Novel Strategies for Granulocyte Colony-Stimulating Factor Treatment of Severe Prolonged Neutropenia Suggested by Mathematical Modeling

Continuous Intravenous Administration of Granulocyte-Colony-Stimulating Factors-A Breakthrough in the Treatment of Cancer Patients with Febrile Neutropenia

Background: Febrile neutropenia (FN) remains one of the most challenging problems in medical oncology and is a very severe side effect of chemotherapy. Its late consequences, when it is recurrent or of a severe grade, are dose reduction and therapy delays. Current guidelines allow the administration of granulocyte-colony-stimulating factors (G-CSF) for profound FN (except for the case when a pegylated form of G-CSF is administrated with prophylactic intention) in addition to antibiotics and supportive care. Methods: This is a prospective study that included 96 patients with confirmed malignancy, treated with chemotherapy, who developed FN during their oncological therapy, and were hospitalized. They received standard treatment plus a dose of G-CSF of 16 µg/Kg/day IV continuous infusion. Results: The gender distribution was almost symmetrical: Male patients made up 48.96% and 51.04% were female patients, with no significance on recovery from FN (p = 1.00). The patients who received prophylactic G-CSF made up 20.21%, but this was not a predictive or prognostic factor for the recovery time from aplasia (p = 0.34). The median chemotherapy line where patients with FN were included was two and the number of previous chemotherapy cycles before FN was three. The median serological number of neutrophils (PMN) was 450/mm³ and leucocytes (WBC) 1875/mm³ at the time of FN. Ten patients possess PMN less than 100/mm³. The median time to recovery was 25.5 h for 96 included patients, with one failure in which the patient possessed grade 5 FN. Predictive factors for shorter recovery time were lower levels of C reactive protein (p < 0.001) and procalcitonin (p = 0.002) upon hospital admission and higher WBC (p = 0.006) and PMN (p < 0.001) at the time of the provoking cycle of chemotherapy for FN. The best chance for a shorter duration of FN was a short history of chemotherapy regarding the number of cycles) (p < 0.0001). Conclusions: Continuous IV administration of G-CSF could be an alternative salvage treatment for patients with profound febrile neutropenia, with a very fast recovery time for neutrophiles.

Model-Based Optimal AML Consolidation Treatment

OBJECTIVE

Neutropenia is an adverse event commonly arising during intensive chemotherapy of acute myeloid leukemia (AML). It is often associated with infectious complications. Mathematical modeling, simulation, and optimization of the treatment process would be a valuable tool to support clinical decision making, potentially resulting in less severe side effects and deeper remissions. However, until now, there has been no validated mathematical model available to simulate the effect of chemotherapy treatment on white blood cell (WBC) counts and leukemic cells simultaneously.

METHODS

We developed a population pharmacokinetic/pharmacodynamic (PK/PD) model combining a myelosuppression model considering endogenous granulocyte-colony stimulating factor (G-CSF), a PK model for cytarabine (Ara-C), a subcutaneous absorption model for exogenous G-CSF, and a two-compartment model for leukemic blasts. This model was fitted to data of 44 AML patients during consolidation therapy with a novel Ara-C plus G-CSF schedule from a phase II controlled clinical trial. Additionally, we were able to optimize treatment schedules with respect to disease progression, WBC nadirs, and the amount of Ara-C and G-CSF.

RESULTS

The developed PK/PD model provided good prediction accuracies and an interpretation of the interaction between WBCs, G-CSF, and blasts. For 14 patients (those with available bone marrow blast counts), we achieved a median 4.2-fold higher WBC count at nadir, which is the most critical time during consolidation therapy. The simulation results showed that relative bone marrow blast counts remained below the clinically important threshold of 5%, with a median of 60% reduction in Ara-C.

CONCLUSION

These in silico findings demonstrate the benefits of optimized treatment schedules for AML patients.

SIGNIFICANCE

Until 2017, no new drug had been approved for the treatment of AML, fostering the optimal use of currently available drugs.

