Multiscale cancer modeling: In the line of fast simulation and chemotherapy. (English) Zbl 1165.92307
Summary: Although multiscale cancer modeling has a realistic view in the process of tumor growth, its numerical algorithm is time consuming. Therefore, it is problematic to run and to find the best treatment plan for chemotherapy, even in case of a small size of tissue. Using an artificial neural network, this paper simulates the multiscale cancer model faster than its numerical algorithm. In order to find the best treatment plan, it suggests applying a simpler avascular model called Gompertz. By using these proposed methods, multiscale cancer modeling may be extendable to chemotherapy for a realistic size of tissue.In order to simulate the multiscale model, a hierarchical neural network, called nested hierarchical self organizing map (NHSOM) is used.
The basis of the NHSOM is an enhanced version of SOM, with an adaptive vigilance parameter. The corresponding parameters and the overall bottom-up design guarantee the quality of clustering, and the embedded top-down architecture reduces the computational complexity. Although by applying NHSOM, the process of simulation runs faster compared with that of the numerical algorithm, it is not possible to check a simple search space. As a result, a set containing the best treatment plans of a simpler model (Gompertz) is used.
Additionally, it is assumed that the distribution of drugs in the vessels has a linear relation with the blood flow rate. The technical advantage of this assumption is that by using a simple linear relation, a given diffusion of a drug dosage may be scaled to the desired one. By extracting a proper feature vector from the multiscale model and using NHSOM, applying the scaled-best treatment plan of the Gompertz model is done for a small size of tissue. In addition, simulating the effect of stress reduction on normal tissue after chemotherapy is another advantage of using NHSOM, which is a kind of “emergent”.
The basis of the NHSOM is an enhanced version of SOM, with an adaptive vigilance parameter. The corresponding parameters and the overall bottom-up design guarantee the quality of clustering, and the embedded top-down architecture reduces the computational complexity. Although by applying NHSOM, the process of simulation runs faster compared with that of the numerical algorithm, it is not possible to check a simple search space. As a result, a set containing the best treatment plans of a simpler model (Gompertz) is used.
Additionally, it is assumed that the distribution of drugs in the vessels has a linear relation with the blood flow rate. The technical advantage of this assumption is that by using a simple linear relation, a given diffusion of a drug dosage may be scaled to the desired one. By extracting a proper feature vector from the multiscale model and using NHSOM, applying the scaled-best treatment plan of the Gompertz model is done for a small size of tissue. In addition, simulating the effect of stress reduction on normal tissue after chemotherapy is another advantage of using NHSOM, which is a kind of “emergent”.
MSC:
| 92C50 | Medical applications (general) |
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 92-08 | Computational methods for problems pertaining to biology |
References:
| [1] | Haga, E., Computer Techniques In Biomedicine And Medicine: Simulation And Modeling, Health Care, And Image Processing (1973), Auerbach Publishers |
| [2] | Hoppensteadt, F. C.; Peskin, C. S., Modeling and Simulation in Medicine and the Life Sciences (2002), Springer · Zbl 1013.92001 |
| [3] | Cotin, S.; Metaxas, D. N., Medical Simulation: International Symposium, ISMS 2004, Cambridge, MA, USA, June 2004, Proceedings (2004), Springer |
| [4] | Preziosi, L., (Cancer Modelling and Simulation. Cancer Modelling and Simulation, Mathematical and Computational Biology, vol. 3 (2003), CRC Press) · Zbl 1039.92022 |
| [5] | Alarcon, T.; Byrne, H. M.; Maini, P. K., A cellular automaton model for tumour growth in inhomogeneous environment, Journal of Theoretical Biology, 225, 257-274 (2003) · Zbl 1464.92060 |
| [6] | Alarcon, T.; Byrne, H. M.; Maini, P. K., A multiple scalel model for tumor growth, Multiscale Modeling Simulation, 3, 2, 440-475 (2005) · Zbl 1107.92019 |
| [7] | Byrne, H. M.; Owen, M. R., Modelling the response of vascular tumors to chemotherapy: A multiscale approach, Mathematical Models and Methods in Applied Sciences, 16, 7S, 1219-1241 (2006) · Zbl 1094.92038 |
