Absence of convection in solid tumors caused by raised interstitial fluid pressure severely limits success of chemotherapy—a numerical study in cancers

Bertin Hoffmann; Udo Schumacher; Gero Wedemann; Bertin Hoffmann; Udo Schumacher; Gero Wedemann

doi:10.3934/mbe.2020325

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 6128-6148. doi: 10.3934/mbe.2020325

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Absence of convection in solid tumors caused by raised interstitial fluid pressure severely limits success of chemotherapy—a numerical study in cancers

1.
Competence Center Bioinformatics, Institute for Applied Computer Science, University of Applied Sciences Stralsund, Zur Schwedenschanze 15, 18435 Stralsund, Germany
2.
Institute for Anatomy and Experimental Morphology, University Cancer Center, University Medical Center Hamburg-Eppendorf, Martinistraße 52, 20246 Hamburg, Germany

Received: 03 July 2020 Accepted: 27 August 2020 Published: 14 September 2020

In comparison with lymphomas and leukemias, chemotherapy of solid neoplasms, i.e., cancer, has much more limited success in curing the patient. This lack of efficacy of chemotherapy has been attributed to increased interstitial fluid pressure within cancers, which obstructs convection and only permits diffusion of oxygen and nutrients about 100 μm from blood vessels. As diffusion is limited to this distance, hypoxic and necrotic fractions within the tumor are observed beyond this region. The comparably small number of cancer cells that can be targeted with drugs inevitably leads to an ineffective treatment response. This study presents an analysis of the influence of interstitial fluid pressure on the chemotherapeutic effect in an HT29 human colon cancer xenograft mouse tumor model. To investigate the limited distribution of drugs into primary tumor and metastases, we developed a mathematical model describing tumor growth dynamics of oxygenated, hypoxic, and necrotic fractions, combined with a pharmacokinetic–pharmacodynamic model describing the behavior and effectivity of the chemotherapeutic agent. According to the numerical simulations, the age of the tumor at treatment was the decisive factor in the reduction in size of the primary tumor. This effect is mediated by the rapid decrease in the percentage of oxygenated cells within the tumor, which reduces the fraction of cells that can be affected by the drug. As in the primary tumor, interstitial fluid pressure builds up in metastases when they reach a specific size, leading to the formation of tumor fractions. This behavior is absent if the metastasis enters a dormant phase before the threshold for the development of interstitial fluid pressure has been reached. The small size of these metastases maximizes therapeutic success since they consist only of oxygenated cells, and the drug therefore affects all the cells.
- computer simulation,
- hypoxic and necrotic fractions,
- mathematical model,
- parameter estimation,
- therapeutic efficacy,
- tumor growth,
- tumor interstitial fluid pressure
Citation: Bertin Hoffmann, Udo Schumacher, Gero Wedemann. Absence of convection in solid tumors caused by raised interstitial fluid pressure severely limits success of chemotherapy—a numerical study in cancers[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 6128-6148. doi: 10.3934/mbe.2020325

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Abstract

In comparison with lymphomas and leukemias, chemotherapy of solid neoplasms, i.e., cancer, has much more limited success in curing the patient. This lack of efficacy of chemotherapy has been attributed to increased interstitial fluid pressure within cancers, which obstructs convection and only permits diffusion of oxygen and nutrients about 100 μm from blood vessels. As diffusion is limited to this distance, hypoxic and necrotic fractions within the tumor are observed beyond this region. The comparably small number of cancer cells that can be targeted with drugs inevitably leads to an ineffective treatment response. This study presents an analysis of the influence of interstitial fluid pressure on the chemotherapeutic effect in an HT29 human colon cancer xenograft mouse tumor model. To investigate the limited distribution of drugs into primary tumor and metastases, we developed a mathematical model describing tumor growth dynamics of oxygenated, hypoxic, and necrotic fractions, combined with a pharmacokinetic–pharmacodynamic model describing the behavior and effectivity of the chemotherapeutic agent. According to the numerical simulations, the age of the tumor at treatment was the decisive factor in the reduction in size of the primary tumor. This effect is mediated by the rapid decrease in the percentage of oxygenated cells within the tumor, which reduces the fraction of cells that can be affected by the drug. As in the primary tumor, interstitial fluid pressure builds up in metastases when they reach a specific size, leading to the formation of tumor fractions. This behavior is absent if the metastasis enters a dormant phase before the threshold for the development of interstitial fluid pressure has been reached. The small size of these metastases maximizes therapeutic success since they consist only of oxygenated cells, and the drug therefore affects all the cells.

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