Bridging the Gap between mesoscopic and macroscopic models: the case of multicellular tumor spheroids.

Multicellular tumor spheroids are valuable experimental tools in cancer research. By introducing an intermediate model, we have been able to successfully relate mesoscopic and macroscopic descriptions of spheroid growth. Since these descriptions stem from completely different roots (cell dynamics, and energy conservation and scaling arguments, respectively), their consistency validates both approaches and allows us to establish a direct correspondence between parameters characterizing processes occurring at different scales. Our approach may find applications as an example of bridging the gap between models at different scale levels in other contexts.

[1]  A universal scaling relation in high-temperature superconductors , 2004, Nature.

[2]  Mike Martin.  Researchers suggest that universal 'law' governs tumor growth. , 2003, Journal of the National Cancer Institute.

[3]  Paolo A. Netti,et al.  Solid stress inhibits the growth of multicellular tumor spheroids , 1997, Nature Biotechnology.

[4]  D Liberati,et al.  Forecasting the growth of multicell tumour spheroids: implications for the dynamic growth of solid tumours , 2000, Cell proliferation.

[5]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[6]  J. Freyer,et al.  Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply. , 1986, Cancer research.

[7]  Pier Paolo Delsanto,et al.  On the universality of nonclassical nonlinear phenomena and their classification , 2004 .

[8]  J P Freyer,et al.  Proliferative and clonogenic heterogeneity of cells from EMT6/Ro multicellular spheroids induced by the glucose and oxygen supply. , 1986, Cancer research.

[9]  Pier Paolo Delsanto,et al.  Nutrient competition as a determinant for cancer growth , 1999 .

[10]  James H. Brown,et al.  The fourth dimension of life: fractal geometry and allometric scaling of organisms. , 1999, Science.

[11]  J. Weitz,et al.  Re-examination of the "3/4-law" of metabolism. , 2000, Journal of theoretical biology.

[12]  Pier Paolo Delsanto,et al.  Growth model for multicellular tumor spheroids , 2003, physics/0307136.

[13]  Geoffrey B. West,et al.  Life's Universal Scaling Laws , 2004 .

[14]  W. Mueller‐Klieser.  Tumor biology and experimental therapeutics. , 2000, Critical reviews in oncology/hematology.

[15]  Pier Paolo Delsanto,et al.  Modeling nonclassical nonlinearity, conditioning, and slow dynamics effects in mesoscopic elastic materials , 2003 .

[16]  Alberto Carpinteri,et al.  One-, two- and three-dimensional universal laws for fragmentation due to impact and explosion , 2002 .

[17]  James H. Brown,et al.  A general model for ontogenetic growth , 2001, Nature.

[18]  M Scalerandi,et al.  Diffusion with evolving sources and competing sinks: development of angiogenesis. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  M Scalerandi,et al.  Inhibition of vascularization in tumor growth. , 2002, Physical review letters.

[20]  Pier Paolo Delsanto,et al.  Does tumor growth follow a "universal law"? , 2003, Journal of theoretical biology.

[21]  R. S. Schechter,et al.  Real-Time Parallel Computation and Visualization of Ultrasonic Pulses in Solids , 1994, Science.

[22]  Raul K. Suarez,et al.  Allometric cascade as a unifying principle of body mass effects on metabolism , 2002, Nature.

[23]  L. Fan,et al.  Modeling growth of a heterogeneous tumor. , 2003, Journal of theoretical biology.