Mathematical Modeling of Leukemia Chemotherapy in Bone Marrow

Acute Lymphoblastic Leukemia (ALL) accounts for the 80% of leukemias when coming down to pediatric ages. Survival of these patients has increased by a considerable amount in recent years. However, around 15-20% of treatments are unsuccessful. For this reason, it is definitely required to come up with new strategies to study and select which patients are at higher risk of relapse. Thus the importance to monitor the amount of leukemic cells to predict relapses in the first treatment phase. In this work we develop a mathematical model describing the behavior of ALL, examining the evolution of a leukemic clone when treatment is applied. In the study of this model it can be observed how the risk of relapse is connected with the response in the first treatment phase. This model is able to simulate cell dynamics without treatment, representing a virtual patient bone marrow behavior. Furthermore, several parameters are related to treatment dynamics, therefore proposing a basis for future works regarding childhood ALL survival improvement.Comment: 20 pages and a supplementary information documen

A Mathematical Description of the Bone Marrow Dynamics during CAR T-Cell Therapy in B-Cell Childhood Acute Lymphoblastic Leukemia

Chimeric Antigen Receptor (CAR) T-cell therapy has demonstrated high rates of response in recurrent B-cell Acute Lymphoblastic Leukemia in children and young adults. Despite this success, a fraction of patients' experience relapse after treatment. Relapse is often preceded by recovery of healthy B cells, which suggests loss or dysfunction of CAR T-cells in bone marrow. This site is harder to access, and thus is not monitored as frequently as peripheral blood. Understanding the interplay between B cells, leukemic cells, and CAR T-cells in bone marrow is paramount in ascertaining the causes of lack of response. In this paper, we put forward a mathematical model representing the interaction between constantly renewing B cells, CAR T-cells, and leukemic cells in the bone marrow. Our model accounts for the maturation dynamics of B cells and incorporates effector and memory CAR T-cells. The model provides a plausible description of the dynamics of the various cellular compartments in bone marrow after CAR T infusion. After exploration of the parameter space, we found that the dynamics of CAR T product and disease were independent of the dose injected, initial B-cell load, and leukemia burden. We also show theoretically the importance of CAR T product attributes in determining therapy outcome, and have studied a variety of possible response scenarios, including second dosage schemes. We conclude by setting out ideas for the refinement of the model.This work was partially supported by the Fundacion Espanola para la Ciencia y la Tecnologia (UCA PR214), the Asociacion Pablo Ugarte (APU, Spain), Junta de Comunidades de Castilla-La Mancha (SBPLY/17/180501/000154), Ministry of Science and Technology, Spain (PID2019110895RB-I00), and Inversion Territorial Integrada de la Provincia de Cadiz (ITI-0038-2019)

High-Dimensional Analysis of Single-Cell Flow Cytometry Data Predicts Relapse in Childhood Acute Lymphoblastic Leukaemia

B-cell Acute Lymphoblastic Leukaemia is one of the most common cancers in childhood, with 20% of patients eventually relapsing. Flow cytometry is routinely used for diagnosis and follow-up, but it currently does not provide prognostic value at diagnosis. The volume and the high-dimensional character of this data makes it ideal for its exploitation by means of Artificial Intelligence methods. We collected flow cytometry data from 56 patients from two hospitals. We analysed differences in intensity of marker expression in order to predict relapse at the moment of diagnosis. We finally correlated this data with biomolecular information, constructing a classifier based on CD38 expression. Artificial intelligence methods may help in unveiling information that is hidden in high-dimensional oncological data. Flow cytometry studies of haematological malignancies provide quantitative data with the potential to be used for the construction of response biomarkers. Many computational methods from the bioinformatics toolbox can be applied to these data, but they have not been exploited in their full potential in leukaemias, specifically for the case of childhood B-cell Acute Lymphoblastic Leukaemia. In this paper, we analysed flow cytometry data that were obtained at diagnosis from 56 paediatric B-cell Acute Lymphoblastic Leukaemia patients from two local institutions. Our aim was to assess the prognostic potential of immunophenotypical marker expression intensity. We constructed classifiers that are based on the Fisher's Ratio to quantify differences between patients with relapsing and non-relapsing disease. We also correlated this with genetic information. The main result that arises from the data was the association between subexpression of marker CD38 and the probability of relapse

