Doctoral Thesis BMED 9000
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This 0 page Class Notes was uploaded by Juliet Ryan on Monday November 2, 2015. The Class Notes belongs to BMED 9000 at Georgia Institute of Technology - Main Campus taught by Andres Garcia in Fall. Since its upload, it has received 14 views. For similar materials see /class/233984/bmed-9000-georgia-institute-of-technology-main-campus in Biomedical Engineering at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
MECHBEBMED 6782 Cellular Engineering Measuring Shear Modulus of RBC Membrane Micropipette Aspiration and Shear Flow Motivation Mechanical forces affect many aspects of cell biology eg Cells deform under mechanical forces Deformability of red blood cells is important to circulation An easiest and most extensively studies example of cell mechanics Scanning Electron Micrograph of a Human Red Blood Cell AEEroaches for a rlng Mechanlcal Propertles of Cells Apply known loree measure deformation 7 Indentation experiment a Micropipette aspiration 7 Flow chamloer 7 Magnetic twisting cytomecry Take advantage ofrandom forces and Brawnian motions 7 Red hlnnd cell membrane flickering 7 Thermal fluctuations of actin filaments and microtuhules Dif culties Small sire and complex geometry Measuring Shear Modulus of RBC Membrane Nnnrunifnrm and time clap Endent stressstrain Reversed Problem Approach Assume a stressscrain relationship with unknown coell icients Solve the hnundary value prololem Fit the solution to the data to test the validity or the model Start over with a new model irthe test result is negative Evaluate the parameter values irthe test result is positive Problem Parameter values mayhe models and techniquedependent Solution Cnn duct separate experiments using distinct techniques 9 D ace 3 SS Mechanical Properties of Human Red Blood Cells Mechanical model for the human red blood cell I A liquid bag enclosed by a membrane I The liquid can be modeled as a Newtonian viscous fluid I The membrane can be modeled as an elastic sheet Mechanical properties of human red blood cells I Membrane shear modulus u 69 pNpm 69 x 10396 Nm I Membrane area modulus K 45 x 105 pNpun 045 Nm I Membrane bending modulus E 44 i 5 kBT I Hemoglobin solution viscosity 6 x 10393 Nsmz Micropipette Aspiration Experiment T T Freebody diagram Model as an Neglect T inlinite sheet constraint or elastic of m y membrane 2H 9 Po RBC T Cl d m W Polar coordinates shape T Force balance SLaW of LaPlacel 170 p 2TmRp l Neglecting friction at the pipette wall RBC membrane Stress Analysis of an Elementary Membrane Segment Rearranging terms d 7 dT 7 T 7 Tyrr Axisymmetric 39rr Integrating Problem T W T floral a T and T are 0 I RP39T 7 Tpdrr iunctions oI r LaPlace law only Ty R ApRPZ Rearranging terms A17 7 211 gm 7 T39Mrr Force balance in the radial direction T dTr and T 7 sindy2Tdr 7 sindl2T dTyr o n l39 T 7 T 0 Force balance in the circumferential direction cosd 2T 4Tdr 7 cosd 2TIr o iTap 0 Area prior to deiormation An oz mapping Area rem ain s constant dun39n deform a on Differentiation JAZl r 12 Zd r Boundary conditions 421 1 Anal sis of Deformation Hemi7spherical cap T A 211 Cylindrical segment Area modulus K 45 x 105 pNum gtgt shear modulusl 679 pNum Consmnt area avquot 2xRP2 23RPL 7R 02 7122 Radial stretch ratio A a 4272 1 RPZr2LRP 7 1 A2 szrL 712 Circular ring 131 R 2LR StressStrain Relation 1 A N 39 quot l TiTM 1 12 W Stresses or r A gt lt r k Stralns or Ta mnX Kai Ma Stretch ratios 1 Shear stresses or strains 3 Area strains 41171 Constant area 411 1 Assume linear elasticity T Tr WV 4 2 1M 4392 Rearrangingternis Environz Tswana A11 2Rp In r Tdrr Sm 2Rplgvquotii12 7 14drr My Layla a 1quot4131 a 21 A We M 7 we Layla 1quot111 llRFHZLRp 1 ln2LRp UR Is the above solution applicable for L lt RP Why or Why not Measurin the BRC Shear Modulus by the Flow Chamber zzzznzzzz 1 quot quot Equilibrium ZdTxy cm 1 v 2y zyTx ZyTx Integrauon lyTxJ 1x rsty EM M dA 37quot an x at mappin mm y w of Deformation An al Anton 302 Am h Rnsinq R eosq 1nRa1 05 n n Rosina Ar Roaeirsinei easel eossh 1 xnR y 9 Mia xnR Rama Constant area sin 1 r 1 xnRa2 2 A An Ro2cosquot1 i xnRo 7 1 m 17 1 m 2H Stretch ratios 15 mm A yyn xquot quotl xquot quot1 Constant area M 1 4 ampquot Expressing y as a function on yam Rosina1 Rosinlcosquot1 xrRowxrdx Stressstrain relation Tx itz 7 Ag Rearranging wankarr a axarm W R 2 05quot1 mm a 1 xrRo 1 a 1 xnRazlmRasincosquot1 xrRo1dxdxr hawk Rallldrdxncos39ll xnRmk 1 xnRa quot 1 xnRo 1