Математическое моделирование и биомеханический подход к описанию развития, диагностики и лечения онкологических заболеваний

Автор: Кучумов А.Г.

Журнал: Российский журнал биомеханики @journal-biomech

Статья в выпуске: 4 (50) т.14, 2010 года.

Бесплатный доступ

Развитие раковых опухолей связано с различными химическими, генетическими, физиологическими и механическими факторами, которые происходят как на субклеточном и клеточном уровнях, так и на уровнях тканей и органов. В последние десятилетия наблюдается прогресс в выявлении и объяснении процессов, возникающих при развитии раковых заболеваний, а также разработке методов и средств для ранней диагностики и лечения болезни. Значительный вклад в решение данной проблемы, с одной стороны, привнесло развитие биотехнологий и медицины, с другой стороны, такие направления науки, как математическое моделирование и биомеханические исследования, позволяют смоделировать поведение клеток и органов до болезни, при её развитии и лечении, обходясь без сложнейших наблюдений in vivo. В данной работе приведен обзор явлений, которые возникают при зарождении и развитии болезни, описана роль математики и биомеханики в описании и объяснении данных процессов, а также лечении онкологических опухолей. Следует обратить особое внимание на внедрение новых мультимасштабных моделей, которые описывают состояние болезни как на микроуровне, так и на мезо- и макроуровнях.

Еще

Рак, клеточная механика, механотрансдукция, ангиогенез, мультимасштабный подход

Короткий адрес: https://sciup.org/146216007

IDR: 146216007

Список литературы Математическое моделирование и биомеханический подход к описанию развития, диагностики и лечения онкологических заболеваний