| [8] | Alarcon, T.; Byrne, H. M.; Maini, P. K., A mathematical model of the effects of hypoxia on the cell-cycle of normal and cancer cells, Journal of Theoretical Biology, 229, 395-411 (2004) · Zbl 1440.92011 |
| [9] | Alarcon, T.; Byrne, H. M.; Maini, P. K., Towards whole-organ modelling of tumour growth, Progress in Biophysics & Molecular Biology, 85, 451-472 (2004) |
| [10] | Byrne, H. M.; Alarcon, T.; Owen, M. R.; Webb, S. D.; Maini, P. K., Modelling aspects of cancer dynamics: A review, Philosophical Transactions of the Royal Society of London, Series A, 364, 1563-1578 (2006) |
| [11] | Marchiniak-Cozchra, A.; Kimmel, M., Modelling of early lung cancer progression: Infuence of growth factor production and cooperation between partially transformed cells, Mathematical Models & Methods in Applied Sciences, 17, 1693-1720 (2007) · Zbl 1135.92019 |
| [12] | Kim, Y.; Stolarska, M. A.; Othmer, H. G., A hybrid model for tumor spheroid growth in vitro I: Theoretical development and early results, Mathematical Models & Methods in Applied Sciences, 17, 1773-1798 (2007) · Zbl 1135.92016 |
| [13] | Ribba, B.; Marron, K.; Agur, Z.; Alarcon, T.; Maini, P. K., Amathematical model of Doxorubicin treatment efficacy for non-Hodgkin’s lymphoma: Investigation of the current protocol through theoretical modeling results, Bulletin of Mathematical Biology, 67, 79-99 (2005) · Zbl 1334.92207 |
| [14] | Day, R. S., Challenges of biological realism and validation in simulation-based medical education, Artificial Intelligence in Medicine, 38, 47-66 (2006) |
| [15] | Bellomo, N.; Li, N. K.; Maini, P. K., On the foundations of cancer modelling: Selected topics, speculations, and perspectives, Mathematical Models & Methods in Applied Sciences, 18, 593-646 (2008) · Zbl 1151.92014 |
| [16] | (Mollica, F.; Preziosi, L.; Rajagopal, K. R., Modelling Biological Tissues (2006), Birkäuser: Birkäuser Boston) |
| [17] | Martin, R. B., Optimal control drug scheduling of cancer chemotherapy, Automatica, 6, 1113-1123 (1992) |
| [18] | E. Bavafa, M.J. Yazdanpanah, B. Kalaghchi, Chemotherapy using linear analysis and swarm intelligence, in: International Federation of Automatic Control (IFAC), 2008, pp. 5233-5238; E. Bavafa, M.J. Yazdanpanah, B. Kalaghchi, Chemotherapy using linear analysis and swarm intelligence, in: International Federation of Automatic Control (IFAC), 2008, pp. 5233-5238 |
| [19] | Swiernlak, A.; Ledzewicz, U.; Schättler, H., Optimal control for a class of compartmental models in cancer chemotherapy, International Journal on Applied Mathematics and Computer Science, 13, 3, 357-368 (2003) · Zbl 1052.92032 |
| [20] | Kimmel, M.; Swierniak, A., Using control theory to make cancer chemotherapy beneficial from phase dependence and resistant to drug resistance, Archives of Control Science, 14, 2, 105-145 (2004) · Zbl 1151.93310 |
| [21] | Mantzaris, N. V.; Webb, S.; Othmer, H. G., Mathematical modeling of tumor-induced angiogenesis, Journal of Mathematical Biology, 233-257 (2004) · Zbl 1109.92020 |
| [22] | Levine, H. A.; Pamuk, S.; Sleeman, B.; Nilsen-Hamilton, M., Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma, Bulletin of Mathematical Biology, 63, 801-863 (2001) · Zbl 1323.92029 |
| [23] | Sleeman, B. D.; Wallis, I. P., Tumour induced angiogenesis as a reinforced random walk: Modelling capillary network formation without endothelial cell proliferation, Mathematical and Computer Modelling, 36, 339-358 (2002) · Zbl 1021.92016 |
| [24] | Hillen, T.; Othmer, H., The diffusion limit of transport equations derived from velocity jump processes, SIAM Journal on Applied Mathematics, 61, 751-775 (2000) · Zbl 1002.35120 |
| [25] | Dolak, Y.; Schmeiser, C., Kinetic models for chemotaxis: Hydrodynamic limits and spatio temporal mechanisms, Journal of Mathematical Biology, 51, 595-615 (2005) · Zbl 1077.92003 |
| [26] | Chalub, F. A.; Dolak-Struss, Y.; Markowich, P.; Oeltz, D.; Schmeiser, C.; Soref, A., Model hierarchies for cell aggregation by chemotaxis, Mathematical Models & Methods in Applied Sciences, 16, 1173-1198 (2006) · Zbl 1094.92009 |
| [27] | Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J., Multicellular growing systems: Hyperbolic limits towards macroscopic description, Mathematical Models & Methods in Applied Sciences, 17, 1675-1693 (2007) · Zbl 1135.92009 |
| [28] | DeVita, V. T.; Hellman, S.; Rosenberg, S., (Williams, Lippincott, Cancer: Principles and Practice of Oncology (2005)) |
