1. In an implantable device (see schematic below) envisioned for use in the treatment of diabetes, therapeutic cells (e.g., insulin producing B cells found in the islets of Langerhans) are sandwiched between two permselective membranes, i.e., porous membranes that allow for the transport of nutrients to the cells, but not the components of the host immune system. The device is vascularized by the host. The following data are given: • Partial pressure of oxygen (species A) at the interface between the membrane and the vascularized tissue region = 68 mm of Hg ▪ Metabolic O₂ consumption rate by the cells, R = 25.9 μM/s = 25.9 μmol/(liters) Half thickness of the cell layer, h = 100 μm, void fraction of the cell layer, & = 0.80 . • Effective diffusion coefficient of oxygen through the cell layer, D = 1.5 x 10³ cm²/s • Membrane permeability for oxygen, k, = 10² cm/s Henry's law constant for oxygen solubility in the membrane, H=1.35 µM/mm Hg. a. Identify the engineering problem. b. Derive an expression for the oxygen concentration profile within the cell layer. c. Plot C, vs. z within the cell layer. d. Based on your understanding gained from the article by Pedraza et al. (PNAS, 109 (11): 4245- 4250 (2012)), assess the adequacy of the design to prevent hypoxia. Symmetry line z=0 100 µm C₁=7 z=h+ CHP₁ -B Cells →→→Membrane Vascularized region

Human Physiology: From Cells to Systems (MindTap Course List)

9th Edition

ISBN:9781285866932

Author:Lauralee Sherwood

Publisher:Lauralee Sherwood

Chapter12: Body Defenses

Section: Chapter Questions

Problem 1ACR

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$1. In an implantable device (see schematic below) envisioned for use in the treatment of diabetes, therapeutic cells (e.g., insulin producing B cells found in the islets of Langerhans) are sandwiched between two permselective membranes, i.e., porous membranes that allow for the transport of nutrients to the cells, but not the components of the host immune system. The device is vascularized by the host. The following data are given: ■ Partial pressure of oxygen (species A) at the interface between the membrane and the vascularized tissue region = 68 mm of Hg Metabolic O₂ consumption rate by the cells, R = 25.9 μM/s = 25.9 μmol/(liters) • • Half thickness of the cell layer, h = 100 μm, void fraction of the cell layer, & = 0.80 • Effective diffusion coefficient of oxygen through the cell layer, De = 1.5 x 105 cm²/s . • Membrane permeability for oxygen, k, = 10² cm/s ▪ Henry's law constant for oxygen solubility in the membrane, H = 1.35 μM/mm Hg. a. Identify the engineering problem. b. Derive an expression for the oxygen concentration profile within the cell layer. c. Plot C₁ vs. z within the cell layer. d. Based on your understanding gained from the article by Pedraza et al. (PNAS, 109 (11): 4245- 4250 (2012)), assess the adequacy of the design to prevent hypoxia. Symmetry line z = 0 + 100 μm CAN=? z=h+ ConHpre -ß Cells Membrane Vascularized region$

Transcribed Image Text:1. In an implantable device (see schematic below) envisioned for use in the treatment of diabetes, therapeutic cells (e.g., insulin producing B cells found in the islets of Langerhans) are sandwiched between two permselective membranes, i.e., porous membranes that allow for the transport of nutrients to the cells, but not the components of the host immune system. The device is vascularized by the host. The following data are given: ■ Partial pressure of oxygen (species A) at the interface between the membrane and the vascularized tissue region = 68 mm of Hg Metabolic O₂ consumption rate by the cells, R = 25.9 μM/s = 25.9 μmol/(liters) • • Half thickness of the cell layer, h = 100 μm, void fraction of the cell layer, & = 0.80 • Effective diffusion coefficient of oxygen through the cell layer, De = 1.5 x 105 cm²/s . • Membrane permeability for oxygen, k, = 10² cm/s ▪ Henry's law constant for oxygen solubility in the membrane, H = 1.35 μM/mm Hg. a. Identify the engineering problem. b. Derive an expression for the oxygen concentration profile within the cell layer. c. Plot C₁ vs. z within the cell layer. d. Based on your understanding gained from the article by Pedraza et al. (PNAS, 109 (11): 4245- 4250 (2012)), assess the adequacy of the design to prevent hypoxia. Symmetry line z = 0 + 100 μm CAN=? z=h+ ConHpre -ß Cells Membrane Vascularized region

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