Exam2_FormulaSheet

# Exam2_FormulaSheet - of x from its equilibrium position u x...

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Equation list for BIOE 398BS Spring 2008: Exam 2 Bioengineering Department, University of Illinois at Urbana-Champaign. April 9, 2008 RESPIRATION Law of Laplace for spherical alveolus, radius R P = 2 T R Alveolar Pressure Relationship P alv = P el + P pl Ideal Gas Law, P is pressure, V is volume, n is number of molecules of gas, k is Boltzmann’s constant, T is absolute temperature, c A is concentration in molecules per volume, ˆ c A is concentration in moles/volume, and R is the gas constant. PV = nkT P A = kTc A P A = RT ˆ c A k = 1 . 381 × 10 - 23 JK - 1 R = 8 . 314 JK - 1 mol - 1 Simple solution, where σ A is the solubility factor of gas A . c A = σ A P A Other equations from respiratory simulation, simple solution r = V A Q C A = rc I + c v r + σkT c a = σkT rc I + c v r + σkT f = ( P I - P v ) r r + σkT f = σ ( P I - P v ) Q 0 E E = 1 Q 0 X i Q i r i r i + σkT Respiratory simulation, non-simple solution rc I + c v = c a + rH ( c a ) kT

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f = X i Q i ( c a ( r i ) - c v ) H ( c ) = P * ± c c * - c ² 1 / 3 P * = 25 mmHg M = N X i =1 ( V A ) i ( c I - ( c A ) i ) = N X i =1 Q i (( c a ) i - c v ) MUSCLE Hill Force-velocity curve V = b P 0 - P P + a Cross-bridge cycle model with n 0 as number of crossbridges in a half- sarcomere, p ( x ) the force on a thin ﬁlament due to a crossbridge displacement
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Unformatted text preview: of x from its equilibrium position, u ( x ) the population distrubution function for crossbridge displacements from equilibrium, v is the velocity of shortening of a half-sarcomere, V is the macroscopic velocity of shortening of the muscle, N is the number of sarcomeres along the length of the muscle, and P is the force at the end of the muscle. U = Z ∞-∞ u ( x ) dx < 1 P = n Z ∞-∞ p ( x ) u ( x ) dx v = V 2 N αn (1-U ) = βn Z A x u ( x ) dx + vn u ( x ) v du dx = βu u ( x ) = αβ e β ( x-A v ) v ( α + β ) P = αβ v ( α + β ) Z A-∞ n p ( x ) e β ( x-A v ) dx p ( x ) = p 1 ( e γx-1 ) P = ± αn p 1 α + β ² ( e γA-1 )-( γv β ) 1 + γv β P = n X i =1 p ( x ( i ))...
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Exam2_FormulaSheet - of x from its equilibrium position u x...

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