  • Акулич Ю.В. Математическая модель процесса внутренней адаптационной перестройки спонгиозной и кортикальной костных тканей человека//Механика композиционных материалов и конструкций. -2005. -Т. 11, № 2. -С. 157-168.
  • Бардычев Д.М., Иванов В.К. Математическое моделирование кинетики гетерогенной клеточной популяции в процессе опухолевого роста//Цитология. -1984. -Т. 26, № 12. -С. 1357-1364.
  • Герасимова Е.И., Наймарк О.Б. Применение инфракрасного сканирования при диагностике опухолевых заболеваний//Материалы XVIII Всерос. школы-конференции молодых учёных и студентов (1-3 октября 2009). -Пермь, 2009. -С. 23.
  • Косевич А.М., Кругликов И.Л. Диффузионная модель роста солидной опухоли//Докл. АН СССР. -1980. -Т. 251, № 1. -С. 226-230.
  • Наймарк О.Б. Локализованные моды дисторсии в структуре двойной спирали ДНК//Российский журнал биомеханики. -2006. -Т. 10, № 4. -С. 18-42.
  • Панин В.Е., Егорушкин В.Е., Панин А.В. Физическая мезомеханика деформируемого твердого тела как многоуровневой системы. Ч. I: Физические основы многоуровневого подхода//Физическая мезомеханика. -2006. -Т. 9, № 3. -С. 9-22.
  • Панин В.Е. Основы физической мезомеханики//Физическая мезомеханика. -1998. -Т. 1, № 1. -С. 5-22.
  • Победря Б.Е., Курочкина Ю.В. Об идентификации в механике нанокомпозитов//Изв. РАН. МТТ. -2007. -№ 3. -С. 6-12.
  • Регирер С.А. Приложения биомеханики в исследованиях роста опухолей//Современные проблемы биомеханики. -2000. -Вып. 10. -С. 268-290.
  • Adam J. A mathematical model of tumor growth by diffusion//Mathematical and Computer Modelling -1988. -Vol. 11. -P. 455-451.
  • Asa Dr., Barber H. The world of nano-biomechanics. -Elsevier, 2008. -248 p.
  • Andreykiv A., van Keulen F., Prendergast P.J. Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells//Biomechan. Model. Mechanobiol.-2008. -Vol. 7. -P. 443.-461.
  • Araujo R.P., McElwain L.S. A history of the study of solid tumour growth: the contribution of mathematical modelling//Bulletin of Mathematical Biology. -2004. -Vol. 66. -P. 1039-1091.
  • Aoubiza B., Crolet J.M., Meunier A. On the mechanical characterization of compact bone structure using the homogenization theory//Journal of Biomechanics. -1996. -Vol. 29, No. 12. -P. 6674-6686.
  • Bacer E.L., Zaman M.H. The biomechanical integrin//Journal of Biomechanics. -2010. -Vol. 43. -P. 38-44.
  • Bavafaye-Haghighi E., Yazdanpanah M.J., Kalaghchi B., Soltanian-Zadeh H. Multiscale cancer modelling: in the line of fast of simulation and chemotherapy//Mathematical and Computer Modelling. -2009. -Vol. 49. -P. 1449-1464.
  • Bellomo N., Delitala M. From the mathematical, kinetic, and stochastic game theory to modelling mutations, onset, progression, and immune competition of cancer cells//Physics of Life Reviews. -2008. -Vol. 5. -P. 183-206.
  • Bellomo N., Bellouquid A. From a class of kinetic models to macroscopic equations for multicellular systems in biology//Discrete Contin. Dyn. Syst. -2004. -Vol. 4. -P. 59-80.
  • Bellomo N., Bellouquid A., Delitala M. From the mathematical kinetic theory of active particles to multiscale modelling of complex biological systems//Mathematical and Computer Modelling. -2008. -Vol. 47. -P. 687-698.
  • Bertuzzi A., Bruni C., Fasano A., Gandolfi A., Papa F., Sinisgalli C. Response of tumor spheroids to radiation: modeling and parameter estimation//Bulletin of Mathematical Biology. -2009. -Vol. 25. -P. 1-23.
  • Byrne H.M., van Leeuwen I.M.M., Owen M.R., Alarcon T., Maini P.K. Multiscale modelling of solid tumour growth//Selected Topics in Cancer Modeling. -2008. -Vol. 12, No. 1. -P. 449-473.
  • Byrne H.M., Chaplain M.A. A mathematical model of trophoblast invasion//Journal Theor. Med. -1993. -Vol. 2. -P. 27-39.
  • Byrne H.M., Chaplain M.A. Growth of nonnecrotic tumors in the presence and absence of inhibitors//Math. Biosci. -1995. -Vol. 130. -P. 151-181.
  • Capasso V., Micheletti A. Stochastic geometry and related statistical problems in biomedicine//Modeling and Simulation in Science, Engineering and Technology. -2008. -Vol. 7. -P. 1-37.
