Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications

Mathematical modelling, selection and hierarchical inference to determine the minimal dose in IFNα therapy against myeloproliferative neoplasms

Myeloproliferative neoplasms (MPN) are blood cancers that appear after acquiring a driver mutation in a hematopoietic stem cell. These hematological malignancies result in the overproduction of mature blood cells and, if not treated, induce a risk of cardiovascular events and thrombosis. Pegylated IFN$\alpha $ is commonly used to treat MPN, but no clear guidelines exist concerning the dose prescribed to patients. We applied a model selection procedure and ran a hierarchical Bayesian inference method to decipher how dose variations impact the response to the therapy. We inferred that IFN$\alpha $ acts on mutated stem cells by inducing their differentiation into progenitor cells; the higher the dose, the higher the effect. We found that the treatment can induce long-term remission when a sufficient (patient-dependent) dose is reached. We determined this minimal dose for individuals in a cohort of patients and estimated the most suitable starting dose to give to a new patient to increase the chances of being cured.

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.

Interplay of mutations, alternate mechanisms, and treatment breaks in leukaemia: Understanding and implications studied with stochastic models

Bcr-Abl1 kinase domain mutations are the most prevalent cause of treatment resistance in chronic myeloid leukaemia (CML). Alternate resistance pathways nevertheless exist, and cell line experiments show certain patterns in the gain, and loss, of some of these alternate adaptations. These adaptations have clinical consequences when the tumour develops mechanisms that are beneficial to its growth under treatment, but slow down its growth when not treated. The results of temporarily halting treatment in CML have not been widely discussed in the clinic and there is no robust theoretical model that could suggest when such a pause in therapy can be tolerated. We constructed a dynamic model of how mechanisms such as Bcr-Abl1 overexpression and drug transporter upregulation evolve to produce resistance in cell lines, and investigate its behaviour subject to different treatment schedules, in particular when the treatment is paused ('drug holiday'). Our study results suggest that the presence of additional resistance mechanisms creates an environment which favours mutations that are either preexisting or occur late during treatment. Importantly, the results suggest the existence of tumour drug addiction, where cancer cells become dependent on the drug for (optimal) survival, which could be exploited through a treatment holiday. All simulation code is available at https://github.com/Sandalmoth/dual-adaptation.

e14a2 Transcript Favors Treatment-Free Remission in Chronic Myeloid Leukemia When Associated with Longer Treatment with Tyrosine Kinase Inhibitors and Sustained Deep Molecular Response

e13a2 and e14a2 are the most frequent transcript types of the BCR::ABL1 fusion gene in chronic myeloid leukemia (CML). The current goal with tyrosine kinase inhibitors (TKI) is to achieve sustained deep molecular response (DMR) in order to discontinue TKI treatment and remain in the so-called treatment-free remission (TFR) phase, but biological factors associated with these goals are not well established. This study aimed to determine the effect of transcript type on TFR in patients receiving frontline treatment with imatinib (IM) or second-generation TKI (2G-TKI). Patients treated at least 119 months with IM presented less post-discontinuation relapse than those that discontinued IM before 119 months (p = 0.005). In addition, cases with the e14a2 transcript type treated at least 119 months with IM presented a better TFR (p = 0.024). On the other hand, the type of transcript did not affect the cytogenetic or molecular response in 2G-TKI treated patients; however, the use of 2G-TKI may be associated with higher and earlier DMR in patients with the e14a2 transcript.

Immune modulation in chronic myeloid leukaemia patients treated with nilotinib and interferon-alpha

The addition of interferon to tyrosine kinase inhibitors (TKIs), to improve deep molecular response (DMR) and potentially treatment-free remission (TFR) rates in chronic-phase chronic myeloid leukaemia (CP-CML) patients is under active investigation. However, the immunobiology of this combination is poorly understood. We performed a comprehensive longitudinal assessment of immunological changes in CML patients treated with nilotinib and interferon-alpha (IFN-α) within the ALLG CML11 trial (n = 12) or nilotinib alone (n = 17). We demonstrate that nilotinib+IFN transiently reduced absolute counts of natural killer (NK) cells, compared with nilotinib alone. Furthermore, CD16+ -cytolytic and CD57+ CD62L- -mature NK cells were transiently reduced during IFN therapy, without affecting NK-cell function. IFN transiently increased cytotoxic T-lymphocyte (CTL) responses to leukaemia-associated antigens (LAAs) proteinase-3, BMI-1 and PRAME; and had no effect on regulatory T cells, or myeloid-derived suppressor cells. Patients on nilotinib+IFN who achieved MR4.5 by 12 months had a significantly higher proportion of NK cells expressing NKp46, NKp30 and NKG2D compared with patients not achieving this milestone. This difference was not observed in the nilotinib-alone group. The addition of IFN to nilotinib drives an increase in NK-activating receptors, CTLs responding to LAAs and results in transient immune modulation, which may influence earlier DMR, and its effect on long-term outcomes warrants further investigation.

