Mathematical modeling of the impact of cytokine response of acute myeloid leukemia cells on patient prognosis

Discovery of Dynamic Models for AML Disease Progression from Longitudinal Multi-Modal Clinical Data Using Explainable Machine Learning

Acute Myeloid Leukemia (AML) is a complex and heterogeneous disease identified by severe clinical progression, fast cellular proliferation, and often high mortality rates. Incorporating diverse longitudinal information on patients' medical histories is essential for developing effective disease predictive models applicable to both research and clinical settings. Here, we present a robust methodology for discovering dynamic predictive models to elucidate AML disease progression dynamics from a novel longitudinal multimodal clinical dataset of patients diagnosed with AML. The clinical dataset was analyzed to reveal the main clinical, genetic, and treatment features modulating disease progression. To discover mathematical models-including interactions, parameters, and nodes-predictive of AML progression, we present an explainable machine learning algorithm based on high-performance evolutionary computation. The results demonstrate that the predictive methodology could accurately estimate the clinical dynamics of AML progression in terms of blast percentages for both training and novel patients. This study demonstrates that the developed explainable machine learning approach can successfully predict AML progression by leveraging the heterogeneous and longitudinal dynamics of patients' clinical data. More importantly, this methodology shows significant potential for application in modeling the progression dynamics of other acute diseases, providing a flexible and adaptable framework for advancing clinical and translational research.

Stem cell graft dose and composition could impact on the expansion of donor-derived clones after allogeneic hematopoietic stem cell transplantation - a virtual clinical trial

Introduction

Hematopoietic stem cell transplantation is a potentially curative intervention for a broad range of diseases. However, there is evidence that malignant or pre-malignant clones contained in the transplant can expand in the recipient and trigger donor-derived malignancies. This observation has gained much attention in the context of clonal hematopoiesis, a medical condition where significant amounts of healthy blood cells are derived from a small number of hematopoietic stem cell clones. In many cases the dominating clones carry mutations conferring a growth advantage and thus could undergo malignant transformation in the recipient. Since clonal hematopoiesis exists in a significant proportion of potential stem cell donors, a more detailed understanding of its role for stem cell transplantation is required.

Methods

We propose mechanistic computational models and perform virtual clinical trials to investigate clonal dynamics during and after allogenic hematopoietic stem cell transplantation. Different mechanisms of clonal expansion are considered, including mutation-related changes of stem cell proliferation and self-renewal, aberrant response of mutated cells to systemic signals, and self-sustaining chronic inflammation triggered by the mutated cells.

Results

Model simulations suggest that an aberrant response of mutated cells to systemic signals is sufficient to explain the frequently observed quick expansion of the mutated clone shortly after transplantation which is followed by a stabilization of the mutated cell number at a constant value. In contrary, a mutation-related increase of self-renewal or self-sustaining chronic inflammation lead to ongoing clonal expansion. Our virtual clinical trials suggest that a low number of transplanted stem cells per kg of body weight increases the transplantation-related expansion of donor-derived clones, whereas the transplanted progenitor dose or growth factor support after transplantation have no impact on clonal dynamics. Furthermore, in our simulations the change of the donors' variant allele frequencies in the year before stem cell donation is associated with the expansion of donor-derived clones in the recipient.

Discussion

This in silico study provides insights in the mechanisms leading to clonal expansion and identifies questions that could be addressed in future clinical trials.

Modelling post-chemotherapy stem cell dynamics in the bone marrow niche of AML patients

