2016, 13(6): 1169-1183. doi: 10.3934/mbe.2016037

A model of thermotherapy treatment for bladder cancer

1. 

School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland, Ireland

Received  December 2015 Revised  March 2016 Published  August 2016

In this work, we investigate chemo- thermotherapy, a recently clinically-approved post-surgery treatment of non muscle invasive urothelial bladder carcinoma. We developed a mathematical model and numerically simulated the physical processes related to this treatment. The model is based on the conductive Maxwell's equations used to simulate the therapy administration and Convection-Diffusion equation for incompressible fluid to study heat propagation through the bladder tissue. The model parameters correspond to the data provided by the thermotherapy device manufacturer. We base our computational domain on a CT image of a human bladder. Our numerical simulations can be applied to further research on the effects of chemo- thermotherapy on bladder and surrounding tissues and for treatment personalization in order to maximize the effect of the therapy while avoiding burning of the bladder.
Citation: Christoph Sadée, Eugene Kashdan. A model of thermotherapy treatment for bladder cancer. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1169-1183. doi: 10.3934/mbe.2016037
References:
[1]

, Radiating device for hyperthermia,, US Patent RE37, (). Google Scholar

[2]

, Water and Microwaves,, , (). Google Scholar

[3]

, Radiofrequency induced thermo-chemotherapy effect for the treatment of non-muscle invasive bladder cancer,, , (). Google Scholar

[4]

, Tissue parameters virtual family,, , (). Google Scholar

[5]

, Dielectric Properties of Body Tissues,, , (). Google Scholar

[6]

J. L.-S. Au, et al., Methods to improve efficacy of intravesical mitomycin c: Results of a randomized phase III trial,, J. of the National Cancer Institute, 93 (2001), 597. Google Scholar

[7]

M. Babjuk, et al., EAU guidelines on non-muscle-invasive urothelial carcinoma of the bladder,, European J. of Urology, 54 (2008), 303. doi: 10.1016/j.eururo.2008.04.051. Google Scholar

[8]

T. Cebeci, Convective Heat Transfer,, Springer, (2002). Google Scholar

[9]

R. Colombo, et al., Long-term outcomes of a randomized controlled trial comparing thermochemotherapy with mitomycin-C alone as adjuvant treatment for non-muscle-invasive bladder cancer (NMIBC),, British J. of Urolology Int., 107 (2011), 912. Google Scholar

[10]

O. N. Gofrit, et al., Combined local bladder hyperthermia and intravesical chemotherapy for the treatment of high-grade superficial bladder cancer,, Urology, 63 (2004), 466. doi: 10.1016/j.urology.2003.10.036. Google Scholar

[11]

M. C. Hall, et al., Guideline for the management of non muscle invasive bladder cancer (stages Ta, T1, and Tis): 2007 update,, J. of Urology, 178 (2007), 2314. Google Scholar

[12]

A. G. Van der Heijden, et al., Preliminary European results of local microwave hyperthermia and chemotherapy treatment in intermediate or high risk superficial transitional cell carcinoma of the bladder,, European J. of Urology, 46 (2004), 65. Google Scholar

[13]

J. M. Hill and M. J. Jennings, Formulation of model equations for heating by microwave radiation,, Applied Mathematical Modelling, 17 (1993), 369. doi: 10.1016/0307-904X(93)90061-K. Google Scholar

[14]

J. Holman, Heat Transfer,, McGraw-Hill, (2009). Google Scholar

[15]

A. Jemal, et al., Global cancer statistics,, CA:A Cancer J. for Clinicians, 61 (2011), 69. doi: 10.3322/caac.20107. Google Scholar

[16]

V. Kumar, A. K. Abbas and N. Fausto, Robbins and Cotran pathological basis of disease,, Elsevier, (2005). Google Scholar

[17]

R. J. M. Lammers, et al., The role of a combined regimen with intravesical chemotherapy and hyperthermia in the management of non-muscle-invasive bladder cancer: a systematic review,, European Urology, 60 (2011), 81. Google Scholar

[18]

B. Moskovitz, et al., 10-year single-center experience of combined intravesical chemohyperthermia for nonmuscle invasive bladder cancer,, Future Oncology, 8 (2012), 1041. Google Scholar

[19]

D. Shier, J. Butler and R. Lewis, Hole's Human Anatomy and Physiology,, McGraw-Hill, (2012). Google Scholar

[20]