Efficacy of Neulasta or Neupogen on H-ARS and GI-ARS Mortality and Hematopoietic Recovery in Nonhuman Primates After 10-Gy Irradiation With 2.5% Bone Marrow Sparing

A nonhuman primate model of acute, partial-body, high-dose irradiation with minimal (2.5%) bone marrow sparing was used to assess endogenous gastrointestinal and hematopoietic recovery and the ability of Neulasta (pegylated granulocyte colony-stimulating factor) or Neupogen (granulocyte colony-stimulating factor) to enhance recovery from myelosuppression when administered at an increased interval between exposure and initiation of treatment. A secondary objective was to assess the effect of Neulasta or Neupogen on mortality and morbidity due to the hematopoietic acute radiation syndrome and concomitant gastrointestinal acute radiation syndrome. Nonhuman primates were exposed to 10.0 Gy, 6 MV, linear accelerator-derived photons delivered at 0.80 Gy min. All nonhuman primates received subject-based medical management. Nonhuman primates were dosed daily with control article (5% dextrose in water), initiated on day 1 postexposure; Neulasta (300 μg kg), administered on days 1, 8, and 15 or days 3, 10, and 17 postexposure; or Neupogen (10 μg kg), administered daily postexposure following its initiation on day 1 or day 3 until neutrophil recovery (absolute neutrophil count ≥1,000 cells μL for 3 consecutive days). Mortality in the irradiated cohorts suggested that administration of Neulasta or Neupogen on either schedule did not affect mortality due to gastrointestinal acute radiation syndrome or mitigate mortality due to hematopoietic acute radiation syndrome (plus gastrointestinal damage). Following 10.0 Gy partial-body irradiation with 2.5% bone marrow sparing, the mean duration of neutropenia (absolute neutrophil count <500 cells μL) was 22.4 d in the control cohort vs. 13.0 and 15.3 d in the Neulasta day 1, 8, 15 and day 3, 10, 17 cohorts, relative to 16.2 and 17.4 d in the Neupogen cohorts initiated on day 1 and day 3, respectively. The absolute neutrophil count nadirs were 48 cells μL in the controls; 117 cells μL and 40 cells μL in the Neulasta days 1, 8, and 15 or days 3, 10, and 17 cohorts, respectively; and 75 cells μL and 37 cells μL in the Neupogen day 1 and day 3 cohorts, respectively. Therefore, the earlier administration of Neulasta or Neupogen was more effective in this model of marginal 2.5% bone marrow sparing. The approximate 2.5% bone marrow sparing may approach the threshold for efficacy of the lineage-specific medical countermeasure. The partial-body irradiation with 2.5% bone marrow sparing model can be used to assess medical countermeasure efficacy in the context of the concomitant gastrointestinal and hematopoietic acute radiation syndrome sequelae.

Modeling therapeutic response to radioiodine in metastatic thyroid cancer: a proof-of-concept study for individualized medicine

Purpose

Radioiodine therapy (RAI) has traditionally been used as treatment for metastatic thyroid cancer, based on its ability to concentrate iodine. Propositions to maximize tumor response with minimizing toxicity, must recognize the infinite possibilities of empirical tests. Therefore, an approach of this study was to build a mathematical model describing tumor growth with the kinetics of thyroglobulin (Tg) concentrations over time, following RAI for metastatic thyroid cancer.

Experimental Design

Data from 50 patients with metastatic papillary thyroid carcinoma treated within eight French institutions, followed over 3 years after initial RAI treatments, were included in the model. A semi-mechanistic mathematical model that describes the tumor growth under RAI treatment was designed.

Results

Our model was able to separate patients who responded to RAI from those who did not, concordant with the physicians' determination of therapeutic response. The estimated tumor doubling-time (Td was found to be the most informative parameter for the distinction between responders and non-responders. The model was also able to reclassify particular patients in early treatment stages.

Conclusions

The results of the model present classification criteria that could indicate whether patients will respond or not to RAI treatment, and provide the opportunity to perform personalized management plans.

Granulocyte Colony-Stimulating Factor and Its Potential Application for Skeletal Muscle Repair and Regeneration

Granulocyte colony-stimulating factor (G-CSF) was originally discovered in the context of hematopoiesis. However, the identification of the G-CSF receptor (G-CSFR) being expressed outside the hematopoietic system has revealed wider roles for G-CSF, particularly in tissue repair and regeneration. Skeletal muscle damage, including that following strenuous exercise, induces an elevation in plasma G-CSF, implicating it as a potential mediator of skeletal muscle repair. This has been supported by preclinical studies and clinical trials investigating G-CSF as a potential therapeutic agent in relevant disease states. This review focuses on the growing literature associated with G-CSF and G-CSFR in skeletal muscle under healthy and disease conditions and highlights the current controversies.