Acute myeloid leukemia (AML) is a stem cell-driven malignancy of the blood forming (hematopoietic) system. Despite of high dose chemotherapy with toxic side effects, many patients eventually relapse. The "7+3 regimen", which consists of 7 days of cytarabine in combination with daunorubicin during the first 3 days, is a widely used therapy protocol. Since peripheral blood cells are easily accessible to longitudinal sampling, significant research efforts have been undertaken to characterize and reduce adverse effects on circulating blood cells. However, much less is known about the impact of the 7+3 regimen on human hematopoietic stem cells and their physiological micro-environments, the so-called stem cell niches. One reason for this is the technical inability to observe human stem cells in vivo and the discomfort related to bone marrow biopsies. To better understand the treatment effects on human stem cells, we consider a mechanistic mathematical model of the stem cell niche before, during and after chemotherapy. The model accounts for different maturation stages of leukemic and hematopoietic cells and considers key processes such as cell proliferation, self-renewal, differentiation and therapy-induced cell death. In the model, hematopoietic (HSCs) and leukemic stem cells (LSCs) compete for a joint niche and respond to both systemic and niche-derived signals. We relate the model to clinical trial data from literature which longitudinally quantifies the counts of hematopoietic stem like (CD34+CD38-ALDH+) cells at diagnosis and after therapy. The proposed model can capture the clinically observed interindividual heterogeneity and reproduce the non-monotonous dynamics of the hematopoietic stem like cells observed in relapsing patients. Our model allows to simulate different scenarios proposed in literature such as therapy-related impairment of the stem cell niche or niche-mediated resistance. Model simulations suggest that during the post-therapy phase a more than 10-fold increase of hematopoietic stem-like cell proliferation rates is required to recapitulate the measured cell dynamics in patients achieving complete remission. We fit the model to data of 7 individual patients and simulate variations of the treatment protocol. These simulations are in line with the clinical finding that G-CSF priming can improve the treatment outcome. Furthermore, our model suggests that a decline of HSC counts during remission might serve as an indication for salvage therapy in patients lacking MRD (minimal residual disease) markers.

Computational modeling reveals key factors driving treatment-free remission in chronic myeloid leukemia patients

Patients with chronic myeloid leukemia (CML) who receive tyrosine kinase inhibitors (TKIs) have been known to achieve treatment-free remission (TFR) upon discontinuing treatment. However, the underlying mechanisms of this phenomenon remain incompletely understood. This study aims to elucidate the mechanism of TFR in CML patients, focusing on the feedback interaction between leukemia stem cells and the bone marrow microenvironment. We have developed a mathematical model to explore the interplay between leukemia stem cells and the bone marrow microenvironment, allowing for the simulation of CML progression dynamics. Our proposed model reveals a dichotomous response following TKI discontinuation, with two distinct patient groups emerging: one prone to early molecular relapse and the other capable of achieving long-term TFR after treatment cessation. This finding aligns with clinical observations and underscores the essential role of feedback interaction between leukemic cells and the tumor microenvironment in sustaining TFR. Notably, we have shown that the ratio of leukemia cells in peripheral blood (PBLC) and the tumor microenvironment (TME) index can be a valuable predictive tool for identifying patients likely to achieve TFR after discontinuing treatment. This study provides fresh insights into the mechanism of TFR in CML patients and underscores the significance of microenvironmental control in achieving TFR.

AML consolidation therapy: timing matters

PURPOSE

Infections due to severe neutropenia are the most common therapy-associated causes of mortality in patients with acute myeloid leukemia (AML). New strategies to lessen the severity and duration of neutropenia are needed.

METHODS

Cytarabine is commonly used for AML consolidation therapy; we compared high- and intermediate-dose cytarabine administration on days 1, 2, and 3 (AC-123) versus days 1, 3, and 5 (AC-135) in consolidation therapy of AML. Recently, clinical trials demonstrated that high-dose AC-123 resulted in a shortened white blood cell (WBC) recovery time compared with high-dose AC-135. Our main hypothesis is that this is also the case for different cytarabine dosage, granulocyte colony-stimulating factor (G-CSF) administration, and cycle lengths. We analyzed 334 treatment schedules on virtual cohorts of digital twins.

RESULTS

Comparison of 32,565 simulated consolidation cycles resulted in a reduction in the WBC recovery time for AC-123 in 99.6% of the considered cycles (median reduction 3.5 days) without an increase in the number of leukemic blasts (lower value in 94.2% of all cycles), compared to AC-135.

CONCLUSION

Our numerical study supports the use of AC-123 plus G-CSF as standard conventional AML consolidation therapy to reduce the risk for life-threatening infectious complications.

Predictive nonlinear modeling of malignant myelopoiesis and tyrosine kinase inhibitor therapy