A mixed-effects stochastic model reveals clonal dominance in gene therapy safety studies

BACKGROUND

Mathematical models of haematopoiesis can provide insights on abnormal cell expansions (clonal dominance), and in turn can guide safety monitoring in gene therapy clinical applications. Clonal tracking is a recent high-throughput technology that can be used to quantify cells arising from a single haematopoietic stem cell ancestor after a gene therapy treatment. Thus, clonal tracking data can be used to calibrate the stochastic differential equations describing clonal population dynamics and hierarchical relationships in vivo.

RESULTS

In this work we propose a random-effects stochastic framework that allows to investigate the presence of events of clonal dominance from high-dimensional clonal tracking data. Our framework is based on the combination between stochastic reaction networks and mixed-effects generalized linear models. Starting from the Kramers-Moyal approximated Master equation, the dynamics of cells duplication, death and differentiation at clonal level, can be described by a local linear approximation. The parameters of this formulation, which are inferred using a maximum likelihood approach, are assumed to be shared across the clones and are not sufficient to describe situation in which clones exhibit heterogeneity in their fitness that can lead to clonal dominance. In order to overcome this limitation, we extend the base model by introducing random-effects for the clonal parameters. This extended formulation is calibrated to the clonal data using a tailor-made expectation-maximization algorithm. We also provide the companion  package RestoreNet, publicly available for download at https://cran.r-project.org/package=RestoreNet .

CONCLUSIONS

Simulation studies show that our proposed method outperforms the state-of-the-art. The application of our method in two in-vivo studies unveils the dynamics of clonal dominance. Our tool can provide statistical support to biologists in gene therapy safety analyses.

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.

The structure of the hematopoietic system can explain chronic myeloid leukemia progression

Almost all cancer types share the hallmarks of cancer and a similar tumor formation: fueled by stochastic mutations in somatic cells. In case of chronic myeloid leukemia (CML), this evolutionary process can be tracked from an asymptomatic long-lasting chronic phase to a final rapidly evolving blast phase. Somatic evolution in CML occurs in the context of healthy blood production, a hierarchical process of cell division; initiated by stem cells that self-renew and differentiate to produce mature blood cells. Here we introduce a general model of hierarchical cell division explaining the particular progression of CML as resulting from the structure of the hematopoietic system. Driver mutations confer a growth advantage to the cells carrying them, for instance, the BCR::ABL1 gene, which also acts as a marker for CML. We investigated the relation of the BCR::ABL1 mutation strength to the hematopoietic stem cell division rate by employing computer simulations and fitting the model parameters to the reported median duration for the chronic and accelerated phases. Our results demonstrate that driver mutations (additional to the BCR::ABL1 mutation) are necessary to explain CML progression if stem cells divide sufficiently slowly. We observed that the number of mutations accumulated by cells at the more differentiated levels of the hierarchy is not affected by driver mutations present in the stem cells. Our results shed light on somatic evolution in a hierarchical tissue and show that the clinical hallmarks of CML progression result from the structural characteristics of blood production.

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.

Modelling of immune response in chronic myeloid leukemia patients suggests potential for treatment reduction prior to cessation

Introduction

Discontinuation of tyrosine kinase inhibitor (TKI) treatment is emerging as the main therapy goal for Chronic Myeloid Leukemia (CML) patients. The DESTINY trial showed that TKI dose reduction prior to cessation can lead to an increased number of patients achieving sustained treatment free remission (TFR). However, there has been no systematic investigation to evaluate how dose reduction regimens can further improve the success of TKI stop trials.

Methods

Here, we apply an established mathematical model of CML therapy to investigate different TKI dose reduction schemes prior to therapy cessation and evaluate them with respect to the total amount of drug used and the expected TFR success.

Results

Our systematic analysis confirms clinical findings that the overall time of TKI treatment is a major determinant of TFR success, while highlighting that lower dose TKI treatment for the same duration is equally sufficient for many patients. Our results further suggest that a stepwise dose reduction prior to TKI cessation can increase the success rate of TFR, while substantially reducing the amount of administered TKI.

Discussion

Our findings illustrate the potential of dose reduction schemes prior to treatment cessation and suggest corresponding and clinically testable strategies that are applicable to many CML patients.

Why are cell populations maintained via multiple compartments?

We consider the maintenance of 'product' cell populations from 'progenitor' cells via a sequence of one or more cell types, or compartments, where each cell's fate is chosen stochastically. If there is only one compartment then large amplification, that is, a large ratio of product cells to progenitors comes with disadvantages. The product cell population is dominated by large families (cells descended from the same progenitor) and many generations separate, on average, product cells from progenitors. These disadvantages are avoided using suitably constructed sequences of compartments: the amplification factor of a sequence is the product of the amplification factors of each compartment, while the average number of generations is a sum over contributions from each compartment. Passing through multiple compartments is, in fact, an efficient way to maintain a product cell population from a small flux of progenitors, avoiding excessive clonality and minimizing the number of rounds of division en route. We use division, exit and death rates, estimated from measurements of single-positive thymocytes, to choose illustrative parameter values in the single-compartment case. We also consider a five-compartment model of thymocyte differentiation, from double-negative precursors to single-positive product cells.