Neutrophil dynamics during concurrent chemotherapy and G-CSF administration: Mathematical modelling guides dose optimisation to minimise neutropenia

The choice of chemotherapy regimens is often constrained by the patient's tolerance to the side effects of chemotherapeutic agents. This dose-limiting issue is a major concern in dose regimen design, which is typically focused on maximising drug benefits. Chemotherapy-induced neutropenia is one of the most prevalent toxic effects patients experience and frequently threatens the efficient use of chemotherapy. In response, granulocyte colony-stimulating factor (G-CSF) is co-administered during chemotherapy to stimulate neutrophil production, increase neutrophil counts, and hopefully avoid neutropenia. Its clinical use is, however, largely dictated by trial and error processes. Based on up-to-date knowledge and rational considerations, we develop a physiologically realistic model to mathematically characterise the neutrophil production in the bone marrow which we then integrate with pharmacokinetic and pharmacodynamic (PKPD) models of a chemotherapeutic agent and an exogenous form of G-CSF (recombinant human G-CSF, or rhG-CSF). In this work, model parameters represent the average values for a general patient and are extracted from the literature or estimated from available data. The dose effect predicted by the model is confirmed through previously published data. Using our model, we were able to determine clinically relevant dosing regimens that advantageously reduce the number of rhG-CSF administrations compared to original studies while significantly improving the neutropenia status. More particularly, we determine that it could be beneficial to delay the first administration of rhG-CSF to day seven post-chemotherapy and reduce the number of administrations from ten to three or four for a patient undergoing 14-day periodic chemotherapy.

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.

In the present paper, we propose a comprehensive model of chemotherapy toxicity and combine it with our cell kinetic model of granulopoiesis. Major assumptions are: proportionality of cell numbers and cell loss, delayed action of chemotherapy, drug, drug-dose and cell stage specific toxicities, no interaction of drugs and higher toxicity of drugs at the first time of application. Correspondingly, chemotherapies can be characterized by a set of toxicity parameters which can be estimated by fitting the predictions of our model to clinical time series data of patients under therapy. Data were either extracted from the literature or were received from cooperating clinical study groups.

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.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-014-0138-7) contains supplementary material, which is available to authorized users.

Feasibility and safety of a reduced duration of therapy of colony-stimulating factor in a dose-dense regimen

Purpose

The risk of febrile neutropenia (FN) in cancer patients receiving chemotherapy is mainly due to the type of chemotherapy regimen and the presence of specific risk factors in patients. The recent trend of using a dose-dense treatment schedule has enhanced the risk of FN. In the present prospective study, we evaluated the feasibility of a reduction of duration of therapy with colony-stimulating factor (G-CSF) in a dose-dense regimen.

Methods

Between June 2002 and December 2011, 107 patients with a new diagnosis of non-Hodgkin lymphoma (NHL) receiving dose-dense chemotherapy, every 14 days, were included in the study. The primary endpoint was defined as the completion of planned chemotherapy cycles as scheduled. Secondary endpoints were median number of administered G-CSF doses (vials), incidence of FN, hospitalization and toxicity.

Results

The planned chemotherapy cycles (primary endpoint) were completed by 84.1 % of patients. The median number of G-CSF (lenograstim) doses administered for each patient was 24 (range 10–35), which corresponds to a median of five vials (range 0–10) for each cycle. Grades 3–4 toxicities, related to G-CSF administration, included neutropenia and thrombocytopenia (14.0 and 1.9 %, respectively). No grades 3–4 bone pain was detected. The incidence of FN and hospitalization was 9.3 % (10/107) and 4.5 % (5/107), respectively.

Conclusions

Reduced dosage of G-CSF allows dose-dense chemotherapy scheduling, limits exposure to G-CSF and also represents an opportunity for cost savings.

A Type II Arabinogalactan from Anoectochilus formosanus for G-CSF Production in Macrophages and Leukopenia Improvement in CT26-Bearing Mice Treated with 5-Fluorouracil

Anoectochilus formosanus is an herb well known in Asian countries. The polysaccharide isolated from A. formosanus consists of type II arabinogalactan (AGAF), with branched 3,6-Gal as the major moiety. In this study, AGAF was examined for the granulocyte colony-stimulating factor (G-CSF) production and related protein expression in RAW 264.7 murine macrophages. The signaling pathway of G-CSF production involves AGAF and mitogen-activated protein kinases (MAPKs) inhibitors and pattern-recognition receptor antibodies. AGAF was evaluated to ease the leukopenia in CT26-colon-cancer-bearing mice treated with 5-fluorouracil (5-FU). The results of this study showed that AGAF was a stimulant for Toll-like receptor 2 and Dectin-1 and that it induced G-CSF production, through p38 and ERK MAPK, and NF- κ B pathways. In vivo examination showed that the oral administration of AGAF mitigated the side effects of leukopenia caused by 5-FU in colon-cancer-bearing mice. In conclusion, the botanic type II AGAF in this study was a potent G-CSF inducer in vivo and in vitro.