| [29] | Folkman, J., Angiogenesis and apoptosis, Seminars in Cancer Biology, 13, 159-167 (2003) |
| [30] | Franks, L. M.; Teich, N. M., Introduction to the Cellular and Molecular Biology of Cancer (1997), OXFORD |
| [31] | Zurada, J., Introduction to Artificial Neural Systems (1992), West Publishing Company |
| [32] | E. Bavafaye-Haghighi (Bavafa), Applying Intelligent Methods for Chemotherapy of Multiscale Cancer Model, M.Sc. Thesis, School of Electrical and Computer Engineering, University of Tehran, 2008; E. Bavafaye-Haghighi (Bavafa), Applying Intelligent Methods for Chemotherapy of Multiscale Cancer Model, M.Sc. Thesis, School of Electrical and Computer Engineering, University of Tehran, 2008 |
| [33] | E. Bavafa, M.J. Yazdanpanah, Image compression using an enhanced self organizing map algorithm with vigilance parameter, in: International Joint Conference on Neural Networks, 2006, pp. 1923-1928; E. Bavafa, M.J. Yazdanpanah, Image compression using an enhanced self organizing map algorithm with vigilance parameter, in: International Joint Conference on Neural Networks, 2006, pp. 1923-1928 |
| [34] | L. Cinque, G.L. Foresti, A. Gumina, S. Levialdi, A modified fuzzy art for image segmentation, in: 11th International Conference on Image Analysis and Processing, ICIAP’01, 2001, pp. 102-17; L. Cinque, G.L. Foresti, A. Gumina, S. Levialdi, A modified fuzzy art for image segmentation, in: 11th International Conference on Image Analysis and Processing, ICIAP’01, 2001, pp. 102-17 |
| [35] | Theodoridis, S.; Koutroumbas, K., Pattern Recognition (2003), Elsevier Academic Press |
| [36] | Abe, Sh., Pattern Classification, Neuro-Fuzzy Methods, and their Comparison (2001), Springer · Zbl 0978.68114 |
| [37] | J.J. Aleshunas, D.C.St. Clair, W.E. Bond, Classification characteristics of SOM and ART2, in: Proceedings of the ACM Symposium on Applied Computing, 1994, pp. 297-302; J.J. Aleshunas, D.C.St. Clair, W.E. Bond, Classification characteristics of SOM and ART2, in: Proceedings of the ACM Symposium on Applied Computing, 1994, pp. 297-302 |
| [38] | Tagliaferri, R.; Capuano, N.; Gargiulo, G., Automated labeling for unsupervised neural networks: A hierarchical approach, IEEE Transactions on Neural Networks, 10, 199-203 (1999) |
| [39] | Ontrup, J.; Ritter, H., Large-scale data exploration with the hierarchically growing hyperbolic SOM, Neural Networks, 19, 751-761 (2006) · Zbl 1102.68577 |
| [40] | Ditenbach, M.; Rauber, A.; Merkel, D., Uncovering hierarchical structure in data using the growing hierarchical self-organizing map, Neurocomputing, 48, 199-216 (2002) · Zbl 1006.68798 |
| [41] | Gillman, A. G.; Goodman, L., The Pharmacological Basis of Therapeutics (2001), McGraw Hill |
| [43] | Carpenter, G. A.; Grossberg, S., The art of adaptive pattern recognizing by a self organizing neural network, Computer, 21, 3, 77-88 (1988) |
| [44] | T. Kohonen, Things you haven’t heard about the self-organizing map, in: IEEE International Conference on Neural Networks, 1993, pp. 1147-1156; T. Kohonen, Things you haven’t heard about the self-organizing map, in: IEEE International Conference on Neural Networks, 1993, pp. 1147-1156 |
| [45] | Kohonen, T., Comparisons of som point densities based on different criteri, Neural Computation, 11, 2081-2095 (1999) |
| [46] | wiederhold, Gio, File Organization for Database Design (1987), McGraw-Hill · Zbl 0497.68060 |
| [47] | Mataric, M. J., Behavior-based robotics as a tool for synthesis of artificial behavior and analysis of natural behavior, Trends in Cognitive Sciences, 2, 3, 82-87 (1998) |
| [48] | Steels, Luc, Towards a theory of emergent functionality, (From Animals to Animats (Proceedings of the First International Conference on Simulation of Adaptive Behaviour) (1990), Bradford Books, MIT Press), 451-461 |
| [49] | Steels, L., Emergent functionality in robotic agents through on-line evolution, (Proceedings of Artificial life IV (1994), MIT Press: MIT Press Cambridge), 8-14 |
| [50] | Shehory, O.; Kraus, S.; Yadgar, O., Emergent cooperative goal-satisfaction in large scale automated-agent systems, Artificial Intelligence, 110, 1, 1-55 (1999) · Zbl 1046.68637 |
| [51] | Bedau, M. A., (Tomberlin, James, Weak Emergence. Weak Emergence, Philosophical Perspectives: Mind, Causation, and World, vol. 11 (1997), Blackwell Publishers), 375-399 |
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