor cells (CD34+ cells) in healthy individuals allows validation of the model. Predictions are made with this model for reducing the length of time with neutropenia after high-dose chemotherapy. Results based on this model indicate that myelosuppressive treatment together with infusion of CD34+ peripheral blood progenitor cells favours a faster recovery of the haemopoietic system than with granulocyte colony-stimulating factor alone. Additionally, it predicts that infusion of white blood cells and platelets can relieve the symptoms of neutropenia and thrombocytopenia, respectively, without drastically hindering the haemopoietic recovery period after high dose chemotherapy.

Oscillations in cyclical neutropenia: new evidence based on mathematical modeling

We present a dynamical model of the production and regulation of circulating blood neutrophil number. This model is derived from physiologically relevant features of the hematopoietic system, and is analysed using both analytic and numerical methods. Supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles are shown to exist. We make the estimation of kinetic parameters for dogs and then apply the model to cyclical neutropenia (CN) in the grey collie, a rare disorder in which oscillations in all blood cell counts are found. We conclude that the major cause of the oscillations in CN is an increased rate of apoptosis of neutrophil precursors which leads to a destabilization of the hematopoietic stem cell compartment.

The rate of apoptosis in post mitotic neutrophil precursors of normal and neutropenic humans

Using data on the fraction of post-mitotic neutrophil precursors (CD15+ cells) displaying positive markers for apoptosis in 12 normal humans, and a simple mathematical model, we have estimated the apoptotic rate to be about 0.28/day in this compartment. This implies that the influx of myelocytes into the post-mitotic compartment exceeds twice the granulocyte turnover rate (GTR), and that about 55% of the cells entering this compartment die before being released into the blood. The normal half life of apoptotic post-mitotic neutrophil precursors is calculated to be 10.4 h. Comparable calculations for patients indicate apoptosis rates in the post-mitotic compartment of about 17 times normal for one myelokathexis patient and rates of about 13 times normal for the one cyclical neutropenic patient and two severe congenital neutropenic patients. The estimated half life for apoptotic post-mitotic neutrophil precursors in the myelokathexis patient was about 0.4 h, 1.4 h in the cyclical neutropenia patient, and about 0.6 h in the severe congenital neutropenic patients.

Cell kinetic status of haematopoietic stem cells

The haematopoietic stem cell (HSC) population supports a tremendous cellular production over the course of an animal's lifetime, e.g. adult humans produce their body weight in red cells, white cells and platelets every 7 years, while the mouse produces about 60% of its body weight in the course of a 2 year lifespan. Understanding how the HSC population carries this out is of interest and importance, and a first step in that understanding involves the characterization of HSC kinetics. Using previously published continuous labelling data (of Bradford et al. 1997 and Cheshier et al. 1999) from mouse HSC and a standard G0 model for the cell cycle, the steady state parameters characterizing these HSC populations are derived. It is calculated that in the mouse the differentiation rate ranges between about 0.01 and 0.02, the rate of cell re-entry from G0 back into the proliferative phase is between 0.02 and 0.05, the rate of apoptosis from the proliferative phase is between 0.07 and 0.23 (all units are days(-1)), and the duration of the proliferative phase is between 1.4 and 4.3 days. These values are compared with previously obtained values derived from the modelling by Abkowitz and colleagues of long-term haematopoietic reconstitution in the cat (Abkowitz et al. 1996) and the mouse (Abkowitz et al. 2000). It is further calculated using the estimates derived in this paper and other data on mice that between the HSC and the circulating blood cells there are between 17 and 19.5 effective cell divisions giving a net amplification of between approximately 170 000 and approximately 720 000.