Dynamics and Potential Impact of the Immune Response to Chronic Myelogenous Leukemia

Recent mathematical models have been developed to study the dynamics of chronic myelogenous leukemia (CML) under imatinib treatment. None of these models incorporates the anti-leukemia immune response. Recent experimental data show that imatinib treatment may promote the development of anti-leukemia immune responses as patients enter remission. Using these experimental data we develop a mathematical model to gain insights into the dynamics and potential impact of the resulting anti-leukemia immune response on CML. We model the immune response using a system of delay differential equations, where the delay term accounts for the duration of cell division. The mathematical model suggests that anti-leukemia T cell responses may play a critical role in maintaining CML patients in remission under imatinib therapy. Furthermore, it proposes a novel concept of an “optimal load zone” for leukemic cells in which the anti-leukemia immune response is most effective. Imatinib therapy may drive leukemic cell populations to enter and fall below this optimal load zone too rapidly to sustain the anti-leukemia T cell response. As a potential therapeutic strategy, the model shows that vaccination approaches in combination with imatinib therapy may optimally sustain the anti-leukemia T cell response to potentially eradicate residual leukemic cells for a durable cure of CML. The approach presented in this paper accounts for the role of the anti-leukemia specific immune response in the dynamics of CML. By combining experimental data and mathematical models, we demonstrate that persistence of anti-leukemia T cells even at low levels seems to prevent the leukemia from relapsing (for at least 50 months). As a consequence, we hypothesize that anti-leukemia T cell responses may help maintain remission under imatinib therapy. The mathematical model together with the new experimental data imply that there may be a feasible, low-risk, clinical approach to enhancing the effects of imatinib treatment

Helical tomotherapy for total marrow and total skin irradiation : Optimisation, verification, and clinical results

In modern cancer therapy, radiotherapy (RT) is a vital part of most treatments. Most RT treatments in Sweden are performed using intensity-modulated radiotherapy (IMRT) with fixed or dynamic arc delivery. The dose gradients outside the target are steep, the margins are small, and the treatment delivery is complicated. Complicated treatments increase the requirement for control of the uncertainties in planning and delivery. This requires robust treatments and mitigation of the various uncertainties. In addition, robust planning and rigorous quality assurance (QA) of the patient treatments that takes account of all types of uncertainties are essential. A TomoTherapy device (Accuray Inc., Madison, WI, USA) is an RT device with a linear accelerator mounted on a slip-ring construction, giving it the ability to irradiate while continuously rotating around the patient, very similar to a CT scanner but with megavoltage instead of X-ray energy generation. Since helical tomotherapy can entail long and complicated irradiations, new treatment types targeting RT to large parts of the body have emerged. These new techniques are challenging regarding the optimization and verification of the planning and treatment process. Recurring blood cancers (leukaemias) can be treated with RT and chemotherapy before stem cell transplantation. Traditionally, the patient is irradiated with whole-body irradiation using a conventional linac at a large distance. The treatment can be performed with helical tomotherapy to avoid organs at risks to a greater extent. Another emerging treatment with helical tomotherapy is irradiation of whole-body neoplastic skin lesions, such as mycosis fungoides. These patients were traditionally treated with electron irradiation in different positions, subsequently complemented with x-ray fields in ‘hard-to-reach’ sites. Delivering this treatment with photons is complex but opens the possibility for integrated boost treatments of lesions and simultaneously avoiding OAR and previously treated areas.The clinical follow-up illustrated the potential and usefulness of helical tomotherapy targeting the bone marrow, with more patients surviving without severe complications after one year, than with the previous technique. Further, we showed the possibility to implement irradiation of the entire skin with helical tomotherapy. Overall, we demonstrated the usefulness of helical tomotherapy, and solutions to overcome challenges in implementing large-target techniques

Clonal evolution in patients with chronic lymphocytic leukaemia developing resistance to BTK inhibition