Early dynamics of chronic myeloid leukemia on nilotinib predicts deep molecular response

Chronic myeloid leukemia (CML) is a myeloproliferative disorder caused by the BCR-ABL1 tyrosine kinase. Although ABL1-specific tyrosine kinase inhibitors (TKIs) including nilotinib have dramatically improved the prognosis of patients with CML, the TKI efficacy depends on the individual patient. In this work, we found that the patients with different nilotinib responses can be classified by using the estimated parameters of our simple dynamical model with two common laboratory findings. Furthermore, our proposed method identified patients who failed to achieve a treatment goal with high fidelity according to the data collected only at three initial time points during nilotinib therapy. Since our model relies on the general properties of TKI response, our framework would be applicable to CML patients who receive frontline nilotinib or other TKIs.

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).

Exposure-Efficacy Analysis of Asciminib in Philadelphia Chromosome-Positive Chronic Myeloid Leukemia in Chronic Phase

Asciminib is a first-in-class BCR::ABL1 inhibitor that works by specifically targeting the ABL myristoyl pocket (STAMP) and has potent activity against the T315I mutation. This study aimed to characterize the effect of asciminib exposure on disease progression and to elucidate factors influencing efficacy. Our analysis included 303 patients with chronic myeloid leukemia in chronic phase (CML-CP) recruited in a Phase 1 study with dose ranging from 10 to 200 mg twice a day (bid) or 40 to 200 mg once a day (qd) (NCT02081378) and in the Phase 3 ASCEMBL study receiving asciminib 40 mg bid (NCT03106779). A total of 67 patients harbored the T315I mutation. A longitudinal PK/PD model was developed to characterize the exposure-efficacy relationship, in which the efficacy was assessed through BCR::ABL1 transcript levels over time. Specifically, a three-compartment model representing quiescent leukemic stem cells, proliferating bone marrow cells, and resistant cells was developed. Drug killing of the proliferating cells by asciminib was characterized by a power model. A subgroup analysis was performed on the patients with T315I mutation using E_max model to characterize the drug effect. The model demonstrated the appropriateness of a total daily dose of asciminib 80 mg in patients without the T315I mutation and 200 mg bid in patients with the T315I mutation with further validation in light of safety data. This model captured key characteristics of patients' response to asciminib and helped inform dosing rationale for resistant and difficult-to-treat populations.

A systematic review of modeling and simulation approaches in designing targeted treatment technologies for Leukemia Cancer in low and middle income countries

Virtual experimentation is a widely used approach for predicting systems behaviour especially in situations where resources for physical experiments are very limited. For example, targeted treatment inside the human body is particularly challenging, and as such, modeling and simulation is utilised to aid planning before a specific treatment is administered. In such approaches, precise treatment, as it is the case in radiotherapy, is used to administer a maximum dose to the infected regions while minimizing the effect on normal tissue. Complicated cancers such as leukemia present even greater challenges due to their presentation in liquid form and not being localised in one area. As such, science has led to the development of targeted drug delivery, where the infected cells can be specifically targeted anywhere in the body. Despite the great prospects and advances of these modeling and simulation tools in the design and delivery of targeted drugs, their use by Low and Middle Income Countries (LMICs) researchers and clinicians is still very limited. This paper therefore reviews the modeling and simulation approaches for leukemia treatment using nanoparticles as an example for virtual experimentation. A systematic review from various databases was carried out for studies that involved cancer treatment approaches through modeling and simulation with emphasis to data collected from LMICs. Results indicated that whereas there is an increasing trend in the use of modeling and simulation approaches, their uptake in LMICs is still limited. According to the review data collected, there is a clear need to employ these tools as key approaches for the planning of targeted drug treatment approaches.

Treatment-Free Remission in Chronic Myeloid Leukemia: Can We Identify Prognostic Factors?

Simple Summary

Chronic myeloid leukemia (CML) is a blood cancer. Unlike other cancers CML treatment is lifelong and many patients experience side effects. For those patients who respond well to treatment and achieve deep molecular remission, quality of life is impacted because of continuous treatment. In this review, we look at emerging clinical trials which aim to investigate which patients can safely stop treatment. Treatment-free remission is the ultimate goal for CML patients, but there is still a gap in our knowledge as to why some patients can achieve treatment-free remission, while others relapse when treatment is stopped. Here we discuss if there are any prognostic factors that can predict the best candidates who qualify for treatment discontinuation, with a view to keeping them in remission.

Abstract

Following the development of tyrosine kinase inhibitors (TKI), the survival of patients with chronic myeloid leukaemia (CML) drastically improved. With the introduction of these agents, CML is now considered a chronic disease for some patients. Taking into consideration the side effects, toxicity, and high cost, discontinuing TKI became a goal for patients with chronic phase CML. Patients who achieved deep molecular response (DMR) and discontinued TKI, remained in treatment-free remission (TFR). Currently, the data from the published literature demonstrate that 40–60% of patients achieve TFR, with relapses occurring within the first six months. In addition, almost all patients who relapsed regained a molecular response upon retreatment, indicating TKI discontinuation is safe. However, there is still a gap in understanding the mechanisms behind TFR, and whether there are prognostic factors that can predict the best candidates who qualify for TKI discontinuation with a view to keeping them in TFR. Furthermore, the information about a second TFR attempt and the role of gradual de-escalation of TKI before complete cessation is limited. This review highlights the factors predicting success or failure of TFR. In addition, it examines the feasibility of a second TFR attempt after the failure of the first one, and the current guidelines concerning TFR in clinical practice.