Chronic myeloid leukemia (CML) is a blood cancer characterized by dysregulated production of maturing myeloid cells driven by the product of the Philadelphia chromosome, the BCR-ABL1 tyrosine kinase. Tyrosine kinase inhibitors (TKIs) have proved effective in treating CML, but there is still a cohort of patients who do not respond to TKI therapy even in the absence of mutations in the BCR-ABL1 kinase domain that mediate drug resistance. To discover novel strategies to improve TKI therapy in CML, we developed a nonlinear mathematical model of CML hematopoiesis that incorporates feedback control and lineage branching. Cell-cell interactions were constrained using an automated model selection method together with previous observations and new in vivo data from a chimeric BCR-ABL1 transgenic mouse model of CML. The resulting quantitative model captures the dynamics of normal and CML cells at various stages of the disease and exhibits variable responses to TKI treatment, consistent with those of CML patients. The model predicts that an increase in the proportion of CML stem cells in the bone marrow would decrease the tendency of the disease to respond to TKI therapy, in concordance with clinical data and confirmed experimentally in mice. The model further suggests that, under our assumed similarities between normal and leukemic cells, a key predictor of refractory response to TKI treatment is an increased maximum probability of self-renewal of normal hematopoietic stem cells. We use these insights to develop a clinical prognostic criterion to predict the efficacy of TKI treatment and design strategies to improve treatment response. The model predicts that stimulating the differentiation of leukemic stem cells while applying TKI therapy can significantly improve treatment outcomes.

HSC Niche Dynamics in Regeneration, Pre-malignancy, and Cancer: Insights From Mathematical Modeling

The hematopoietic stem cell (HSC) niche is a crucial driver of regeneration and malignancy. Its interaction with hematopoietic and malignant stem cells is highly complex and direct experimental observations are challenging. We here develop a mathematical model which helps relate processes in the niche to measurable changes of stem and non-stem cell counts. HSC attached to the niche are assumed to be quiescent. After detachment HSC become activated and divide or differentiate. To maintain their stemness, the progeny originating from division must reattach to the niche. We use mouse data from literature to parametrize the model. By combining mathematical analysis and computer simulations, we systematically investigate the impact of stem cell proliferation, differentiation, niche attachment, and detachment on clinically relevant scenarios. These include bone marrow transplantation, clonal competition, and eradication of malignant cells. According to our model, sampling of blood or bulk marrow provides only limited information about cellular interactions in the niche and the clonal composition of the stem cell population. Furthermore, we investigate how interference with processes in the stem cell niche could help to increase the effect of low-dose chemotherapy or to improve the homing of genetically engineered cells.

Understanding Hematopoietic Stem Cell Dynamics—Insights from Mathematical Modelling

Purpose of review

Hematopoietic stem cells (HSCs) drive blood-cell production (hematopoiesis). Out-competition of HSCs by malignant cells occurs in many hematologic malignancies like acute myeloid leukemia (AML). Through mathematical modelling, HSC dynamics and their impact on healthy blood cell formation can be studied, using mathematical analysis and computer simulations. We review important work within this field and discuss mathematical modelling as a tool for attaining biological insight.

Recent findings

Various mechanism-based models of HSC dynamics have been proposed in recent years. Key properties of such models agree with observations and medical knowledge and suggest relations between stem cell properties, e.g., rates of division and the temporal evolution of the HSC population. This has made it possible to study how HSC properties shape clinically relevant processes, including engraftment following an HSC transplantation and the response to different treatment.

Summary

Understanding how properties of HSCs affect hematopoiesis is important for efficient treatment of diseases. Mathematical modelling can contribute significantly to these efforts.

An integrative systems biology approach to overcome venetoclax resistance in acute myeloid leukemia

The over-expression of the Bcl-2 protein is a common feature of many solid cancers and hematological malignancies, and it is typically associated with poor prognosis and resistance to chemotherapy. Bcl-2-specific inhibitors, such as venetoclax, have recently been approved for the treatment of chronic lymphocytic leukemia and small lymphocytic lymphoma, and they are showing promise in clinical trials as a targeted therapy for patients with relapsed or refractory acute myeloid leukemia (AML). However, successful treatment of AML with Bcl-2-specific inhibitors is often followed by the rapid development of drug resistance. An emerging paradigm for overcoming drug resistance in cancer treatment is through the targeting of mitochondrial energetics and metabolism. In AML in particular, it was recently observed that inhibition of mitochondrial translation via administration of the antibiotic tedizolid significantly affects mitochondrial bioenergetics, activating the integrated stress response (ISR) and subsequently sensitizing drug-resistant AML cells to venetoclax. Here we develop an integrative systems biology approach to acquire a deeper understanding of the molecular mechanisms behind this process, and in particular, of the specific role of the ISR in the commitment of cells to apoptosis. Our multi-scale mathematical model couples the ISR to the intrinsic apoptosis pathway in venetoclax-resistant AML cells, includes the metabolic effects of treatment, and integrates RNA, protein level, and cellular viability data. Using the mathematical model, we identify the dominant mechanisms by which ISR activation helps to overcome venetoclax resistance, and we study the temporal sequencing of combination treatment to determine the most efficient and robust combination treatment protocol.

