Modeling studies of SSF that illustrate the complexity introduced by attempts to describe the intra-particle phenomena

Georgiou G, Shuler ML (1986) A computer model for the growth and differentiation of a fungal colony on solid substrate. Biotechnol Bioeng 28:405-416 Mitchell DA, Do DD, Greenfield PF, Doelle HW (1991) A semi-mechanistic mathematical model for growth of Rhizopus oligosporus in a model solid-state fermentation system. Biotechnol Bioeng 38:353-362 Rajagopalan S, Modak JM (1995) Evaluation of relative growth limitation due to depletion of glucose and oxygen during fungal growth on a spherical solid particle. Chem Eng Sci 50:803-811

Rajagopalan S, Rockstraw DA, Munson-McGee SH (1997) Modeling substrate particle degradation by Bacillus coagulans biofilm. Bioresource Technol 61:175-183 Rottenbacher L, Schossler M, Bauer W (1987) Modelling a solid-state fluidized bed fermenter for ethanol production with Saccharomyces cerevisiae. Bioprocess Eng 2:25-31

A model that segregates the biomass into several different physiological states Georgiou G, Shuler ML (1986) A computer model for the growth and differentiation of a fungal colony on solid substrate. Biotechnol Bioeng 28:405-416

A review of modeling of intra-particle phenomena in SSF, demonstrating the complexity of the equations involved

Mitchell DA, von Meien OF, Krieger N, Dalsenter FDH (2004) A review of recent developments in modeling of microbial growth kinetics and intraparticle phenomena in solid-state fermentation. Biochem Eng J 17:15-26

Spatial distribution of hyphae in artificial SSF systems and the complexity of trying to describe the extension and branching of individual hyphae Nopharatana M, Mitchell DA, Howes T (2003) Use of confocal microscopy to follow the development of penetrative hyphae during growth of Rhizopus oligosporus in an artificial solid-state fermentation system. Biotechnol Bioeng 81:438-447 Nopharatana M, Mitchell DA, Howes T (2003) Use of confocal scanning laser microscopy to measure the concentrations of aerial and penetrative hyphae during growth of Rhizopus oligosporus on a solid surface. Biotechnol Bioeng 84:71-77 Yang H, Reichl U, King R, Gilles ED (1992) Measurement and simulation of the morphological development of filamentous microorganisms. Biotechnol Bioeng 39:44-48

Schutyser MA, Padding JT, Weber FJ, Briels WJ (2001) Discrete particle simulations predicting mixing behavior of solid substrate particles in a rotating drum fermenter. Biotechnol Bioeng 75:666-675 Schutyser MAI, Briels WJ, Rinzema A, Boom RM (2003) Numerical simulation and PEPT measurements of a 3D conical helical-blade mixer: A high potential solids mixer for solid-state fermentation. Biotechnol Bioeng 84:29-39

Use of numerical methods for solving partial differential equations

Petzold LR, Brenan KE, Campbell SL (1989) Numerical solution of initial-value problems in differential-algebraic equations. Elsevier, New York Villadsen J, Michelsen ML (1978) Solution of differential equation models by polynomial approximation. Prentice Hall, Englewood Cliffs, New Jersey

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