Mathematical Modeling of Clonal Selection and Therapy Resistance in Acute Leukemias
AbstractLeukemia is a disease of the blood forming system leading to extensive expansion of malignant cells. Similar as the blood В system, leukemias are maintained by a small population of leukemic stem cells that resist treatment and trigger relapse. Recent experimental evidence suggests that acute myeloid leukemias may В originate from multiple clones of malignant cells. Nevertheless it is not known В how В the вЂ observed В clones may differ with respect to cell properties such as proliferation В andвЂ self-renewal. В There are scarcely any data on how these cell properties change В due В to вЂ chemotherapy and relapse. We propose a new mathematical model to В investigate the вЂ impact В of cell properties on multi-clonal composition of leukemias.вЂ Considering a continuum of leukemic clones leads to a В structured population model consisting В ofвЂ integro-differential equations with a nonlinear and nonlocal coupling. вЂ WeвЂ show that such coupling leads to mass concentration in points corresponding to вЂ maximum of the self-renewal potential and the model solutions tend asymptotically to a linear combination of Dirac measures.вЂ Model results В imply вЂ that В enhanced self-renewal may be a key mechanism in the clonal selection process.вЂ Simulations suggest that fast proliferating and highly self-renewing cells dominate atвЂ primary diagnosis while relapse following therapy-induced remission is triggered mostlyвЂ by В highly self-renewing but slowly proliferating cells. вЂ вЂ Comparison of simulation results вЂ to В patient В data В demonstrates that the proposed model is consistent with clinically observedвЂ dynamics based on a clonal selection process.вЂ Model based interpretation of clinical data allows to assess parameters that cannot be measured directly. This might have clinical implications for future treatment and follow-up strategies.
The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).