Modelling lymphoma therapy and outcome

Bull Math Biol. 2014 Feb;76(2):401-30. doi: 10.1007/s11538-013-9925-3. Epub 2013 Dec 14.


Dose and time intensifications of chemotherapy improved the outcome of lymphoma therapy. However, recent study results show that too intense therapies can result in inferior tumour control. We hypothesise that the immune system plays a key role in controlling residual tumour cells after treatment. More intense therapies result in a stronger depletion of immune cells allowing an early re-growth of the tumour.We propose a differential equations model of the dynamics and interactions of tumour and immune cells under chemotherapy. Major model features are an exponential tumour growth, a modulation of the production of effector cells by the presence of the tumour (immunogenicity), and mutual destruction of tumour and immune cells. Chemotherapy causes damage to both, immune and tumour cells. Growth rate, chemosensitivity, immunogenicity, and initial size of the tumour are assumed to be patient-specific, resulting in heterogeneity regarding therapy outcome. Maximum-entropy distributions of these parameters were estimated on the basis of clinical survival data. The resulting model can explain the outcome of five different chemotherapeutic regimens and corresponding hazard-ratios.We conclude that our model explains observed paradox effects in lymphoma therapy by the simple assumption of a relevant anti-tumour effect of the immune system. Heterogeneity of therapy outcomes can be explained by distributions of model parameters, which can be estimated on the basis of clinical survival data. We demonstrate how the model can be used to make predictions regarding yet untested therapy options.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Antineoplastic Agents / administration & dosage
  • Antineoplastic Agents / adverse effects
  • Antineoplastic Combined Chemotherapy Protocols / administration & dosage
  • Antineoplastic Combined Chemotherapy Protocols / adverse effects
  • Computer Simulation
  • Disease-Free Survival
  • Humans
  • Immune System / drug effects
  • Lymphoma / drug therapy*
  • Lymphoma / immunology*
  • Lymphoma / pathology
  • Lymphoma, Large B-Cell, Diffuse / drug therapy
  • Lymphoma, Large B-Cell, Diffuse / immunology
  • Lymphoma, Non-Hodgkin / drug therapy
  • Lymphoma, Non-Hodgkin / immunology
  • Mathematical Concepts
  • Models, Biological*
  • Models, Immunological
  • Treatment Outcome


  • Antineoplastic Agents