In this work, we develop a multi-scale systems biology approach to study the mechanisms by which the integrated stress response (ISR) activation helps to overcome venetoclax resistance in acute myeloid leukemia (AML). The multi-scale model enables the integration of RNA-level, protein-level, and cellular viability and proliferation data. The model developed in this work can predict several important features of the resistant AML cell lines that are consistent with experimental data. Further, our integrative systems biology approach led to the determination of the optimal combination treatment protocol.

Patient-specific molecular response dynamics can predict the possibility of relapse during the second treatment-free remission attempt in chronic myelogenous leukemia

In chronic myelogenous leukemia (CML), treatment-free remission (TFR) is defined as maintaining a major molecular response (MMR) without a tyrosine kinase inhibitor (TKI), such as imatinib (IM). Several studies have investigated the safety of the first TFR (TFR₁) attempt and suggested recommendation guidelines for such an attempt. However, the plausibility and predictive factors for a second TFR (TFR₂) have yet to be reported. The present study included 21 patients in chronic myeloid leukemia who participated in twice repeated treatment stop attempts. We develop a mathematical model to analyze and explain the outcomes of TFR₂. Our mathematical model framework can explain patient-specific molecular response dynamics. Fitting the model to longitudinal BCR-ABL1 transcripts from the patients generated patient-specific parameters. Binary tree decision analyses of the model parameters suggested a model based predictive binary classification factor that separated patients into low- and high-risk groups of TFR₂ attempts with an overall accuracy of 76.2% (sensitivity of 81.1% and specificity of 69.9%). The low-risk group maintained a median TFR₂ of 28.2 months, while the high-risk group relapsed at a median time of 3.25 months. Further, our model predicted a patient-specific optimal IM treatment duration before the second IM stop that could achieve the desired TFR₂ (e.g., 5 years).

Spatial dynamics of feedback and feedforward regulation in cell lineages

Feedback mechanisms within cell lineages are thought to be important for maintaining tissue homeostasis. Mathematical models that assume well-mixed cell populations, together with experimental data, have suggested that negative feedback from differentiated cells on the stem cell self-renewal probability can maintain a stable equilibrium and hence homeostasis. Cell lineage dynamics, however, are characterized by spatial structure, which can lead to different properties. Here, we investigate these dynamics using spatially explicit computational models, including cell division, differentiation, death, and migration / diffusion processes. According to these models, the negative feedback loop on stem cell self-renewal fails to maintain homeostasis, both under the assumption of strong spatial restrictions and fast migration / diffusion. Although homeostasis cannot be maintained, this feedback can regulate cell density and promote the formation of spatial structures in the model. Tissue homeostasis, however, can be achieved if spatially restricted negative feedback on self-renewal is combined with an experimentally documented spatial feedforward loop, in which stem cells regulate the fate of transit amplifying cells. This indicates that the dynamics of feedback regulation in tissue cell lineages are more complex than previously thought, and that combinations of spatially explicit control mechanisms are likely instrumental.

Targeting TKI-Activated NFKB2-MIF/CXCLs-CXCR2 Signaling Pathways in FLT3 Mutated Acute Myeloid Leukemia Reduced Blast Viability

Disease relapse is a common cause of treatment failure in FMS-like tyrosine kinase 3 (FLT3) mutated acute myeloid leukemia (AML). In this study, to identify therapeutic targets responsible for the survival and proliferation of leukemic cells (blasts) with FLT3 mutations after gilteritinib (GILT, a 2nd generation tyrosine kinase inhibitor (TKI)) treatment, we performed proteomic screening of cytokine release and in vitro/ex vivo studies to investigate their associated signaling pathways and transcriptional regulation. Here, we report that macrophage migration inhibition factor (MIF) was significantly increased in the supernatant of GILT-treated blasts when compared to untreated controls. Additionally, the GILT-treated blasts that survived were found to exhibit higher expressions of the CXCR2 gene and protein, a common receptor for MIF and pro-inflammatory cytokines. The supplementation of exogenous MIF to GILT-treated blasts revealed a group of CD44High+ cells that might be responsible for the relapse. Furthermore, we identified the highly activated non-classical NFKB2 pathway after GILT-treatment. The siRNA transient knockdown of NFKB2 significantly reduced the gene expressions of MIF, CXCR2, and CXCL5. Finally, treatments of AML patient samples ex vivo demonstrated that the combination of a pharmaceutical inhibitor of the NFKB family and GILT can effectively suppress primary blasts’ secretion of tumor-promoting cytokines, such as CXCL1/5/8. In summary, we provide the first evidence that targeting treatment-activated compensatory pathways, such as the NFKB2-MIF/CXCLs-CXCR2 axis could be a novel therapeutic strategy to overcome TKI-resistance and effectively treat AML patients with FLT3 mutations.

Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation

In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (leukemic cells) undergoing mutation and clonal selection. We prove existence and uniqueness of non-trivial steady states and study their asymptotic stability. The results are compared to those of the system without mutation. Existence of equilibria is proved by formulating the steady state problem as an eigenvalue problem and applying a version of the Krein-Rutmann theorem for Banach lattices. The stability at equilibrium is analysed using linearisation and the Weinstein-Aronszajn determinant which allows to conclude local asymptotic stability.

Clinically Relevant Oxygraphic Assay to Assess Mitochondrial Energy Metabolism in Acute Myeloid Leukemia Patients

Resistant acute myeloid leukemia (AML) exhibits mitochondrial energy metabolism changes compared to newly diagnosed AML. This phenotype is often observed by evaluating the mitochondrial oxygen consumption of blasts, but most of the oximetry protocols were established from leukemia cell lines without validation on primary leukemia cells. Moreover, the cultures and storage conditions of blasts freshly extracted from patient blood or bone marrow cause stress, which must be evaluated before determining oxidative phosphorylation (OXPHOS). Herein, we evaluated different conditions to measure the oxygen consumption of blasts using extracellular flow analyzers. We first determined the minimum number of blasts required to measure OXPHOS. Next, we compared the OXPHOS of blasts cultured for 3 h and 18 h after collection and found that to maintain metabolic organization for 18 h, cytokine supplementation is necessary. Cytokines are also needed when measuring OXPHOS in cryopreserved, thawed and recultured blasts. Next, the concentrations of respiratory chain inhibitors and uncoupler FCCP were established. We found that the FCCP concentration required to reach the maximal respiration of blasts varied depending on the patient sample analyzed. These protocols provided can be used in future clinical studies to evaluate OXPHOS as a biomarker and assess the efficacy of treatments targeting mitochondria.

Multistage hematopoietic stem cell regulation in the mouse: A combined biological and mathematical approach

We have reconciled steady-state and stress hematopoiesis in a single mathematical model based on murine in vivo experiments and with a focus on hematopoietic stem and progenitor cells. A phenylhydrazine stress was first applied to mice. A reduced cell number in each progenitor compartment was evidenced during the next 7 days through a drastic level of differentiation without proliferation, followed by a huge proliferative response in all compartments including long-term hematopoietic stem cells, before a return to normal levels. Data analysis led to the addition to the 6-compartment model, of time-dependent regulation that depended indirectly on the compartment sizes. The resulting model was finely calibrated using a stochastic optimization algorithm and could reproduce biological data in silico when applied to different stress conditions (bleeding, chemotherapy, HSC depletion). In conclusion, our multi-step and time-dependent model of immature hematopoiesis provides new avenues to a better understanding of both normal and pathological hematopoiesis.

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We describe a new 6-compartment time-dependent regulated model of hematopoiesis

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Biological data under steady state and stress and cell dynamics were used

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Modeling is able to recapitulate effects from chemotherapy, bleeding, or HSC depletion

Computational Reconstruction of Clonal Hierarchies From Bulk Sequencing Data of Acute Myeloid Leukemia Samples

Acute myeloid leukemia is an aggressive cancer of the blood forming system. The malignant cell population is composed of multiple clones that evolve over time. Clonal data reflect the mechanisms governing treatment response and relapse. Single cell sequencing provides most direct insights into the clonal composition of the leukemic cells, however it is still not routinely available in clinical practice. In this work we develop a computational algorithm that allows identifying all clonal hierarchies that are compatible with bulk variant allele frequencies measured in a patient sample. The clonal hierarchies represent descendance relations between the different clones and reveal the order in which mutations have been acquired. The proposed computational approach is tested using single cell sequencing data that allow comparing the outcome of the algorithm with the true structure of the clonal hierarchy. We investigate which problems occur during reconstruction of clonal hierarchies from bulk sequencing data. Our results suggest that in many cases only a small number of possible hierarchies fits the bulk data. This implies that bulk sequencing data can be used to obtain insights in clonal evolution.