STABILITY ANALYSIS OF A MATHEMATICAL MODEL FOR CHRONIC MYELOID LEUKEMIA ERADICATION

We analyze a mathematical model for the treatment of chronic myeloid leukemia (CML). The model is designed for complete recovery of CML patients after treatment. The model developed in the paper [Bunimovich-Mendrazitsky S, Kronik N, Vainstein V, Optimization of interferon-alpha and imatinib combination therapy for CML: A modeling approach, Adv Theory Simul 2(1):1800081, 2018] introduced a combined treatment of CML based on imatinib therapy and immunotherapy. Immunotherapy based on Interferon alpha-2a (IFN-[Formula: see text]) affects stem and mature cancer cell mortality, and leads to outcome improvements in the combined therapy. The qualitative character of our results shows that additional therapy for the complete cure of CML patients is required. This additional treatment is tumor infiltrating lymphocytes (TIL) along with a combination imatinib and IFN-[Formula: see text] treatment. The model examines the interaction between CML cancer cells and effector cells, using an ODE system. Stability analysis of the model defines conditions when imatinib treatment might lead to the eradication of CML with IFN-[Formula: see text] and TIL. Three equilibria are investigated for the proposed model. Stability conditions for equilibria are formulated in terms of the linear matrix inequalities (LMIs).

Inferring Tumor Proliferative Organization from Phylogenetic Tree Measures in a Computational Model

We use a computational modeling approach to explore whether it is possible to infer a solid tumor's cellular proliferative hierarchy under the assumptions of the cancer stem cell hypothesis and neutral evolution. We work towards inferring the symmetric division probability for cancer stem cells, since this is believed to be a key driver of progression and therapeutic response. Motivated by the advent of multiregion sampling and resulting opportunities to infer tumor evolutionary history, we focus on a suite of statistical measures of the phylogenetic trees resulting from the tumor's evolution in different regions of parameter space and through time. We find strikingly different patterns in these measures for changing symmetric division probability which hinge on the inclusion of spatial constraints. These results give us a starting point to begin stratifying tumors by this biological parameter and also generate a number of actionable clinical and biological hypotheses regarding changes during therapy, and through tumor evolutionary time. [Cancer; evolution; phylogenetics.].

Myasthenia Gravis and Myeloproliferative Neoplasms - Mere Association or Paraneoplastic Neurologic Syndrome: A Mini-Review

Myasthenia Gravis (MG) is a rare neurological condition characterized by muscle weakness that worsens after use. Myeloproliferative Neoplasms (MPNs) are disorders due to stem-cell hyperplasia characterized by an increased peripheral blood cell count, overactive bone marrow, and proliferation of mature hematopoietic cells. MPNs may be Philadelphia (Ph) chromosome-positive or Negative .A systematic review of case reports was conducted by searching PubMed, Scopus, and Google scholar to identify case reports in which there is an association between MG and MPN and know whether MG can be considered a possible neurological paraneoplastic syndrome in patients with MPNs. A total of 13 cases of MPNs associated with MG were identified. The most common type of MPN associated with MG was chronic myeloid leukemia (CML) (10 out of 13 patients).  In most of the patients, MG symptoms appeared after a diagnosis of MPN was made. Considering that 10 out of the 13 patients in our cohort had positive auto-antibodies though only 4 of them had thymic hyperplasia, we hypothesize that bone marrow proliferation was responsible for the production of autoantibodies in these patients.As the clonal cell population cannot be eliminated entirely in the bone marrow even after treatment with tyrosine kinase inhibitors (TKI) in Ph +ve MPNs and JAK2 inhibitors in Ph -ve MPNS, MG can occur even in patients who are treated with these agents. A high index of suspicion is needed to diagnose it early, and treatment should be initiated immediately with steroids and anticholinergic agents.

Overlooking the obvious? On the potential of treatment alterations to predict patient-specific therapy response

Prognostic or therapeutic classification of diseases is often based on clinical or genetic characteristics at diagnosis or response landmarks determined at a certain time point of treatment. On the other hand, there are more and more means, such as molecular markers and sensor data, that allow for quantification of disease or therapeutic parameters over time. Although a general value of time-resolved disease monitoring is widely accepted, the full potential of using the available information on disease and treatment dynamics in the context of outcome prediction or individualized treatment optimization still seems to be, at least partially, overlooked. Within this Perspective, we summarize the conceptual idea of using dynamic information to obtain a better understanding of complex pathophysiological processes within their particular "host environment," which also allows us to intrinsically map patient-specific heterogeneity. Specifically, we discuss to which extent treatment alterations can provide additional information to understand a patient's individual condition and use this information to further adapt the therapeutic strategy. This conceptual discussion is illustrated by using examples from myeloid leukemias to which we recently applied this concept using statistical and mathematical modeling.

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.

