Biomedical Engineering Reference
In-Depth Information
14.4 Summary and Perspectives of Future Research
In this chapter, a numerical study has been made to predict the onset and
evolution of bioconvection in porous media. A Hele-Shaw apparatus has been
used as a model to study bioconvection phenomena in Tetrahymena culture.
Our experiments have reproduced stationary as well as time-varying two-
dimensional bioconvection patterns.
It should be noted that in an experimental monoculture, the growth of
TP is characterized by a logarithmic growth phase, a prestationary growth
phase, and a stationary phase. In the logarithmic phase, which may last from
a few hours to two days depending on inoculums, cell density increases log-
arithmically, the generation time being 3-7 h. In the prestationary phase,
growth decreases for a few generations before entering the last stationary
phase (Sauvant et al. 1999).
If the growth rate is taken into account, there will be a significant effect of
density-dependent growth on pattern formation because the concentration and
the Rayleigh number would both increase. We so far assumed that the coe-
cient of diffusion D c and the swimming speed, V c are independent constants
and there is no interaction between the mobile TP cells. In the case of the
population growth, there should be an important interaction between cells as
density increases and both D c and V c should vary. Some fundamental questions
naturally arise in the study of TP bioconvection with population growth: How
is the dynamics of such populations affected by their motions? What regimes
(stationary, oscillatory or chaotic...)canbeestablished? Similar studies of dif-
fusive instabilities and pattern formation in populations showed that the time
scale of population growth relative to those of convection states are of critical
importance to predict the maintenance of spatial heterogeneity in dynamic
populations (Holmes et al. 1994; Malchow et al. 2001; Okubo and Levin 2002)
and the nonlinear nature of biophysical systems is crucial in understanding
self-organized phenomena over the ecological and evolutionary scales. Our
results suggest that the Rayleigh and the Peclet numbers may be two impor-
tant parameters in this kind of systems. Therefore, further studies at high
Rayleigh and high Peclet numbers are necessary to better understand the
development of time-dependent bioconvection.
It should be noted that the Hele-Shaw model is capable to qualita-
tively represent a system behaving as a two-dimensional porous medium, but
surely with certain limitations. An “exact” analogy of Hele-Shaw with porous
medium is impossible and a Hele-Shaw model can never replace a real porous
medium . Therefore, although the study of gravitactic bioconvection in porous
media might be simulated by a Hele-Shaw apparatus, further studies should
be done in a real porous system. This remains one of the most challenging
di culties because the pattern visualization through a porous medium is not
easy to realize.
 
Search WWH ::




Custom Search