Pathogenic and therapeutic roles of cytokines in acute myeloid leukemia

Acute myeloid leukemia (AML) is a heterogeneous disease with high mortality that accounts for the most common acute leukemia in adults. Despite all progress in the therapeutic strategies and increased rate of complete remission, many patients will eventually relapse and die from the disease. Cytokines as molecular messengers play a pivotal role in the immune system. The imbalance release of cytokine has been shown to exert a significant influence on the progression of hematopoietic malignancies including acute myeloid leukemia. This article aimed to summarize current knowledge about cytokines and their critical roles in the pathogenesis, treatment, and survival of AML patients.

Small molecule inhibition of Dynamin-dependent endocytosis targets multiple niche signals and impairs leukemia stem cells

Intensive chemotherapy for acute leukemia can usually induce complete remission, but fails in many patients to eradicate the leukemia stem cells responsible for relapse. There is accumulating evidence that these relapse-inducing cells are maintained and protected by signals provided by the microenvironment. Thus, inhibition of niche signals is a proposed strategy to target leukemia stem cells but this requires knowledge of the critical signals and may be subject to compensatory mechanisms. Signals from the niche require receptor-mediated endocytosis, a generic process dependent on the Dynamin family of large GTPases. Here, we show that Dynole 34-2, a potent inhibitor of Dynamin GTPase activity, can block transduction of key signalling pathways and overcome chemoresistance of leukemia stem cells. Our results provide a significant conceptual advance in therapeutic strategies for acute leukemia that may be applicable to other malignancies in which signals from the niche are involved in disease progression and chemoresistance.

The tumour microenvironment provides signals to support leukaemic stem cells (LSC) maintenance and chemoresistance. Here, the authors show that disrupting niche-associated signalling by inhibiting receptor-mediated endocytosis with a dynamin GTPase inhibitor overcomes chemoresistance of LSC.

Using mathematical models to improve risk-scoring in acute myeloid leukemia

Acute myeloid leukemia (AML) is an aggressive cancer of the blood forming (hematopoietic) system. Due to the high patient variability of disease dynamics, risk-scoring is an important part of its clinical management. AML is characterized by impaired blood cell formation and the accumulation of so-called leukemic blasts in the bone marrow of patients. Recently, it has been proposed to use counts of blood-producing (hematopoietic) stem cells (HSCs) as a biomarker for patient prognosis. In this work, we use a non-linear mathematical model to provide mechanistic evidence for the suitability of HSC counts as a prognostic marker. Using model analysis and computer simulations, we compare different risk-scores involving HSC quantification. We propose and validate a simple approach to improve risk prediction based on HSC and blast counts measured at the time of diagnosis.

Effect of feedback regulation on stem cell fractions in tissues and tumors: Understanding chemoresistance in cancer

While resistance mutations are often implicated in the failure of cancer therapy, lack of response also occurs without such mutants. In bladder cancer mouse xenografts, repeated chemotherapy cycles have resulted in cancer stem cell (CSC) enrichment, and consequent loss of therapy response due to the reduced susceptibility of CSCs to drugs. A particular feedback loop present in the xenografts has been shown to promote CSC enrichment in this system. Yet, many other regulatory loops might also be operational and might promote CSC enrichment. Their identification is central to improving therapy response. Here, we perform a comprehensive mathematical analysis to define what types of regulatory feedback loops can and cannot contribute to CSC enrichment, providing guidance to the experimental identification of feedback molecules. We derive a formula that reveals whether or not the cell population experiences CSC enrichment over time, based on the properties of the feedback. We find that negative feedback on the CSC division rate or positive feedback on differentiated cell death rate can lead to CSC enrichment. Further, the feedback mediators that achieve CSC enrichment can be secreted by either CSCs or by more differentiated cells. The extent of enrichment is determined by the CSC death rate, the CSC self-renewal probability, and by feedback strength. Defining these general characteristics of feedback loops can guide the experimental screening for and identification of feedback mediators that can promote CSC enrichment in bladder cancer and potentially other tumors. This can help understand and overcome the phenomenon of CSC-based therapy resistance.

