Bioartificial Breast Implant

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Bioartificial breast implant Let us assume to produce a bioartificial breast implant by using expanded autologous fibroblasts. Such implant is uniformly seeded on a porous spherical scaffold (diameter of 4 cm). Calculate the oxygen concentration profile in the cell -populated construct in steady state. Assume a constant cell consumption. Furthermore, assume the oxygen concentration outside the cell construct after being implanted subcutaneously is constant as well. Problem a) Evaluate whether oxygen deficiency conditions occur within the cellularised construct (the conditions of hypoxia is pO 2<20 mmHg). To assess such issue, calculate i) the critical radius below which hypoxia occurs within the construct, and ii) the volume fraction of the cell - populated construct where normoxic conditions occur (pO2>20 mmHg) Data: pO2 outside the cell construct p s=40 mmHg, the oxygen solubility coefficient in the cellularised construct α=1 nmol/cm 3/mmHg, the oxygen diffusion coefficient in the cellularised construct D=1.3•10-5 cm2/s, the oxygen consumption Vm=3•10-12 mol/cm3/s, the cell unpopulated volume fraction of the construct ε=0.3. Problem b) Assume that, to avoid hypoxia, a central, non -cellularized sphere is used, whose radius is equal to the critical radius determined at Problem a. Solve the mass transfer problem again in this new condition. Solution a) Mass conservation equation in the control volume: 0 ≤ r ≤ R. 𝜕𝜕𝜕𝜕 𝜕𝜕𝜕𝜕= 𝐷𝐷𝛻𝛻2𝑐𝑐− 𝑉𝑉+ 𝑃𝑃− (𝒗𝒗⋅∇)𝑐𝑐 By assuming i) stationary conditions, ii) no production, iii) constant consumption, iv) no convection: 𝐷𝐷𝛻𝛻 2𝑐𝑐= 𝑉𝑉(1 − 𝜀𝜀) (1) where 𝜀𝜀 = 0.3 is the cell-unpopulated volume fraction of the construct (no consumption occurs). By assuming a spherical symmetry of the concentration, the mass balance equation results: 𝐷𝐷 [ 1 𝑟𝑟2…