Fa1 - BIEN 130 Bioinstrumentation F June 8, 2009 _/100...

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BIEN 130 Bioinstrumentation F June 8, 2009 _______/100 Name: _____________________________________ Score: _______/30.0
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1. a. Derive the complex transfer function for this circuit. (Hint: break the circuit down into smaller components) 11 1 1 1 1 1 in C VR R j R C Z j R C R jC ω == = ++ + 00 VV +− =⇒ ≈ 2 21 3 1 3 0 V VI RV I R −= = = 24 3423 out out R R =− 4 2 1 3 2 1 1 out out in in R R jRC V V R R j L j R C ωω ⎛⎞ ⎜⎟ + + ⎝⎠ b. What is the phase difference between the input and output? () ( ) ( ) ( ) ( ) ( ) 124 32 1 2 1 1 2 12 2 1 22 2 2 3 1 1 1 out in V RRRC j R j L j R C jR jL R R jL R jL jRC j j RRC R RLC j L R RLR C RR L −−+ + + −+ + ( ) 2 2 1 2 2 1 1 RRC L j R RC + 2 Im tan tan Re R φ −− + in V 1 R 2 R out V 3 R 4 R C L 0 I + 1 f I I = − 2 2 L R Z Rj L 0 I 4 4 0 out out f f V R V I R = =
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2. You are given the task of making an artificial arm (illustrated below) made with as much biological tissue as possible (as opposed to purely mechanical parts). Squid giant axons are used as the nerves in the device. Assume the nerves has a threshold potential of -40 mV, and all normal conditions (below) apply unless otherwise indicated. 26 @ 298 RT mV T K F == : : 1.00 : 0.04: 0.45 KN aC l PP P = at rest : : 1.00 : 20.0: 0.45 l = at peak 400 50 52 20 440 560 Ion K Na Cl Cytoplasm mM mM mM Extracellular mM mM mM ++ a. Electrodes placed on the skin will read a differential measurement in response to action potential propagation that is proportional to the difference between a nerve’s resting membrane potential and that at the peak of depolarization. In other words, if hypothetical nerve 1 has a resting membrane potential of -60 mV and a peak depolarization of 40 mV, and hypothetical nerve 2 has values of -40 mV and 40 mV, a pair of electrodes around nerve 1 will read 1.25 times as much as a pair of electrodes around nerve 2 (assuming everything else is comparable). If 12 8 EE Vm V = when the nerve fires under normal conditions, what will the reading be if a chemical that blocks half of all Na-channels is applied? The GHK equation is ln a C l oo i m a C l ii o PK P N a PC l RT V F a l ⎤⎡ ⎦⎣ = . Under normal conditions, the resting and peak membrane potentials are given by () ( ) ( ) () ( ) , 1.0 20 0.04 440 0.45 52 26ln 61.6 1.0 400 0.04 50 0.45 560 mres t V ( ) ( ) ( ) , 1.0 20 20.0 440 0.45 52 43.7 1.0 400 20.0 50 0.45 560 mp ea k V ,, 105.3 m peak m rest VV m V −= When half the Na-channels are blocked, the permeability of Na will be cut in half. The
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This note was uploaded on 02/17/2010 for the course BIEN 130 taught by Professor Park during the Spring '10 term at UC Riverside.

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Fa1 - BIEN 130 Bioinstrumentation F June 8, 2009 _/100...

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