Differential response to cytotoxic therapy explains treatment dynamics of acute myeloid leukaemia patients: insights from a mathematical modelling approach

Disease response and durability of remission are very heterogeneous in patients with acute myeloid leukaemia (AML). There is increasing evidence that the individual risk of early relapse can be predicted based on the initial treatment response. However, it is unclear how such a correlation is linked to functional aspects of AML progression and treatment. We suggest a mathematical model in which leukaemia-initiating cells and normal/healthy haematopoietic stem and progenitor cells reversibly change between an active state characterized by proliferation and chemosensitivity and a quiescent state, in which the cells do not divide, but are also insensitive to chemotherapy. Applying this model to 275 molecular time courses of nucleophosmin 1-mutated patients, we conclude that the differential chemosensitivity of the leukaemia-initiating cells together with the cells' intrinsic proliferative capacity is sufficient to reproduce both, early relapse as well as long-lasting remission. We can, furthermore, show that the model parameters associated with individual chemosensitivity and proliferative advantage of the leukaemic cells are closely linked to the patients' time to relapse, while a reliable prediction based on early response only is not possible based on the currently available data. Although we demonstrate with our approach, that the complete response data is sufficient to quantify the aggressiveness of the disease, further investigations are necessary to study how an intensive early sampling strategy may prospectively improve risk assessment and help to optimize individual treatments.

Mathematical Modeling Provides Evidence for Niche Competition in Human AML and Serves as a Tool to Improve Risk Stratification

Acute myeloid leukemia (AML) is a stem cell-driven malignant disease. There is evidence that leukemic stem cells (LSC) interact with stem cell niches and outcompete hematopoietic stem cells (HSC). The impact of this interaction on the clinical course of the disease remains poorly understood. We developed and validated a mathematical model of stem cell competition in the human HSC niche. Model simulations predicted how processes in the stem cell niche affect the speed of disease progression. Combining the mathematical model with data of individual patients, we quantified the selective pressure LSCs exert on HSCs and demonstrated the model's prognostic significance. A novel model-based risk-stratification approach allowed extraction of prognostic information from counts of healthy and malignant cells at the time of diagnosis. This model's feasibility was demonstrable based on a cohort of patients with ALDH-rare AML and shows that the model-based risk stratification is an independent predictor of disease-free and overall survival. This proof-of-concept study shows how model-based interpretation of patient data can improve prognostic scoring and contribute to personalized medicine. SIGNIFICANCE: Combining a novel mathematical model of the human hematopoietic stem cell niche with individual patient data enables quantification of properties of leukemic stem cells and improves risk stratification in acute myeloid leukemia.

An Optimal Control Framework for the Automated Design of Personalized Cancer Treatments

One of the key challenges in current cancer research is the development of computational strategies to support clinicians in the identification of successful personalized treatments. Control theory might be an effective approach to this end, as proven by the long-established application to therapy design and testing. In this respect, we here introduce the Control Theory for Therapy Design (CT4TD) framework, which employs optimal control theory on patient-specific pharmacokinetics (PK) and pharmacodynamics (PD) models, to deliver optimized therapeutic strategies. The definition of personalized PK/PD models allows to explicitly consider the physiological heterogeneity of individuals and to adapt the therapy accordingly, as opposed to standard clinical practices. CT4TD can be used in two distinct scenarios. At the time of the diagnosis, CT4TD allows to set optimized personalized administration strategies, aimed at reaching selected target drug concentrations, while minimizing the costs in terms of toxicity and adverse effects. Moreover, if longitudinal data on patients under treatment are available, our approach allows to adjust the ongoing therapy, by relying on simplified models of cancer population dynamics, with the goal of minimizing or controlling the tumor burden. CT4TD is highly scalable, as it employs the efficient dCRAB/RedCRAB optimization algorithm, and the results are robust, as proven by extensive tests on synthetic data. Furthermore, the theoretical framework is general, and it might be applied to any therapy for which a PK/PD model can be estimated, and for any kind of administration and cost. As a proof of principle, we present the application of CT4TD to Imatinib administration in Chronic Myeloid leukemia, in which we adopt a simplified model of cancer population dynamics. In particular, we show that the optimized therapeutic strategies are diversified among patients, and display improvements with respect to the current standard regime.