  • Chaplain M.A.J. Mathematical modelling of angiogenesis//Journal of Neuro-Oncology. -2000. -Vol. 50. -P. 37-51.
  • Coelho P.G., Fernandes P.R., Rodrigues H.C., Cardoso J.B., Guedes J.M. Numerical modeling of bone tissue adaptation -a hierarchical approach for bone apparent density and trabecular structure//Journal of Biomechanics. -2009. -Vol. 42. -P. 830-837.
  • Crick S.L., Yin F. Assessing micromechanical properties of cells with atomic force microscopy: importance of the contact point//Biomechan. Model. Mechanobiol. -2007. -Vol. 6. -P. 199-210.
  • Dao M., Lim C.T., Suresh S. Mechanics of the human red blod cell deformed by optical twezers//Journal of the Mechanics and Physics of Solids. -2003. -Vol. 51. -P. 2259-2280.
  • Decraene J., Mitchell G.G., McMullin B. Evolving artificial cell signaling networks: perspectives and methods//Studies in Computational Intelligence. -2009. -Vol. 69. -P. 167-186.
  • Dixit A., Torkamani A., Schork N.J., Verkhivker G. Computational modeling of structurally conserved cancer mutations in the RET and MET kinases: the impact on protein structure dynamics, and stability//Biophysical Journal. -2009. -Vol. 96. -P. 858-874.
  • Eftimie R., Bramson J.L., Earn D. Interactions between the immune system and cancer: a brief review of non-spatial mathematical models//Bulletin of Mathematical Biology. -2010. -Vol. 26. -P. 22-54.
  • Fasano A., Bertuzzi A., Gandolfi A. Mathematical modelling of tumour growth and treatment//Bulletin of Mathematical Biology. -2010. -Vol. 26. -P. 71-108.
  • Folkman J. Tumor angiogenesis//Adv. Cancer Res. -1985. -Vol. 43. -P. 175-203.
  • Ghanbari I., Naghdabadi R. Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure//Journal of Biomechanics. -2009. -Vol. 42. -P. 1560-1565.
  • Gibson R.F. A review of recent research on mechanics of multifunctional composite materials and structures//Composite Structures. -2010. -Vol. 179. -P. 51-60.
  • Godin L.M., Suzuki S., Jacobs C.R., Donahue H.J., Donahue S.W. Mechanically induced intracellular calcium waves in osteoblasts demonstrate calcium fingerprints in bone cell mechanotransduction//Biomechan. Model. Mechanobiol. -2007. -Vol. 6. -P. 391-398.
  • Gompertz G. On the nature of the function expressive of the law of human mortality, and on the new mode of determining the value of life contingencies//Philos. Trans. R. Soc. London. -1825. -Vol. 115. -P. 513-585.
  • Graziano L., Preziosi L. Mechanics in tumor growth//Modeling of Biological Materials. -2008. -Vol. 14. -P. 263-321.
  • Greenspan H.P. On the growth and stability of cell cultures and solid tumors//J. Theor. Biol. -1976. -Vol. 56. -P. 229-242.
  • Greller A., Bellomo N. Models with space structure and the derivation of macroscopic equations//Journal of Applied Biomechanics. -2007. -Vol. 15. -P. 119-149.
  • Groh A., Louis A.K. Stochastic modelling of biased cell migration and collagen matrix modification//Journal Math. Biol. -2009. -Vol. 23. -P. 13-34.
  • Guilak F., Mow V. The mechanical environment of the chodrocyte: a biphasic finite element model of cell -matrix interactions in articular cartilage//Journal of Biomechanics. -2000. -Vol. 33, No. 12. -P. 1663-1673.
  • Hartmann D. A multiscale model for red blood cell mechanics//Biomechan. Model. Mechanobiol.-2010. -Vol. 9. -P. 1-17.
  • Ilic S., Hackl K., Gilbert R. Application of the multiscale FEM to the modeling of cancellous bone//Biomechan. Model. Mechanobiol.-2010. -Vol. 9. -P. 87-102.
  • Issakson H., Wilson W., van Donkelaar C., Huiskes R., Ito K. Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing//Journal of Biomechanics. -2006. -Vol. 29. -P. 1507-1516.
  • Jain R. Transport of molecules across tumor vasculature//Cancer Metastasis Rev. -1987. -Vol. 6. -P. 559-593.
  • Jasiuk I., Ostoja-Starzewski M. Modeling of bone at a single lamella level//Biomechan. Model. Mechanobiol. -2004. -Vol. 3. -P. 67-74.