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design,, Wiley, (2012). Google Scholar

[21]

A. Taflove and C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method,, (Artech House, (2005). Google Scholar

[22]

M. G. Wientjes, et al., Penetration of mitomycin c in human bladder,, Cancer Research, 53 (1993), 3314. Google Scholar

[23]

P. J. Woodroffe, et al., Modelling cell signalling and differentiation in the urothelium,, Bull of Math Biology, 67 (2005), 369. doi: 10.1016/j.bulm.2004.08.006. Google Scholar

show all references

References:
[1]

, Radiating device for hyperthermia,, US Patent RE37, (). Google Scholar

[2]

, Water and Microwaves,, , (). Google Scholar

[3]

, Radiofrequency induced thermo-chemotherapy effect for the treatment of non-muscle invasive bladder cancer,, , (). Google Scholar

[4]

, Tissue parameters virtual family,, , (). Google Scholar

[5]

, Dielectric Properties of Body Tissues,, , (). Google Scholar

[6]

J. L.-S. Au, et al., Methods to improve efficacy of intravesical mitomycin c: Results of a randomized phase III trial,, J. of the National Cancer Institute, 93 (2001), 597. Google Scholar

[7]

M. Babjuk, et al., EAU guidelines on non-muscle-invasive urothelial carcinoma of the bladder,, European J. of Urology, 54 (2008), 303. doi: 10.1016/j.eururo.2008.04.051. Google Scholar

[8]

T. Cebeci, Convective Heat Transfer,, Springer, (2002). Google Scholar

[9]

R. Colombo, et al., Long-term outcomes of a randomized controlled trial comparing thermochemotherapy with mitomycin-C alone as adjuvant treatment for non-muscle-invasive bladder cancer (NMIBC),, British J. of Urolology Int., 107 (2011), 912. Google Scholar

[10]

O. N. Gofrit, et al., Combined local bladder hyperthermia and intravesical chemotherapy for the treatment of high-grade superficial bladder cancer,, Urology, 63 (2004), 466. doi: 10.1016/j.urology.2003.10.036. Google Scholar

[11]

M. C. Hall, et al., Guideline for the management of non muscle invasive bladder cancer (stages Ta, T1, and Tis): 2007 update,, J. of Urology, 178 (2007), 2314. Google Scholar

[12]

A. G. Van der Heijden, et al., Preliminary European results of local microwave hyperthermia and chemotherapy treatment in intermediate or high risk superficial transitional cell carcinoma of the bladder,, European J. of Urology, 46 (2004), 65. Google Scholar

[13]

J. M. Hill and M. J. Jennings, Formulation of model equations for heating by microwave radiation,, Applied Mathematical Modelling, 17 (1993), 369. doi: 10.1016/0307-904X(93)90061-K. Google Scholar

[14]

J. Holman, Heat Transfer,, McGraw-Hill, (2009). Google Scholar

[15]

A. Jemal, et al., Global cancer statistics,, CA:A Cancer J. for Clinicians, 61 (2011), 69. doi: 10.3322/caac.20107. Google Scholar

[16]

V. Kumar, A. K. Abbas and N. Fausto, Robbins and Cotran pathological basis of disease,, Elsevier, (2005). Google Scholar

[17]

R. J. M. Lammers, et al., The role of a combined regimen with intravesical chemotherapy and hyperthermia in the management of non-muscle-invasive bladder cancer: a systematic review,, European Urology, 60 (2011), 81. Google Scholar

[18]

B. Moskovitz, et al., 10-year single-center experience of combined intravesical chemohyperthermia for nonmuscle invasive bladder cancer,, Future Oncology, 8 (2012), 1041. Google Scholar

[19]

D. Shier, J. Butler and R. Lewis, Hole's Human Anatomy and Physiology,, McGraw-Hill, (2012). Google Scholar

[20]

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design,, Wiley, (2012). Google Scholar

[21]

A. Taflove and C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method,, (Artech House, (2005). Google Scholar

[22]

M. G. Wientjes, et al., Penetration of mitomycin c in human bladder,, Cancer Research, 53 (1993), 3314. Google Scholar

[23]

P. J. Woodroffe, et al., Modelling cell signalling and differentiation in the urothelium,, Bull of Math Biology, 67 (2005), 369. doi: 10.1016/j.bulm.2004.08.006. Google Scholar

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