High-Dimensional Analysis of Single-Cell Flow Cytometry Data Predicts Relapse in Childhood Acute Lymphoblastic Leukaemia

Artificial intelligence methods may help in unveiling information that is hidden in high-dimensional oncological data. Flow cytometry studies of haematological malignancies provide quantitative data with the potential to be used for the construction of response biomarkers. Many computational methods from the bioinformatics toolbox can be applied to these data, but they have not been exploited in their full potential in leukaemias, specifically for the case of childhood B-cell Acute Lymphoblastic Leukaemia. In this paper, we analysed flow cytometry data that were obtained at diagnosis from 56 paediatric B-cell Acute Lymphoblastic Leukaemia patients from two local institutions. Our aim was to assess the prognostic potential of immunophenotypical marker expression intensity. We constructed classifiers that are based on the Fisher’s Ratio to quantify differences between patients with relapsing and non-relapsing disease. We also correlated this with genetic information. The main result that arises from the data was the association between subexpression of marker CD38 and the probability of relapse.Junta de Andalucía (Spain)Mathematical Oncology Laboratory Group from the University of Castilla-La Mancha.Ministery of Science and Technology, SpainInversión Territorial Integrada de la Provincia de Cádi

Dynamical properties of feedback signalling in B lymphopoiesis: A mathematical modelling approach.

Haematopoiesis is the process of generation of blood cells. Lymphopoiesis generates lymphocytes, the cells in charge of the adaptive immune response. Disruptions of this process are associated with diseases like leukaemia, which is especially incident in children. The characteristics of self-regulation of this process make them suitable for a mathematical study. In this paper we develop mathematical models of lymphopoiesis using currently available data. We do this by drawing inspiration from existing structured models of cell lineage development and integrating them with paediatric bone marrow data, with special focus on regulatory mechanisms. A formal analysis of the models is carried out, giving steady states and their stability conditions. We use this analysis to obtain biologically relevant regions of the parameter space and to understand the dynamical behaviour of B-cell renovation. Finally, we use numerical simulations to obtain further insight into the influence of proliferation and maturation rates on the reconstitution of the cells in the B line. We conclude that a model including feedback regulation of cell proliferation represents a biologically plausible depiction for B-cell reconstitution in bone marrow. Research into haematological disorders could benefit from a precise dynamical description of B lymphopoiesis

The shape of cancer relapse: Topological data analysis predicts recurrence in paediatric acute lymphoblastic leukaemia.

Although children and adolescents with acute lymphoblastic leukaemia (ALL) have high survival rates, approximately 15-20% of patients relapse. Risk of relapse is routinely estimated at diagnosis by biological factors, including flow cytometry data. This high-dimensional data is typically manually assessed by projecting it onto a subset of biomarkers. Cell density and "empty spaces" in 2D projections of the data, i.e. regions devoid of cells, are then used for qualitative assessment. Here, we use topological data analysis (TDA), which quantifies shapes, including empty spaces, in data, to analyse pre-treatment ALL datasets with known patient outcomes. We combine these fully unsupervised analyses with Machine Learning (ML) to identify significant shape characteristics and demonstrate that they accurately predict risk of relapse, particularly for patients previously classified as 'low risk'. We independently confirm the predictive power of CD10, CD20, CD38, and CD45 as biomarkers for ALL diagnosis. Based on our analyses, we propose three increasingly detailed prognostic pipelines for analysing flow cytometry data from ALL patients depending on technical and technological availability: 1. Visual inspection of specific biological features in biparametric projections of the data; 2. Computation of quantitative topological descriptors of such projections; 3. A combined analysis, using TDA and ML, in the four-parameter space defined by CD10, CD20, CD38 and CD45. Our analyses readily extend to other haematological malignancies