  • Ji B., Gao H. Mechanical properties of nanostructure of biological materials//Journal of the Mechanics and Physics of Solids. -2004. -Vol. 52. -P. 1963-1990.
  • Jiang Y., Pjesivac-Grbovic J., Cantrell C., Freyer J.P. A multiscale model for avascular tumor growth//Biophysical Journal. -2005. -Vol. 89. -P. 3884-3894.
  • Kim Y., Friedman A. Interaction of tumor with its micro-environment: a mathematical model//Bulletin of Mathematical Biology. -2009. -Vol. 25. -P. 34-45.
  • Komarova N.L. Loss-and Gain-of-Function mutations in cancer: mass-action, spatial and hierarchical models//Journal of Statistical Physics. -2007. -Vol. 128. -P. 413-446.
  • Korb T., Schluter K., Enns A., Spiegel H., Senninger N., Nicolson G.L., Haier J. Integrity of actin fibers and microtubules influences metastatic tumor cell adhesion//Experimental Cell Research. -2004. -Vol. 299. -P. 236-247.
  • Kotha S.P., Guzelsu N. Tensile behavior of cortical bone: dependence of organic matrix material properties on bone mineral content//Journal of Biomechanics. -2007. -Vol. 40. -P. 36-45.
  • Kumar S., Maxwell I.Z., Heisterkamp A., Polte T.R., Lele T.P., Salanga M., Mazur E., Ingber D.E. Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics//Biophysical Journal. -2006. -Vol. 90. -P. 3762-3773.
  • Kumar S., LeDuc P.R. Dissecting the molecular basis of the mechanics of living cells//Experimental Mechanics. -2009. -Vol. 49. -P. 11-23.
  • Lee G.Y.H., Lim C.T. Biomechanics approaches to studying human diseases//Trends in Biotechnology. -2006. -Vol. 25, No. 3. -P. 579-586.
  • Lekka M. Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy//Eur. Biophys. Journal. -1999. -Vol. 28. -P. 312-331.
  • Li Q.S., Lee G.Y.H., Ong C.N., Lim C.T. AFM indentation study of breast cancer cells//Biochemical and Biophysical Research Communications. -2008. -Vol. 374. -P. 609-613.
  • Lim C.T., Zhou E.H., Quek S.T. Mechanical models for living cells -a review//Journal of Biomechanics. -2006. -Vol. 39. -P. 195-216.
  • Liu W.K., Liu Y., Farrell D., Zhang L., Wang X.S., Fukui Y., Patankar N., Zhang Y., Bajaj C., Lee J.,
  • Hong J., Chen X., Hsu H. Immersed finite element method and its applications to biological systems//Comput. Methods Appl. Mech. Engrg. -2006. -Vol. 195. -P. 1722-1749.
  • Loboa E.G., Wren T.A., Beaupre G.S., Carter D.R. Mechanobiology of soft skeletal tissue differentiation -a computational approach of a fiber-reinforced poroelastic model based on homogeneous and isotropic simplifications//Biomechan. Model. Mechanobiol. -2003. -Vol. 2. -P. 83-96.
  • Lurie S., Belov P., Volkov-Bogorodsky D., Tuchkova N. Nanomechanical modeling of the nanostructures and dispersed composites//Computational Materials Science. -2003. -Vol. 28. -P. 529-539.
  • Maceri F., Marino M., Vairo G. A unified multiscale mechanical model for soft collagenous tissues with regular fiber arrangement//Journal of Biomechanics. -2010. -Vol. 43. -P. 355-363.
  • Madri J.A., Pratt B.M. Endothelial cell-matrix interactions in vitro models of angiogenesis//J. Histochem. Cytochem. -1986. -Vol. 34. -P. 85-91.
  • Maggelakis S.A., Adam J.A. Mathematical model of prevascular growth of a spherical carcinoma//Math. Comput. Modelling. -1990. -Vol. 13. -P. 23-38.
  • Maher K.O., Pizarro C., Gidding S.S., Januszewska K., Malec E., Norwood W.I., Murphy J.D. Hemodynamic profile after the Norwood procedure with right ventricle to pulmonary artery conduit//Circulation. -2003. -Vol. 108. -P. 782-784.
  • Malec E., Januszewska K., Kolcz J., Mroczek T. Right ventricle-to-pulmonary artery shunt versus modified Blalock-Taussig shunt in the Norwood procedure for hypoplastic left heart syndrome-influence on early and late haemodynamic status//European Journal of Cardiothoracic Surgery. -2003. -Vol. 23. -P. 728-733.
  • Mansury Y., Deisboeck T.S. Modeling tumors as complex biosystems: an agent-based approach//International Topics in Biomedical Engineering. -2006. -Vol. 6. -P. 573-602.