Analysis of chronic myeloid leukaemia during deep molecular response by genomic PCR: a traffic light stratification model with impact on treatment-free remission

This work investigated patient-specific genomic BCR-ABL1 fusions as markers of measurable residual disease (MRD) in chronic myeloid leukaemia, with a focus on relevance to treatment-free remission (TFR) after achievement of deep molecular response (DMR) on tyrosine kinase inhibitor (TKI) therapy. DNA and mRNA BCR-ABL1 measurements by qPCR were compared in 2189 samples (129 patients) and by digital PCR in 1279 sample (62 patients). A high correlation was found at levels of disease above MR4, but there was a poor correlation for samples during DMR. A combination of DNA and RNA MRD measurements resulted in a better prediction of molecular relapse-free survival (MRFS) after TKI stop (n = 17) or scheduled interruption (n = 25). At 18 months after treatment cessation, patients with stopped or interrupted TKI therapy who were DNA negative/RNA negative during DMR maintenance (green group) had an MRFS of 80% and 100%, respectively, compared with those who were DNA positive/RNA negative (MRFS = 57% and 67%, respectively; yellow group) or DNA positive/RNA positive (MRFS = 20% for both cohorts; red group). Thus, we propose a "traffic light" stratification as a TFR predictor based on DNA and mRNA BCR-ABL1 measurements during DMR maintenance before TKI cessation.

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.

The leukaemia stem cell: similarities, differences and clinical prospects in CML and AML

For two decades, leukaemia stem cells (LSCs) in chronic myeloid leukaemia (CML) and acute myeloid leukaemia (AML) have been advanced paradigms for the cancer stem cell field. In CML, the acquisition of the fusion tyrosine kinase BCR-ABL1 in a haematopoietic stem cell drives its transformation to become a LSC. In AML, LSCs can arise from multiple cell types through the activity of a number of oncogenic drivers and pre-leukaemic events, adding further layers of context and genetic and cellular heterogeneity to AML LSCs not observed in most cases of CML. Furthermore, LSCs from both AML and CML can be refractory to standard-of-care therapies and persist in patients, diversify clonally and serve as reservoirs to drive relapse, recurrence or progression to more aggressive forms. Despite these complexities, LSCs in both diseases share biological features, making them distinct from other CML or AML progenitor cells and from normal haematopoietic stem cells. These features may represent Achilles' heels against which novel therapies can be developed. Here, we review many of the similarities and differences that exist between LSCs in CML and AML and examine the therapeutic strategies that could be used to eradicate them.

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

Background

Individualization and patient-specific optimization of treatment is a major goal of modern health care. One way to achieve this goal is the application of high-resolution diagnostics together with the application of targeted therapies. However, the rising number of different treatment modalities also induces new challenges: Whereas randomized clinical trials focus on proving average treatment effects in specific groups of patients, direct conclusions at the individual patient level are problematic. Thus, the identification of the best patient-specific treatment options remains an open question. Systems medicine, specifically mechanistic mathematical models, can substantially support individual treatment optimization. In addition to providing a better general understanding of disease mechanisms and treatment effects, these models allow for an identification of patient-specific parameterizations and, therefore, provide individualized predictions for the effect of different treatment modalities.

Results

In the following we describe a software framework that facilitates the integration of mathematical models and computer simulations into routine clinical processes to support decision-making. This is achieved by combining standard data management and data exploration tools, with the generation and visualization of mathematical model predictions for treatment options at an individual patient level.

Conclusions

By integrating model results in an audit trail compatible manner into established clinical workflows, our framework has the potential to foster the use of systems-medical approaches in clinical practice. We illustrate the framework application by two use cases from the field of haematological oncology.

What are the considerations for tyrosine kinase inhibitor discontinuation in chronic-phase chronic myeloid leukemia?

Introduction: The outlook for patients with chronic myeloid leukemia (CML) has changed dramatically with the development of tyrosine kinase inhibitors (TKIs) with the current treatment goal for many patients being to obtain a durable deep molecular remission, discontinue TKI therapy, and remain treatment free.Areas covered: In this article, the authors review the data from the major TKI discontinuation studies, explore potential predictors of discontinuation outcome and look at possible mechanisms to explain the variable outcomes following TKI discontinuation including immune surveillance and leukemic stem cell (LSC) depletion following TKI treatment. Data from relevant articles published on the Pubmed database between January 2007 and January 2020 have been included.Expert opinion: The results from the majority of TKI discontinuation studies show a consistent picture with approximately half of eligible patients achieving treatment free remission (TFR). However, reliable clinical predictors or biomarkers for the outcome of TKI discontinuation remain elusive and the mechanisms to explain the diversity of discontinuation success are not completely understood. Future studies will need to focus on attempts to increase the number of patients eligible for treatment discontinuation and will likely involve drug combinations including novel agents aimed at targeting the residual LSC population and enhancement of immune surveillance mechanisms.