Incidence of chemotherapy-induced neutropenia and current practice of prophylaxis with granulocyte colony-stimulating factors in cancer patients in Spain: a prospective, observational study

We aimed to describe the incidence of neutropenia in breast cancer and lymphoma patients and granulocyte colony-stimulating factors (G-CSF) use in clinical practice. We conducted a multicentre, prospective, observational study including breast cancer and lymphoma patients initiating chemotherapy (≥ 10% febrile neutropenia risk). We included 734 patients with breast cancer and 291 with lymphoma. Over the first four chemotherapy cycles, patients had an incidence of 11.0% grade 3-4 neutropenia (absolute neutrophil count <1.0 × 10(9) /L) and 4.3% febrile neutropenia (absolute neutrophil count <0.5 × 10(9) /L and fever ≥ 38 °C) in the breast cancer cohort, and 40.5% and 14.8% in the lymphoma cohort. Full dose on schedule (>85% of planned chemotherapy dose and ≤ 3 days delay) was achieved by 85.6% of breast cancer and 68.9% of lymphoma patients. Hospitalisation due to febrile neutropenia was required in 2.0% and 12.0% of breast cancer and lymphoma patients respectively. G-CSF was administered to 70.0% of breast cancer and 83.8% of lymphoma patients, and initiated from the first chemotherapy cycle (primary prophylaxis) in 60.6% and 64.2% of cases. Severe neutropenia affects approximately one in 10 breast cancer patients and one in two lymphoma patients receiving chemotherapy with moderate or greater risk of febrile neutropenia. Most patients received treatment with G-CSF in Spanish clinical practice.

Effectiveness of daily versus non-daily granulocyte colony-stimulating factors in patients with solid tumours undergoing chemotherapy: a multivariate analysis of data from current practice

We conducted a multicentre, retrospective, observational study including patients with solid tumours (excluding breast cancer) that received granulocyte colony-stimulating factors (G-CSF) and chemotherapy. We investigated the effectiveness of daily vs. non-daily G-CSFs (pegfilgrastim) adjusting by potential confounders. The study included 391 patients (211 daily G-CSF; 180 pegfilgrastim), from whom 47.3% received primary prophylaxis (PP) (57.8% pegfilgrastim), 26.3% secondary prophylaxis (SP: initiation after cycle 1 and no reactive treatment in any cycle) (51.5% pegfilgrastim) and 26.3% reactive treatment (19.4% pegfilgrastim). Only 42.2% of patients with daily G-CSF and 46.2% with pegfilgrastim initiated prophylaxis within 72 h after chemotherapy, and only 10.5% of patients with daily G-CSF received it for ≥7 days. In the multivariate models, daily G-CSF was associated with higher risk of grade 3-4 neutropenia (G3-4N) vs. pegfilgrastim [odds ratio (OR): 1.73, 95% confidence interval (CI): 1.004–2.97]. Relative to SP, PP protected against G3-4N (OR for SP vs. PP: 6.0, 95%CI: 3.2–11.4) and febrile neutropenia (OR: 3.1, 95%CI: 1.1–8.8), and was associated to less chemotherapy dose delays and reductions (OR for relative dose intensity <85% for SP vs. PP: 3.1, 95%CI: 1.7–5.4) and higher response rate (OR: 2.1, 95%CI: 1.2–3.7). Data suggest that pegfilgrastim, compared with a daily G-CSF, and PP, compared with SP, could be more effective in preventing neutropenia and its related events in the clinical practice.

Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response

Chemotherapy has profound effects on the hematopoietic system, most notably leading to neutropenia. Granulocyte colony stimulating factor (G-CSF) is often used to deal with this neutropenia, but the response is highly variable. In this paper we examine the role of pharmacokinetics and delivery protocols in shaping the neutrophil responses to chemotherapy and G-CSF. Neutrophil responses to different protocols of chemotherapy administration with varying dosages, infusion times, and schedules are studied through a mathematical model. We find that a single dose of chemotherapy produces a damped oscillation in neutrophil levels, and short-term applications of chemotherapy can induce permanent oscillations in neutrophil level if there is a bistability in the system. In addition, we confirm previous findings [Zhuge et al., J. Theor. Biol., 293(2012), 111-120] that when periodic chemotherapy is given, there is a significant period of delivery that induces resonance in the system and exacerbates the corresponding neutropenia. The width of this resonant period peak increases with the recovery rate after a single chemotherapy, which is given by the real part of the dominant eigenvalue pair at the steady state, and both are determined by a single cooperativity coefficient in the feedback function for the neutrophils. Our numerical studies show that the neutropenia caused by chemotherapy can be overcome if G-CSF is given early after chemotherapy but can actually be worsened if G-CSF is given later, consistent with results reported in Zhuge et al. (2012). The nadir in neutrophil level is found to be more sensitive to the dosage of chemotherapy than that of the G-CSF. Furthermore, dependence of our results with changes in key pharmacokinetic parameters as well as initial functions are studied. Thus, this study illuminates the potential for destructive resonance leading to neutropenia in response to periodic chemotherapy, and explores and explains why the timing of G-CSF is so crucial for successful reversal of chemotherapy induced neutropenia.

Evidence for bistable bacteria-neutrophil interaction and its clinical implications

Neutropenia, which may develop as a consequence of chemotherapy, increases the risk of bacterial infection. Similarly, increased risk of bacterial infection appears in disorders of phagocytic functions, such as the genetic disorder chronic granulomatous disease. To elucidate the organizing principles behind these distinct immunodeficiency conditions, we investigated the interaction between in vitro bacteria and human neutrophils by experiments and mathematical modeling. The model and the experiments showed that the in vitro bacterial dynamics exhibit bistability for a certain range of neutrophil concentration and function. Thus, there is a critical bacterial concentration above which infection develops, and below which neutrophils defeat the bacteria. Whereas with normal neutrophil concentration and function, an infection may develop when the initial bacterial concentration is very high, under neutropenic conditions or when there is neutrophil dysfunction, the critical bacterial concentration can be lower, within the clinically relevant range. We conclude that critical bacterial concentration has clinically relevant implications. The individual maximum bearable bacterial concentration depended on neutrophil concentration, phagocytic activity, and patient barrier integrity; thus, the resulting maximal bearable bacterial concentration may vary by orders of magnitude between patients. Understanding the interplay between neutrophils and bacteria may enhance the development of new therapeutic approaches to bacterial infections.

Personalising docetaxel and G-CSF schedules in cancer patients by a clinically validated computational model

Background:

This study was aimed to develop a new method for personalising chemotherapeutic and granulocyte colony-stimulating factor (G-CSF) combined schedules, and use it for suggesting efficacious chemotherapy with reduced neutropenia.

Methods:

Clinical data from 38 docetaxel (Doc)-treated metastatic breast cancer patients were employed for validating a new pharmacokinetic/pharmacodynamics model for Doc, combined with a mathematical model for granulopoiesis. An optimisation procedure was constructed and used for selecting improved treatment schedules.

Results:

The combined model accurately predicted observed nadir timing (r=0.99), grade 3 or 4 neutropenia (86% success) and neutrophil counts over time in individual patients (r=0.63), and showed robustness to CYP3A-induced variability in Doc clearance. For average patients, the predicted optimal support for the standard chemotherapy regimen, Doc 100 μg m⁻² tri-weekly, is G-CSF, 300 μg, Q1D × 3, starting day 7 post-Doc. This regimen largely moderates chemotherapy-induced neutrophil nadir and neutropenia duration. The more intensive Doc dose, 150 mg m⁻², is optimally supported by the slightly less cost-effective G-CSF 300 μg, Q1D × 4, 5 days post-Doc. The latter regimen is optimal for borderline patients (2000 neutrophils per μl) under Doc, 100–150 mg m⁻² tri-weekly.

Conclusions:

The new computational method can serve for tailoring efficacious cytotoxic and supportive treatments, minimising side effects to individual patients. Prospective clinical validation is warranted.

