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

Previous Article Next Article

Research article Special Issues

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

Related Papers:

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.

References

[1]	T. R. Samatov, V. V. Galatenko, A. Block, M. Y. Shkurnikov, A. G. Tonevitsky, U. Schumacher, Novel biomarkers in cancer: The whole is greater than the sum of its parts, Semin. Cancer Biol., 45 (2017), 50-57.
[2]	L. C. Böckelmann, U. Schumacher, Targeting tumor interstitial fluid pressure: Will it yield novel successful therapies for solid tumors?, Expert Opin. Ther. Targets, 23 (2019), 1-10.
[3]	M. Heine, B. Freund, P. Nielsen, C. Jung, R. Reimer, H. Hohenberg, et al., High interstitial fluid pressure is associated with low tumour penetration of diagnostic monoclonal antibodies applied for molecular imaging purposes, PLoS One, 7 (2012), e36258.
[4]	M. Heine, P. Nollau, C. Masslo, P. Nielsen, B. Freund, O.T. Bruns, et al., Investigations on the usefulness of CEACAMs as potential imaging targets for molecular imaging purposes, PLoS One, 6 (2011), e28030.
[5]	A. J. Primeau, A. Rendon, D. Hedley, L. Lilge, I. F. Tannock, The distribution of the anticancer drug Doxorubicin in relation to blood vessels in solid tumors, Clin. Cancer Res., 11 (2005), 8782-8788.
[6]	L. Böckelmann, C. Starzonek, A. C. Niehoff, U. Karst, J. Thomale, H. Schlüter, et al., Detection of doxorubicin, cisplatin and therapeutic antibodies in formalin-fixed paraffin-embedded human cancer cells, Histochem. Cell Biol., 153 (2020), 367-377.
[7]	J. M. Brown, W. R. Wilson, Exploiting tumour hypoxia in cancer treatment, Nat. Rev. Cancer, 4 (2004), 437-447.
[8]	F. Pajonk, E. Vlashi, W. H. McBride, Radiation resistance of cancer stem cells: The 4 R's of radiobiology revisited, Stem Cells, 28 (2010), 639-648.
[9]	J. K. Saggar, I. F. Tannock, Chemotherapy rescues hypoxic tumor cells and induces their reoxygenation and repopulation-an effect that is inhibited by the hypoxia-activated prodrug TH-302, Clin. Cancer Res., 21 (2015), 2107-2114.
[10]	B. Ribba, E. Watkin, M. Tod, P. Girard, E. Grenier, B. You, et al., A model of vascular tumour growth in mice combining longitudinal tumour size data with histological biomarkers, Eur. J. Cancer, 47 (2011), 479-490.
[11]	N. D. Evans, R. J. Dimelow, J. W. T. Yates, Modelling of tumour growth and cytotoxic effect of docetaxel in xenografts, Comput. Methods Programs Biomed., 114 (2014), e3-e13.
[12]	S. Benzekry, A. Gandolfi, P. Hahnfeldt, Global dormancy of metastases due to systemic inhibition of angiogenesis, PLoS One, 9 (2014), e84249.
[13]	H. Enderling, M. A. J. Chaplain, A. R. A. Anderson, J. S. Vaidya, A mathematical model of breast cancer development, local treatment and recurrence, J. Theor. Biol., 246 (2007), 245-259.
[14]	A. Bethge, U. Schumacher, G. Wedemann, Simulation of metastatic progression using a computer model including chemotherapy and radiation therapy, J. Biomed. Inform., 57 (2015), 74-87.
[15]	R. Brady, H. Enderling, Mathematical models of cancer: When to predict novel therapies, and when not to, Bull. Math. Biol., 81 (2019), 3722-3731.
[16]	A. Akanuma, Parameter analysis of Gompertzian function growth model in clinical tumors, Eur. J. Cancer, 14 (1978), 681-688.
[17]	A. K. Laird, Dynamics of tumour growth, Br. J. Cancer, 18 (1964), 490-502.
[18]	V. P. Collins, R. K. Loeffler, H. Tivey, Observations on growth rates of human tumors, AJR Am. J. Roentgenol., 76 (1956), 988-1000.
[19]	L. von Bertalanffy, Quantitative laws in metabolism and growth, Q. Rev. Biophys., 32 (1957), 217-231.