Dasatinib discontinuation in patients with chronic-phase chronic myeloid leukemia and stable deep molecular response: the DASFREE study

Treatment-free remission (TFR) in patients with chronic myeloid leukemia in chronic phase (CML-CP) is considered a feasible option, especially with the ability of second-generation tyrosine kinase inhibitors to induce higher rates of sustained deep molecular response (DMR). DASFREE is an open-label, single-arm, multicenter phase II trial assessing TFR after dasatinib discontinuation in patients with CML-CP (N = 84). At 2 years, TFR was 46% in all patients. Multivariate analyses revealed statistically significant associations between 2-year TFR and duration of prior dasatinib (≥median; p = .0051), line of therapy (first line; p = .0138), and age (>65 years; p = .0012). No disease transformation occurred, and the most common adverse events experienced off treatment were musculoskeletal (observed in 30 patients); however, dasatinib withdrawal events were reported in nine patients (11%) by the investigator. Overall, these findings support the feasibility of discontinuing dasatinib for patients with CML-CP in sustained DMR in the first line and beyond.

Assessing Measurable Residual Disease in Chronic Myeloid Leukemia. BCR-ABL1 IS in the Avant-Garde of Molecular Hematology

Chronic myelogenous leukemia (CML) is a malignancy of the myeloid cell lineage characterized by a recurrent chromosomal abnormality: the Philadelphia chromosome, which results from the reciprocal translocation of the chromosomes 9 and 22. The Philadelphia chromosome contains a fusion gene called BCR-ABL1. The BCR-ABL1 codes for an aberrantly functioning tyrosine kinase that drives the malignant proliferation of the founding clone. The advent of tyrosine kinase inhibitors (TKI) represents a landmark in the treatment of CML, that has led to tremendous improvement in the remission and survival rates. Since the introduction of imatinib, the first TKI, several other TKI have been approved that further broadened the arsenal against CML. Patients treated with TKIs require sensitive monitoring of BCR-ABL1 transcripts with quantitative real-time polymerase chain reaction (qRT-PCT), which has become an essential part of managing patients with CML. In this review, we discuss the importance of the BCR-ABL1 assay, and we highlight the growing importance of BCR-ABL1 dynamics. We also introduce a mathematical correction for the BCR-ABL1 assay that could help homogenizing the use of the ABL1 as a control gene. Finally, we discuss the growing body of evidence concerning treatment-free remission. Along with the continuous improvement in the therapeutic arsenal against CML, the molecular monitoring of CML represents the avant-garde in the struggle to make CML a curable disease.

Detecting the stable point of therapeutic effect of chronic myeloid leukemia based on dynamic network biomarkers

Background

Most researches of chronic myeloid leukemia (CML) are currently focused on the treatment methods, while there are relatively few researches on the progress of patients’ condition after drug treatment. Traditional biomarkers of disease can only distinguish normal state from disease state, and cannot recognize the pre-stable state after drug treatment.

Results

A therapeutic effect recognition strategy based on dynamic network biomarkers (DNB) is provided for CML patients’ gene expression data. With the DNB criteria, the DNB with 250 genes is selected and the therapeutic effect index (TEI) is constructed for the detection of individual disease. The pre-stable state before the disease condition becomes stable is 1 month. Through functional analysis for the DNB, some genes are confirmed as key genes to affect the progress of CML patients’ condition.

Conclusions

The results provide a certain theoretical direction and theoretical basis for medical personnel in the treatment of CML patients, and find new therapeutic targets in the future. The biomarkers of CML can help patients to be treated promptly and minimize drug resistance, treatment failure and relapse, which reduce the mortality of CML significantly.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2738-0) contains supplementary material, which is available to authorized users.

A numerical approach for a discrete Markov model for progressing drug resistance of cancer

The presence of treatment-resistant cells is an important factor that limits the efficacy of cancer therapy, and the prospect of resistance is considered the major cause of the treatment strategy. Several recent studies have employed mathematical models to elucidate the dynamics of generating resistant cancer cells and attempted to predict the probability of emerging resistant cells. The purpose of this paper is to present numerical approach to compute the number of resistant cells and the emerging probability of resistance. Stochastic model was designed and developed a method to approximately but efficiently compute the number of resistant cells and the probability of resistance. To model the progression of cancer, a discrete-state, two-dimensional Markov process whose states are the total number of cells and the number of resistant cells was employed. Then exact analysis and approximate aggregation approaches were proposed to calculate the number of resistant cells and the probability of resistance when the cell population reaches detection size. To confirm the accuracy of computed results of approximation, relative errors between exact analysis and approximation were computed. The numerical values of our approximation method were very close to those of exact analysis calculated in the range of small detection size M = 500, 100, and 1500. Then computer simulation was performed to confirm the accuracy of computed results of approximation when the detection size was M = 10000,30000,50000,100000 and 1000000. All the numerical results of approximation fell between the upper level and the lower level of 95% confidential intervals and our method took less time to compute over a broad range of cell size. The effects of parameter change on emerging probabilities of resistance were also investigated by computed values using approximation method. The results showed that the number of divisions until the cell population reached the detection size is important for emerging the probability of resistance. The next step of numerical approach is to compute the emerging probabilities of resistance under drug administration and with multiple mutation. Another effective approximation would be necessary for the analysis of the latter case.

Bridging blood cancers and inflammation: The reduced Cancitis model

A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.

