Biomedical Engineering Reference
In-Depth Information
The blood perfusion though bone marrow is about 0.08 ml per cc per minute. Cellularity
in marrow is about 500 million cells per cc. Therefore, the cell-specific perfusion rate is
about 2.3 ml/10 million cells/day. Cultures of
mononuclear cell
populations from murine
bone marrow were developed in the mid- to late 1970s. These mouse cultures had long-
term viability, but attempts to use the same culture protocols for human bone marrow
cultures in the early 1980s were largely unsuccessful. The culture protocol called for
medium exchange about once per week.
To perform a dynamic similarity analysis of perfusion rates, or medium exchange rates,
between in vivo and in vitro conditions, the per cell medium exchange rate in culture is
calibrated to that calculated for the preceding in vivo situation. Cell cultures are typically
started with cell densities on the order of a million cells per ml. Therefore, 10 million cells
would be placed in 10 mls of culture medium, which contains about 20 percent serum
(vol/vol). A full daily medium exchange would hence correspond to replacing the serum
at 2 ml/10 million cells/day, which is similar to the number calculated previously.
Experiments using this perfusion rate and the cell densities were performed in the late
1980s and led to the development of prolific cell cultures of human bone marrow. These
cultures were subsequently scaled up to produce a clinically meaningful number of cells
and are currently undergoing clinical trials. Thus, a simple similarity analysis of the in vivo
and in vitro tissue dynamics led to the development of culture protocols that are of clinical
significance. Such conclusions can be derived from tissue spec sheets.
These examples serve to illustrate the type of approximate calculations that assist the
tissue engineering in performing an analysis of a tissue or organ system. Accurate measure-
ments or estimations and well-organized facts (the spec sheets) provide the basic data.
Characteristic time constants, length constants, fluxes, rates, concentrations, and so on can
then be estimated. The relative magnitudes of such characteristics serve as a basis for order
of magnitude judgments, which in turn inform the design of a tissue as well as the process
for fabricating that tissue.
6.3.3 Mass Transfer in 3-D Configurations
An understanding of mass transfer in biological systems is essential in tissue engineering
in order to design and deliver cell therapy products or extracorporeal organs. Although
biological and physiological spec sheets give a global target for mass transfer, the details
of the capillary bed of the smallest physiological units of the tissue are required. Mass trans-
fer depends on the diffusion and convection of nutrients and waste to and from tissue, and
the consumption of nutrients and production of waste by the tissue. Table 6.9 shows typical
convection of blood in the vasculature, and Table 6.12 and Figure 6.29 give the consumption
and diffusion rates of nutrients in the human body. Convection is driven by pressure differ-
ences and dominates in the vasculature, while diffusion is driven by concentration gradi-
ents and dominates in the tissues. Diffusion can be described by Fick's Law, and one can
modify this equation to describe mass transfer in three basic configurations: rectangles,
cylinders, and slabs.
The key to a successful bioreactor design for extracorporeal support or expansion of stem
cells is maintaining adequate mass transfer while at the same time providing a local