[20]	S. Michelson, A. S. Glicksman, J. T. Leith, Growth in solid heterogeneous human colon adenocarcinomas: Comparison of simple logistical models, Cell Tissue Kinet, 20 (1987), 343-355.
[21]	J. A. Spratt, D. von Fournier, J. S. Spratt, E. E. Weber, Decelerating growth and human breast cancer, Cancer, 71 (1993), 2013-2019.
[22]	R. H. Reuning, R. A. Sams, R. E. Notari, Role of pharmacokinetics in drug dosage adjustment. I. pharmacologic effect kinetics and apparent volume of distribution of digoxin, J. Clin. Pharmacol .New Drugs, 13 (1973), 127-141.
[23]	A. Rohatgi, WebPlotDigitizer-Extract Data from Plots, Images, and Maps. Available from: https://automeris.io/WebPlotDigitizer/.
[24]	T. Brodbeck, N. Nehmann, A. Bethge, G. Wedemann, U. Schumacher, Perforin-dependent direct cytotoxicity in natural killer cells induces considerable knockdown of spontaneous lung metastases and computer modelling-proven tumor cell dormancy in a HT29 human colon cancer xenograft mouse model, Mol. Cancer, 13 (2014), 244.
[25]	A. V. Chvetsov, L. Dong, J. R. Palta, R. J. Amdur, Tumor-volume simulation during radiotherapy for head-and-neck cancer using a four-level cell population model, Int. J. Radiat. Oncol. Biol. Phys., 75 (2009), 595-602.
[26]	R. Ruggieri, A. E. Nahum, The impact of hypofractionation on simultaneous dose-boosting to hypoxic tumor subvolumes, Med. Phys., 33 (2006), 4044-4055.
[27]	K. Nakamura, A. Brahme, Evaluation of fractionation regimens in stereotactic radiotherapy using a mathematical model of repopulation and reoxygenation, Radiat. Med., 17 (1999), 219-225.
[28]	T. Frenzel, B. Hoffmann, R. Schmitz, A. Bethge, U. Schumacher, G. Wedemann, Radiotherapy and chemotherapy change vessel tree geometry and metastatic spread in a small cell lung cancer xenograft mouse tumor model, PLoS One, 12 (2017), e0187144.
[29]	K. Iwata, K. Kawasaki, N. Shigesada, A dynamical model for the growth and size distribution of multiple metastatic tumors, J. Theor. Biol., 203 (2000), 177-186.
[30]	J. S. Spratt, J. S. Meyer, J. A. Spratt, Rates of growth of human solid neoplasms: Part I, J. Surg. Oncol., 60 (1995), 137-146.
[31]	B. Hoffmann, T. Lange, V. Labitzky, K. Riecken, A. Wree, U. Schumacher, et al., The initial engraftment of tumor cells is critical for the future growth pattern: a mathematical study based on simulations and animal experiments, BMC Cancer, 20 (2020), 524.
[32]	M. Simeoni, P. Magni, C. Cammia, G. De Nicolao, V. Croci, E. Pesenti, et al., Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents, Cancer Res., 64 (2004), 1094-1101.
[33]	I. F. Tannock, The relation between cell proliferation and the vascular system in a transplanted mouse mammary tumour., Br. J. Cancer, 22 (1968), 258-273.
[34]	R. Seifert, Basic Knowledge of Pharmacology, Springer International Publishing, 2019.
[35]	K. D. Tripathi, Essentials of Medical Pharmacology, Jaypee Brothers Medical Publishers, 2013.
[36]	G. N. Naumov, J. L. Townson, I. C. MacDonald, S. M. Wilson, V. H. C. Bramwell, A. C. Groom, et al., Ineffectiveness of doxorubicin treatment on solitary dormant mammary carcinoma cells or late-developing metastases, Breast Cancer Res. Treat., 82 (2003), 199-206.
[37]	W. Sun, L. M. Schuchter, Metastatic melanoma, Curr. Treat Options Oncol., 2 (2001), 193-202.
[38]	J. C. Panetta, J. Adam, A mathematical model of cycle-specific chemotherapy, Math. Comput. Model, 22 (1995), 67-82.

mbe-17-05-325-Supplementary.pdf

Reader Comments

Your name:*

Email:*
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)