The design of artificial organs for growing transplant able human tissues require that the cell type of

Question:

The design of €œartificial organs€ for growing transplant able human tissues require that the cell type of interest, for example pancreatic cells, be grown and sustained within a three-dimensional array where the cells closely pack together to form a continuous living tissue. Furthermore, engineered systems for maintaining the tissues within the three-dimensional array require that oxygen be delivered to the living tissue for respiration processes, which is a major design challenge. One way to get oxygen to the tissue is by a porous scaffold containing capillary ducts organized into rectangular tissue monolith, as shown in the figure below. Pure oxygen gas flows through the capillary ducts and contacts the tissue, where it dissolves into the tissue by Henry€™s law€”i.e., P_A= H c_A*. Two sides of the monolith are sealed, but the other two sides are composed of a porous mesh like sheath, which contains the tissue, but also exposes it to the surrounding liquid medium, which contains dissolved oxygen of bulk concentration of fixed concentration c_Aˆž. The tissue and the liquid medium surrounding the monolith approximate the physical properties of liquid water. Once dissolved in the tissue, the tissue consumes the dissolved oxygen by a first-order reaction process defined by rate constant k₁. We are interested in predicting the concentration profile of dissolved oxygen within the tissue monolith.

a. Develop the differential model for the concentration profiles of dissolved oxygen (c_A) within quadrant IV of the tissue monolith. Look for symmetry as appropriate. State all reasonable assumptions, and define the system(s), likely source(s), and likely sink(s) for species O₂ (species A) within the tissue monolith.

b. Specify appropriate boundary conditions.

Pressurized Oz gas out O2 gas in See cross section Tissue monolith (side view) Well-mixed liquid medium, cĄ. Sealed Por