Discontinuation of Tyrosine Kinase Inhibitors in Chronic Myeloid Leukemia With Losing Major Molecular Response as a Definition for Molecular Relapse: A Systematic Review and Meta-Analysis

Background: A new goal in treatment of chronic myeloid leukemia (CML) in patients with stable deep molecular response (DMR) is maintaining durable treatment-free remission (TFR) after discontinuing tyrosine kinase inhibitor (TKI) treatment. Methods: We conducted a systematic review and meta-analysis focusing on the efficacy and safety of TKI discontinuation but also exploring the factors contributing to successful TFR. Results: The search yielded 10 trials including 1,601 patients. For patients who discontinued TKIs, the estimated weighted mean incidence of major molecular relapse was 16% (95%CI: 11-21), 34% (95%CI: 29-38), 39% (95%CI: 35-43) and 41% (95%CI: 36-47) at 3, 6, 12, and 24 months, respectively. Of these, 39, 82, and 95% of molecular losses occurred within the first 3, 6, and 12 months. In safety analysis, among patients without TFR, 98% (95% CI: 96-100) were sensitive to TKI retreatment. No new safety issues were identified except TKI withdrawal syndrome, which appeared during the early TFR phase, with a weighted mean incidence of 27% (95%CI: 19-35). Our subgroup analysis suggested better TFR associated with interferon therapy (P = 0.007), depth of molecular response (P = 0.018) and duration of DMR (P < 0.001). Conclusions: TFR as an extension of an approach to optimize management of CML is clinically feasible in approximately 59% of patients with sufficient TKI response. In the remaining 41% of patients with molecular relapse, discontinuing TKIs had no negative impact on clinical outcomes. Given the high heterogeneity among studies, the role of these predictors for successful TFR still requires further investigation.

Statistical and Mathematical Modeling of Spatiotemporal Dynamics of Stem Cells

Statistical and mathematical modeling are crucial to describe, interpret, compare, and predict the behavior of complex biological systems including the organization of hematopoietic stem and progenitor cells in the bone marrow environment. The current prominence of high-resolution and live-cell imaging data provides an unprecedented opportunity to study the spatiotemporal dynamics of these cells within their stem cell niche and learn more about aberrant, but also unperturbed, normal hematopoiesis. However, this requires careful quantitative statistical analysis of the spatial and temporal behavior of cells and the interaction with their microenvironment. Moreover, such quantification is a prerequisite for the construction of hypothesis-driven mathematical models that can provide mechanistic explanations by generating spatiotemporal dynamics that can be directly compared to experimental observations. Here, we provide a brief overview of statistical methods in analyzing spatial distribution of cells, cell motility, cell shapes, and cellular genealogies. We also describe cell-based modeling formalisms that allow researchers to simulate emergent behavior in a multicellular system based on a set of hypothesized mechanisms. Together, these methods provide a quantitative workflow for the analytic and synthetic study of the spatiotemporal behavior of hematopoietic stem and progenitor cells.

Long-term treatment-free remission of chronic myeloid leukemia with falling levels of residual leukemic cells

Following the achievement of deep molecular response on tyrosine kinase inhibitors (TKIs), approximately half of patients with chronic myeloid leukemia (CML) can discontinue TKI and remain in treatment-free remission (TFR). The ALLG CML8 study enrolled 40 imatinib-treated patients with undetectable BCR-ABL1 mRNA (approximately MR^4.5). Molecular relapse was defined as detectable BCR-ABL1 on two consecutive tests or any single value >0.1%. With a median follow-up of 8.6 years (range 5.7-11.2 years), 18 patients remain in continuous TFR (45.0%; 95% confidence interval 31.9-63.4%). The latest relapse detected was 27 months after stopping imatinib. No patient progressed to advanced phase. Twenty-two patients met criteria for imatinib re-treatment and all regained undetectable molecular response. Nine patients in long-term TFR were monitored by highly sensitive individualized BCR-ABL1 DNA PCR in a sufficient number of samples to enable more precise quantification of residual leukemia. BCR-ABL1 DNA decreased from a median of MR^5.0 in the first year of TFR to MR^6.1 in the sixth year of TFR. Our results support the long-term safety and remarkable stability of response after imatinib discontinuation in appropriately selected CML patients. Serial high sensitivity testing provides a new and unexpected finding of gradually reducing CML cells in patients in long-term TFR.

Quantitative prediction of long-term molecular response in TKI-treated CML - Lessons from an imatinib versus dasatinib comparison

Longitudinal monitoring of BCR-ABL transcript levels in peripheral blood of CML patients treated with tyrosine kinase inhibitors (TKI) revealed a typical biphasic response. Although second generation TKIs like dasatinib proved more efficient in achieving molecular remission compared to first generation TKI imatinib, it is unclear how individual responses differ between the drugs and whether mechanisms of drug action can be deduced from the dynamic data. We use time courses from the DASISION trial to address statistical differences in the dynamic response between first line imatinib vs. dasatinib treatment cohorts and we analyze differences between the cohorts by fitting an established mathematical model of functional CML treatment to individual time courses. On average, dasatinib-treated patients show a steeper initial response, while the long-term response only marginally differed between the treatments. Supplementing each patient time course with a corresponding confidence region, we illustrate the consequences of the uncertainty estimate for the underlying mechanisms of CML remission. Our model suggests that the observed BCR-ABL dynamics may result from different, underlying stem cell dynamics. These results illustrate that the perception and description of CML treatment response as a dynamic process on the level of individual patients is a prerequisite for reliable patient-specific response predictions and treatment optimizations.