Resistance to the Bruton’s tyrosine kinase (BTK) inhibitor ibrutinib has been attributed solely to mutations in BTK and related pathway molecules. Using whole-exome and deep-targeted sequencing, we dissect evolution of ibrutinib resistance in serial samples from five chronic lymphocytic leukaemia patients. In two patients, we detect BTK-C481S mutation or multiple PLCG2 mutations. The other three patients exhibit an expansion of clones harbouring del(8p) with additional driver mutations (EP300, MLL2 and EIF2A), with one patient developing trans-differentiation into CD19-negative histiocytic sarcoma. Using droplet-microfluidic technology and growth kinetic analyses, we demonstrate the presence of ibrutinib-resistant subclones and estimate subclone size before treatment initiation. Haploinsufficiency of TRAIL-R, a consequence of del(8p), results in TRAIL insensitivity, which may contribute to ibrutinib resistance. These findings demonstrate that the ibrutinib therapy favours selection and expansion of rare subclones already present before ibrutinib treatment, and provide insight into the heterogeneity of genetic changes associated with ibrutinib resistance.University of Texas M.D. Anderson Cancer Center (Support Grant CA016672)National Science Foundation (U.S.) (DMR-1310266)Harvard University. Materials Research Science and Engineering Center (DMR-1420570)National Natural Science Foundation (China) (81372496

Mathematical Model Studies on the Optimal Scheduling of the Treatment of Systemic Malignant Disease by Radiation

The work reported in this thesis deals with mathematical model studies on the optimal scheduling of treatment of systemic malignant disease by radiation. To provide the necessary background to the original aspects of the work reviews of several fields are required. Chapter 1 is a general review of normal tissue radiobiology. Chapter 2 is a review of human tumour radiobiology. Chapter 3 focusses on one particular isoeffect model, the linear-quadratic or LQ model, which is employed throughout this thesis to describe the effects of radiation on normal tissues. These basic radiobiological principles are applied to the clinical modalities of total body irradiation (TBI) and biologically targeted radiotherapy (BTR). Chapter 4 reviews the principles of TBI. Chapter 5 is a review of published data on the in-vitro radiosensitivities of human leukaemia/lymphoma and neuroblastoma, two conditions which require a systemic approach to treatment. Chapter 8 is a review of the principles of BTR. The original work is contained in the appendix to chapter 3, which examines the correspondence between the LQ model and CRE models for continuous radiation exposures with constant and exponentially decaying dose-rates; chapter 6, Which examines the question of whether fractionated or low dose-rate TBI is the superior method of treatment; chapter 7, where the optimal scheduling of fractionated TBI is investigated; chapter 9, where the LQ isoeffect model and a dosimetric approach is used for the evaluation of alternative therapeutic strategies for the treatment of widespread micrornetastatic disease by BTR. Finally, in chapter 10 a simple model is used to investigate optimal scheduling of BTR, TBI and marrow rescue. CONCLUSIONS 1/ Comparison of the LQ model and the CRE model for continuous radiation exposures: for constant dose-rates it is found that, when late-effect parameter values are used in the LQ model, there is a correspondence between the models' predictions. There is no correspondence between models when acute-effect parameter values are used in the LQ model. In the case of exponentially decaying dose-rates the predictions of the CRE and LQ models appear more divergent, although again the use of late rather than acute-effect parameter values in the LQ model gives a closer match to the CRE. 2/ Fractionated TBI is predicted to be preferable to low dose-rate TBI treatment. Although theoretically the methods can be equivalent, low dose-rate treatments would have to be over impractically long treatment times. 3/ In the case of external beam TBI, fractionated low dose-rate treatments do not appear to offer a significant improvement over fractionated high dose-rate treatments. This is because in order to achieve a significant increase in dose or reduction in toxicity impractically long exposure times are required. It is expected that this finding will be true in general for external beam radiotherapy, not just in the case of TBI. 4/ Optimal fractionation schedules for the treatment of leukaemia/lymphoma and neuroblastoma by TBI are predicted to be accelerated and hyperfractionated. It is suggested that a two fraction per day schedule of 10 fractions of 1.3-1.5 Gy is a suitable candidate for clinical evaluation. 5/ It is concluded that knowledge of ratios for tumours and normal tissues is, by itself, insufficient information to enable prediction of optimal schedules. 6/ In the case of BTR, dose-rate effects are predicted to be important for late-responding tissues. Tolerance doses may be greater or less than those for fractionated radiotherapy depending on the effective radionuclide half-life. 7/ When injected activities of targeted radionuclide are restricted by haemopoietic tolerance, curative therapy is unlikely. 131-I appears to be a better radionuclide warhead for therapy of micrometastases than 90-Y. 8/ The use of bone marrow rescue in conjunction with BTR seems to offer curative potential, however reasons are presented why a combined strategy using BTR, TBI and marrow rescue is likely to be preferable. 9/ For optimal scheduling of BTR, TBI and marrow rescue, the main characteristics of BTR which determine curative potential are its specificity and sensitivity. Specificity is defined here as the ratio of initial dose-rate at the tumour cells to that in the dose-limiting tissue. Sensitivity is inversely related to the proportion of tumour cells which escape targeting. Where biological targeting is highly specific but some tumour cells escape, a phenomenon of "overkill" will largely determine the optimal schedules. It is predicted that these are likely to consist of combinations of BTR and external beam TBI with the TBI component being the greatest in terms of radiation dose to the whole body