  • Martins M.L., Ferreira Jr S.C., Vilela M.J. Multiscale models for the growth of avascular tumors//Physics of Life Reviews. -2007. -Vol. 4. -P. 128-156.
  • McKenna S.L., McGowan A. J., Cotter T. G. Molecular mechanisms of programmed cell death//Advances in Biochemical Engineering/Biotechnology. -1998. -Vol. 62. -P. 3-11.
  • Migliavacca F., Balossino R., Pennati G., Dubini G., Hsia T.Y., de Leval M.R., Bove E.L. Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery//Journal of Biomechanics. -2006. -Vol. 39. -P. 1010-1020.
  • Moreno-Flores S., Benitez R., Vivanco M., Toca-Herrera J.L. Stress relaxation microscopy: imaging local stress in cells//Journal of Biomechanics. -2010. -Vol. 43. -P. 349-354.
  • Murugan R., Ramakrishna S. Development of nanocomposites for bone grafting//Composites Science and Technology. -2005. -Vol. 65. -P. 2385-2406.
  • N'Dri N.A., Shyy W., Tran-Son-Tay R. Computational modeling of cell adhesion and movement using a continuum-kinetics approach//Biophysical Journal. -2003. -Vol. 85. -P. 2273-2286.
  • Na S., Sun Z., Meininger G.A., Humphrey J.D. On atomic force microscopy and the constitutive behavior of living cells//Biomechan. Model. Mechanobiol. -2004. -Vol. 3. -P. 75-84.
  • Netti P.A., Baxter L.T., Boucher Y., Skalak R., Jain R.K. Macro-and microscopic fluid transport in living tissues: application to solid tumors//AIChE J. -1997. -Vol. 43. -P. 818-834.
  • Northen M.T., Turner K.L. Meso-scale adhesion testing of integrated micro-and nano-scale structures//Sensors and Actuators A. -2006. -Vol. 130-131. -P. 583-587.
  • Norwood W.I. Hypoplastic left heart syndrome//The Annals of Thoracic Surgery. -1991. -Vol. 52. -P. 688-695.
  • Nosonovsky M., Bhushan B. Multiscale friction mechanisms and hierarchical surfaces in nano-and bio-tribology//Materials Science and Engineering R. -2007. -Vol. 58. -P. 162-193.
  • Panovska J., Byrne H.M., Maini P.K. Mathematical modelling of vascular tumor growth and implications for therapy//Modeling and Simulation in Science, Engineering and Technology. -2007. -Vol. 1, Part IV. -P. 205-216.
  • Preziosi L., Tosin A. Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications//J. Math. Biol. -2009. -Vol. 58. -P. 625-656.
  • Porter D. Pragmatic multiscale modelling of bone as a natural hybrid nanocomposite//Materials Science and Engineering A. -2004. -Vol. 365. -P. 38-45.
  • Quaranta V., Weaver A.M., Cummings P. T., Anderson A.R.A. Mathematical modeling of cancer: the future of prognosis and treatment//Clinica Chimica Acta. -2005. -Vol. 357. -P. 173-179.
  • Ramis-Conde I., Chaplain M.A.J., Anderson A.R.A. Mathematical modeling of cancer cell invasion of tissue//Mathematical and Computer Modelling. -2008. -Vol. 47. -P. 533-545.
  • Sander E.A., Shimko D. A., Dee K. C., Nauman E. A. Examination of continuum and micro-structural properties of human vertebral cancellous bone using combined cellular solid models//Biomechan. Model. Mechanobiol. -2003. -Vol. 2. -P. 97-107.
  • Sano S., Ishino K., Kawada M., Arai S., Kasahara S., Asai T., Masuda Z., Takeuchi M., Ohtsuki S. Right ventricle pulmonary artery shunt in first-stage palliation of hypoplastic left heart syndrome//Journal of Thoracic and Cardiovascular Surgery. -2003. -Vol. 126. -P. 504-509.
  • Sato H., Suzuki M. Deformability and viability of tumor cells by transcapillary passage, with reference to organ affinity of metastasis in cancer//Fundamental aspects of metastasis. -Amsterdam: North-Holland Publishing Company, 1976.
  • Shipley R., Chapman S.J. Multiscale modelling of fluid and drug transport in vascular tumours//Bulletin of Mathematical Biology. -2010. -Vol. 25. -P. 32-55.
  • Silberschmidt V.V. Account for random microstructure in multiscale models//Multiscale Modeling and Simulation of Composite Materials and Structures, 2008. -Springer. -P. 1-35.
  • Sole R.V., Garcia I.G., Costa J. Spatial dinamics in cancer//International Topics in Biomedical Engineering, 2006. -Springer. -P. 557-572.