BCR-ABL1 genomic DNA PCR response kinetics during first-line imatinib treatment of chronic myeloid leukemia

Accurate quantification of minimal residual disease (MRD) during treatment of chronic myeloid leukemia (CML) guides clinical decisions. The conventional MRD method, RQ-PCR for BCR-ABL1 mRNA, reflects a composite of the number of circulating leukemic cells and the BCR-ABL1 transcripts per cell. BCR-ABL1 genomic DNA only reflects leukemic cell number. We used both methods in parallel to determine the relative contribution of the leukemic cell number to molecular response. BCR-ABL1 DNA PCR and RQ-PCR were monitored up to 24 months in 516 paired samples from 59 newly-diagnosed patients treated with first-line imatinib in the TIDEL-II study. In the first three months of treatment, BCR-ABL1 mRNA values declined more rapidly than DNA. By six months, the two measures aligned closely. The expression of BCR-ABL1 mRNA was normalized to cell number to generate an expression ratio. The expression of e13a2 BCR-ABL1 was lower than that of e14a2 transcripts at multiple time points during treatment. BCR-ABL1 DNA was quantifiable in 48% of samples with undetectable BCR-ABL1 mRNA, resulting in MRD being quantifiable for an additional 5-18 months (median 12 months). These parallel studies show for the first time that the rapid decline in BCR-ABL1 mRNA over the first three months of treatment is due to a reduction in both cell number and transcript level per cell, whereas beyond three months, falling levels of BCR-ABL1 mRNA are proportional to the depletion of leukemic cells.

Reduced tyrosine kinase inhibitor dose is predicted to be as effective as standard dose in chronic myeloid leukemia: a simulation study based on phase III trial data

Continuing tyrosine kinase inhibitor (TKI)-mediated targeting of the BCR-ABL1 oncoprotein is the standard therapy for chronic myeloid leukemia (CML) and allows for a sustained disease control in the majority of patients. While therapy cessation for patients appeared as a safe option for about half of those patients with optimal response, no systematic assessment of long-term TKI dose de-escalation has been made. We use a mathematical model to analyze and consistently describe biphasic treatment responses from TKI-treated patients from two independent clinical phase III trials. Scale estimates reveal that drug efficiency determines the initial response while the long-term behavior is limited by the rare activation of leukemic stem cells. We use this mathematical framework to investigate the influence of different dosing regimens on the treatment outcome. We provide strong evidence to suggest that TKI dose de-escalation (at least 50%) does not lead to a reduction of long-term treatment efficiency for most patients, who have already achieved sustained remission, and maintains the secondary decline of BCR-ABL1 levels. We demonstrate that continuous BCR-ABL1 monitoring provides patient-specific predictions of an optimal reduced dose without decreasing the anti-leukemic effect on residual leukemic stem cells. Our results are consistent with the interim results of the DESTINY trial and provide clinically testable predictions. Our results suggest that dose-halving should be considered as a long-term treatment option for CML patients with good response under continuing maintenance therapy with TKIs. We emphasize the clinical potential of this approach to reduce treatment-related side-effects and treatment costs.

Bayesian inference of agent-based models: a tool for studying kidney branching morphogenesis

The adult mammalian kidney has a complex, highly-branched collecting duct epithelium that arises as a ureteric bud sidebranch from an epithelial tube known as the nephric duct. Subsequent branching of the ureteric bud to form the collecting duct tree is regulated by subcellular interactions between the epithelium and a population of mesenchymal cells that surround the tips of outgrowing branches. The mesenchymal cells produce glial cell-line derived neurotrophic factor (GDNF), that binds with RET receptors on the surface of the epithelial cells to stimulate several subcellular pathways in the epithelium. Such interactions are known to be a prerequisite for normal branching development, although competing theories exist for their role in morphogenesis. Here we introduce the first agent-based model of ex vivo kidney uretic branching. Through comparison with experimental data, we show that growth factor-regulated growth mechanisms can explain early epithelial cell branching, but only if epithelial cell division depends in a switch-like way on the local growth factor concentration; cell division occurring only if the driving growth factor level exceeds a threshold. We also show how a recently-developed method, "Approximate Approximate Bayesian Computation", can be used to infer key model parameters, and reveal the dependency between the parameters controlling a growth factor-dependent growth switch. These results are consistent with a requirement for signals controlling proliferation and chemotaxis, both of which are previously identified roles for GDNF.

Exploring intermediate cell states through the lens of single cells

As our catalog of cell states expands, appropriate characterization of these states and the transitions between them is crucial. Here we discuss the roles of intermediate cell states (ICSs) in this growing collection. We begin with definitions and discuss evidence for the existence of ICSs and their relevance in various tissues. We then provide a list of possible functions for ICSs with examples. Finally, we describe means by which ICSs and their functional roles can be identified from single-cell data or predicted from models.