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

Background Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. Scope of review We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. Major conclusions Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. General significance Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled “System Genetics” Guest Editor: Dr. Yudong Cai and Dr. Tao Huang

How the latent geometry of a biological network provides information on its dynamics: the case of the gene network of chronic myeloid leukaemia

Background: The concept of the latent geometry of a network that can be represented as a graph has emerged from the classrooms of mathematicians and theoretical physicists to become an indispensable tool for determining the structural and dynamic properties of the network in many application areas, including contact networks, social networks, and especially biological networks. It is precisely latent geometry that we discuss in this article to show how the geometry of the metric space of the graph representing the network can influence its dynamics.Methods: We considered the transcriptome network of the Chronic Myeloid Laeukemia K562 cells. We modelled the gene network as a system of springs using a generalization of the Hooke’s law to n-dimension (n ≥ 1). We embedded the network, described by the matrix of spring’s stiffnesses, in Euclidean, hyperbolic, and spherical metric spaces to determine which one of these metric spaces best approximates the network’s latent geometry. We found that the gene network has hyperbolic latent geometry, and, based on this result, we proceeded to cluster the nodes according to their radial coordinate, that in this geometry represents the node popularity.Results: Clustering according to radial coordinate in a hyperbolic metric space when the input to network embedding procedure is the matrix of the stiffnesses of the spring representing the edges, allowed to identify the most popular genes that are also centres of effective spreading and passage of information through the entire network and can therefore be considered the drivers of its dynamics.Conclusion: The correct identification of the latent geometry of the network leads to experimentally confirmed clusters of genes drivers of the dynamics, and, because of this, it is a trustable mean to unveil important information on the dynamics of the network. Not considering the latent metric space of the network, or the assumption of a Euclidean space when this metric structure is not proven to be relevant to the network, especially for complex networks with hierarchical or modularised structure can lead to unreliable network analysis results

Dynamics and potential impact of the immune response to chronic myelogenous leukemia, PLoS

Abstract Recent mathematical models have been developed to study the dynamics of chronic myelogenous leukemia (CML) under imatinib treatment. None of these models incorporates the anti-leukemia immune response. Recent experimental data show that imatinib treatment may promote the development of anti-leukemia immune responses as patients enter remission. Using these experimental data we develop a mathematical model to gain insights into the dynamics and potential impact of the resulting anti-leukemia immune response on CML. We model the immune response using a system of delay differential equations, where the delay term accounts for the duration of cell division. The mathematical model suggests that anti-leukemia T cell responses may play a critical role in maintaining CML patients in remission under imatinib therapy. Furthermore, it proposes a novel concept of an ''optimal load zone'' for leukemic cells in which the anti-leukemia immune response is most effective. Imatinib therapy may drive leukemic cell populations to enter and fall below this optimal load zone too rapidly to sustain the anti-leukemia T cell response. As a potential therapeutic strategy, the model shows that vaccination approaches in combination with imatinib therapy may optimally sustain the anti-leukemia T cell response to potentially eradicate residual leukemic cells for a durable cure of CML. The approach presented in this paper accounts for the role of the anti-leukemia specific immune response in the dynamics of CML. By combining experimental data and mathematical models, we demonstrate that persistence of anti-leukemia T cells even at low levels seems to prevent the leukemia from relapsing (for at least 50 months). As a consequence, we hypothesize that anti-leukemia T cell responses may help maintain remission under imatinib therapy. The mathematical model together with the new experimental data imply that there may be a feasible, low-risk, clinical approach to enhancing the effects of imatinib treatment