  • Speirs D.C.D., de Souza Neto E.A., Peric D. An approach to the mechanical constitutive modelling of arterial tissue based on homogenization and optimization//Journal of Biomechanics. -2008. -Vol. 41. -P. 2673-2680.
  • Stamenovic D., Ingber D.E. Models of cytoskeletal mechanics of adherent cells//Biomechan. Model. Mechanobiol. -2002. -Vol. 1. -P. 95-108.
  • Stamper I.J., Byrne H.M., Owen M.R., Maini P.K. Modelling the role of angiogenesis and vasculogenesis in solid tumour growth//Bulletin of Mathematical Biology.-2007. -Vol. 69. -P. 2737-2772.
  • Stylianopoulos T. et al. Volume-averaging theory for the study of the mechanics of collagen networks//Computer Methods in Applied Mechanics and Engineering. -2007. -P. 2981-2990.
  • Suresh S. Biomechanics and biophysics of cancer cells//Acta Materialia. -2007. -Vol. 55. -P. 3989-4014.
  • Suresh S. Connections between single-cell biomechanics and human disease states: gastrointestinal cancer and malaria//Acta Biomaterialia. -2005. -Vol. 1. -P. 15-30.
  • Tao Y., Guo Q. The competitive dynamics between tumor cells, a replication-competent virus and an immune response//Journal Math. Biol. -2005. -Vol. 51. -P. 37-74.
  • Tao Y., Guo Q. Simulation of a model of tumors with virus-therapy//International Series of Numerical Mathematics. -2006. -Vol. 154. -P. 435-444.
  • Taylor C.A., Humphrey J.D. Open problems in computational vascular biomechanics: hemodynamics and arterial wall mechanics//Comput. Methods Appl. Mech. Engrg. -2009. -Vol. 198. -P. 3514-3523.
  • Tzvetkova-Chevolleau T., Stephanou A., Fuard D., Ohayon J., Schiavone P., Tracqui P. The motility of normal and cancer cells in response to the combined influence of the substrate rigidity and anisotropic microstructure//Biomaterials. -2008. -Vol. 29. -P. 1541-1551. URL: www.biochemistry.ru URL: www.rbk-expert. ural. ru
  • Van Vliet K.J., Bao G., Suresh S. The biomechanics toolbox: experimental approaches for living cells and biomolecules//Acta Materialia. -2003. -Vol. 51. -P. 5881-5905.
  • Wang J.H.-C., Lin J.-S. Cell traction force and measurement methods//Biomechan. Model. Mechanobiol. -2007. -Vol. 6. -P. 361-371.
  • Wang J.H.-C., Thampatty B.P. An introductory review of cell mechanobiology//Biomechan. Model. Mechanobiol. -2006. -Vol. 5. -P. 1-16.
  • Ward J.P., King J.R. Mathematical modelling of drug transport in tumor multicell spheroids and monolayer cultures//Math. Bioscience. -2003. -Vol. 181. -P. 177-207.
  • Ward K.A., Li W.I., Zimmer S., Davis T. Viscoelastic properties of transformed cells: role in tumor cell progression and metastasis formation//Biorheology. -1991. -Vol. 28. -P. 301-313.
  • Wu J.T. Modeling and analysis of a virus that replicates selectively in tumor cells//Bulletin of Mathematical Biology. -2001. -Vol. 63. -P. 731-768.
  • Wu J.T., Kirn D.H., Wein L.M. Analysis of a three-way race between tumor growth, a replication-competent virus and an immune response//Bulletin of Mathematical Biology. -2004. -Vol. 66. -P. 605-625.
  • Yao H., Gao H. Mechanics of robust and releasable adhesion in biology: bottom-up designed hierarchical structures of gecko//Journal of the Mechanics and Physics of Solids. -2006. -Vol. 54. -P. 1120-1146.
  • Yao W., Gu L., Sun D., Ka W., Wen Z., Chien S. Wild type p53 gene causes reorganization of cytoskeleton and therefore the impaired deformability and difficult migration of murine erythroleukemia cells//Cell Motil. Cytoskeleton. -2003. -Vol. 56. -P. 1-12.
  • You S.T., Qian G. A mathematical model of combined therapies against cancer using viruses and inhibitors//Science in China. Series A: Mathematics. -2008. -Vol. 51. -P. 2315-2329.
  • Zhang G., Long M., Wu Z., Yu W. Mechanical properties of hepatocellular carcinoma cells//World Journal of Gastroenterology. -2002. -Vol. 8. -P. 243-249.
  • Zhang L., Wang Z., Sagotsky J. A., Deisboeck T.S. Multiscale agent-based cancer modeling//Journal Math. Biol. -2009. -Vol. 58. -P. 545-559.
Еще
Статья научная