BME 552 HW3 2009 SOLUTION - BME 552 Homework Set 3 Assigned...

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Unformatted text preview: BME 552 Homework Set 3 Assigned Feb 6, 2009 Due Feb 13, 2009 1. Prove that stimulus pulse energy is minimized at chronaxie. The first derivative of U=b2r(1+c/d)2 is minimized at duration d = c (chronaxie) 2. Consider the following strength duration data. A 800 micron diameter electrode is used to apply these pulses. Is the most energy efficient pulse safe with respect to neural damage limits? If not what pulse parameters that are effective also will be considered safe by Shannon’s rule for neural damage. How can you maximize dynamic range of stimulus, assuming linear response characteristics? (added units in solution) Pw (ms) Pa (mA) 0.01 20 0.05 5 0.1 2.6 0.5 0.8 1 0.5 5 0.4 10 0.3 50 0.3 The table below shows the charge at each point, the resultant charge density and the point where Shannon limit (upper limit) still exceeds threshold. Rheobase is 0.3 mA, so chronaxie is the pulse width when threshold is 0.6 mA, which is less than 1 ms. All pulse widths less than 1 ms are safe at threshold, so chronaxie, the most efficient pulse, is safe. Dynamic range is maximized when the largest range of stimuli can be applied between a safe (Shannon limit) and effective (threshold) stimuli. The narrowest pulse uses the least charge, so dynamic range can be maximized by using shorter pulses. shannon limit for qd 158.1139 126.4911 121.6261 79.05694 63.24555 15.81139 10.54093 2.108185 pw 0.01 0.05 0.1 0.5 1 5 10 50 Pa 20 5 2.6 0.8 0.5 0.4 0.3 0.3 Lapicque q qd 24.3 0.2 6.369427 5.1 0.25 7.961783 2.7 0.26 8.280255 0.78 0.4 12.73885 0.54 0.5 15.92357 0.348 2 63.69427 0.324 3 95.5414 0.3048 15 477.707 3. A spinal cord stimulator is being developed that is positioned directly on the dorsal column. The stimulating electrode is 1 mm in diameter (it is a disk). The maximum output specification is 1 uC/ph. Assume an electrochemical limit for platinum of 0.35 mC/cm2. a. What is the neural damage limit for this electrode, assuming Shannon’s model applies? Does the maximum output requirement violate the electrochemical safety limit or the neural damage limit? b. Assume the maximum output specification can be expressed in terms of charge density (this will have the same desired effect on the spinal cord). Given that the total charge will decrease as electrode size decreases, how much will charge/ph and electrode size decrease before the maximum output (expressed in charge density) no longer violates the neural damage limit? a. If Q= 1 uC/ph, then D= 31.6 uC/cm2/ph. If 1 uC is applied via a 1 mm electrode, then D=127 uC/cm2. So the threshold charge density of 127 uC/cm2 violates the neural damage limit, but not the electrochemical safety limit. b. 127 uC/cm2 is required for effective stimulation, so now we simply need to work backwards to find the charge at which this is considered safe, and make sure the electrode is large enough. Q=0.25 uC ‐ > D = 127 uC/cm2. To achieve this D with 0.25 uC, diameter should be 0.5 mm. ...
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