Global dynamics of healthy and cancer cells competing in the hematopoietic system

Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically modelled by Andersen et al. (2017) including the dynamic variables: healthy and cancer stem cells and mature cells, dead cells and an immune system response. Here, we apply a quasi steady state approximation to this model to construct a two dimensional model with four algebraic equations denoted the simple cancitis model. The two dynamic variables are the clinically available quantities JAK2V617F allele burden and the number of white blood cells. The simple cancitis model represents the original model very well. Complete phase space analysis of the simple cancitis model is performed, including proving the existence and location of globally attracting steady states. Hence, parameter values from compartments of stem cells, mature cells and immune cells are directly linked to disease and treatment prognosis, showing the crucial importance of early intervention. The simple cancitis model allows for a complete analysis of the long term evolution of trajectories. In particular, the value of the self renewal of the hematopoietic stem cells divided by the self renewal of the cancer stem cells is found to be an important diagnostic marker and perturbing this parameter value at intervention allows the model to reproduce clinical data. Treatment at low cancer cell numbers allows returning to healthy blood production while the same intervention at a later disease stage can lead to eradication of healthy blood producing cells. Assuming the total number of white blood cells is constant in the early cancer phase while the allele burden increases, a one dimensional model is suggested and explicitly solved, including parameters from all original compartments. The solution explicitly shows that exogenous inflammation promotes blood cancer when cancer stem cells reproduce more efficiently than hematopoietic stem cells.

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.

Mathematical modeling reveals the factors involved in the phenomena of cancer stem cells stabilization

Cancer Stem Cells (CSC), a subset of cancer cells resembling normal stem cells with self-renewal and asymmetric division capabilities, are present at various but low proportions in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. In vitro, most intriguingly, isolated CSCs rapidly regenerate the original population of stem and non-stem cells (non-CSCs) as shown by various investigators. This phenomenon still remains to be explained. We propose a mathematical model of cancer cell population dynamics, based on the main parameters of cell population growth, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and non-CSCs sub-populations, and taking into account the stabilization phenomenon. The analysis of the model allows determination of time-varying corridors of probabilities for different cell fates, given the particular dynamics of cancer cells populations; and determination of a cell-cell communication factors influencing these time-varying probabilities of cell behavior (division, transition) scenarios. Though the results of the model have to be experimentally confirmed, we can anticipate the development of several fundamental and practical applications based on the theoretical results of the model.

Mathematical models for cytarabine-derived myelosuppression in acute myeloid leukaemia

We investigate the personalisation and prediction accuracy of mathematical models for white blood cell (WBC) count dynamics during consolidation treatment using intermediate or high-dose cytarabine (Ara-C) in acute myeloid leukaemia (AML). Ara-C is the clinically most relevant cytotoxic agent for AML treatment. We extend a mathematical model of myelosuppression and a pharmacokinetic model of Ara-C with different hypotheses of Ara-C's pharmacodynamic effects. We cross-validate the 12 model variations using dense WBC count measurements from 23 AML patients. Surprisingly, the prediction accuracy remains satisfactory in each of the models despite different modelling hypotheses. Therefore, we compare average clinical and calculated WBC recovery times for different Ara-C schedules as a successful methodology for model discrimination. As a result, a new hypothesis of a secondary pharmacodynamic effect on the proliferation rate seems plausible. Furthermore, we demonstrate the impact of treatment timing on subsequent nadir values based on personalised predictions as a possibility for influencing/controlling myelosuppression.

A computational model of feedback-mediated hematopoietic stem cell differentiation in vitro

Hematopoietic stem cells (HSCs) play an important physiological role as regulators of all blood and immune cell populations, and are of clinical importance for bone marrow transplants. Regulating HSC biology in vitro for clinical applications requires improved understanding of biological inducers of HSC lineage specification. A significant challenge for controlled HSC expansion and differentiation is the complex network of molecular crosstalk between multiple bone marrow niche components influencing HSC biology. We describe a biology-driven computational approach to model cell kinetics in vitro to gain new insight regarding culture conditions and intercellular signaling networks. We further investigate the balance between self-renewal and differentiation that drives early and late hematopoietic progenitor populations. We demonstrate that changing the feedback driven by cell-secreted biomolecules alters lineage specification in early progenitor populations. Using a first order deterministic model, we are able to predict the impact of media change frequency on cell kinetics, as well as distinctions between primitive long-term HSCs and differentiated myeloid progenitors. Integrating the computational model and sensitivity analyses we identify critical culture parameters for regulating HSC proliferation and myeloid lineage specification. Our analysis suggests that accurately modeling the kinetics of hematopoietic sub-populations in vitro requires direct contributions from early progenitor differentiation along with the more traditionally considered intermediary oligopotent progenitors. While consistent with recent in vivo results, this work suggests the need to revise our perspective on HSC lineage engineering in vitro for expansion of discrete hematopoietic populations.