Intermittent granulocyte colony-stimulating factor maintains dose intensity after ABVD therapy complicated by neutropenia

INTRODUCTION

Granulocyte Colony-Stimulating Factor (G-CSF) is commonly used to maintain dose intensity in patients receiving ABVD chemotherapy (doxorubicin, bleomycin, vinblastine and dacarbazine) for Hodgkin lymphoma. However, the need for growth factor support is unclear, with studies suggesting that dose intensity can be maintained without G-CSF. Moreover, G-CSF is expensive (pegfilgrastim: EUR 1540/cycle; 300 μg filgrastim for 7 days: EUR 700/cycle) and is associated with side effects including bone pain and increased risk of bleomycin lung toxicity. Intermittent G-CSF may be an effective compromise, given that the effect of G-CSF on granulocyte precursors in vitro persists for 4-5 days after administration. After promising results of a pilot study, this schedule has been used subsequently in the majority of our patients receiving G-CSF as secondary prophylaxis for ABVD complicated by neutropenia.

METHODS

Retrospective analysis of the incidence of febrile neutropenia and treatment delay in a variety of different G-CSF schedules used as secondary prophylaxis in patients receiving ABVD.

RESULTS

848 cycles in 85 consecutive patients were evaluated. Most patients (86%) received G-CSF, generally commenced prophylactically for neutropenia when cycle 1B was due. Intermittent G-CSF (typically given on days 4, 8 and 12) was used in 413 cycles compared with daily or pegylated G-CSF in 99 cycles. In patients receiving intermittent G-CSF, the median neutrophil count, across all cycles, was 7.3 × 10(9) /L (range: 1.4-47.1) when the next scheduled chemotherapy was due. There were two cases of febrile neutropenia (0.45%) and no treatment delays. One patient developed possible bleomycin toxicity.

CONCLUSIONS

Intermittent G-CSF is effective in maintaining dose intensity in patients receiving ABVD.

Bacteria-phagocyte dynamics, axiomatic modelling and mass-action kinetics

Axiomatic modeling is ensued to provide a family of models that describe bacterial growth in the presence of phagocytes, or, more generally, prey dynamics in a large spatially homogenous eco-system. A classification of the possible bifurcation diagrams that arise in such models is presented. It is shown that other commonly used models that do not belong to this class may miss important features that are associated with the limited growth curve of the bacteria (prey) and the saturation associated with the phagocytosis (predator kill) term. Notably, these features appear at relatively low concentrations, much below the saturation range. Finally, combining this model with a model of neutrophil dynamics in the blood after chemotherapy treatments we obtain new insights regarding the development of infections under neutropenic conditions.

Bistability and bacterial infections

Bacterial infections occur when the natural host defenses are overwhelmed by invading bacteria. The main component of the host defense is impaired when neutrophil count or function is too low, putting the host at great risk of developing an acute infection. In people with intact immune systems, neutrophil count increases during bacterial infection. However, there are two important clinical cases in which they remain constant: a) in patients with neutropenic-associated conditions, such as those undergoing chemotherapy at the nadir (the minimum clinically observable neutrophil level); b) in ex vivo examination of the patient's neutrophil bactericidal activity. Here we study bacterial population dynamics under fixed neutrophil levels by mathematical modelling. We show that under reasonable biological assumptions, there are only two possible scenarios: 1) Bacterial behavior is monostable: it always converges to a stable equilibrium of bacterial concentration which only depends, in a gradual manner, on the neutrophil level (and not on the initial bacterial level). We call such a behavior type I dynamics. 2) The bacterial dynamics is bistable for some range of neutrophil levels. We call such a behavior type II dynamics. In the bistable case (type II), one equilibrium corresponds to a healthy state whereas the other corresponds to a fulminant bacterial infection. We demonstrate that published data of in vitro Staphylococcus epidermidis bactericidal experiments are inconsistent with both the type I dynamics and the commonly used linear model and are consistent with type II dynamics. We argue that type II dynamics is a plausible mechanism for the development of a fulminant infection.

Mathematical modeling as a tool for planning anticancer therapy

We review a large volume of literature concerning mathematical models of cancer therapy, oriented towards optimization of treatment protocols. The review, although partly idiosyncratic, covers such major areas of therapy optimization as phase-specific chemotherapy, antiangiogenic therapy and therapy under drug resistance. We start from early cell cycle progression models, very simple but admitting explicit mathematical solutions, based on methods of control theory. We continue with more complex models involving evolution of drug resistance and pharmacokinetic and pharmacodynamic effects. Then, we consider two more recent areas: angiogenesis of tumors and molecular signaling within and among cells. We discuss biological background and mathematical techniques of this field, which has a large although only partly realized potential for contributing to cancer treatment.