Name: 
Equation: 
Symbols stand for: 
Use/comments 

Renal 




Starling Reabsorption Forces 
NFP = (P_{c}P_{if})(p_{c}p_{if}) Q= k · [(P_{c}P_{if})  (p_{c}p_{if})s] With s (~1) the reflection coefficient of
proteins, and K the hydraulic permeability of the wall 
P_{if} =
interstitial fluid , P_{c} = capillary hydrostatic pressure p_{c} = capillary osmotic pressure p_{if} = interstitial fluid os. Pressure NFP = net
filtration pressure Q = net capillary
filtration rate 
Increased Pc during exercise results in plasma loss to interstitial fluid In glomerulus _{if} is _{bc} and p_{bc} is zero, otherwise the same. 

Glomerular filtration rate 
GFR= K_{f}
· (P_{cap}P_{bc}p_{cap})
As above except:
I = V·R^{1} and R^{1} = Kf And GFR = NFP · K_{f} 
p = colloid osmotic pressure GFR = glomerular
filtration rate K_{f} =
capillary filtration coefficient (= area · hydraulic conductivity) P = hydrostatic
pressure _{cap}capillary, _{bc}bowman’s capsule 
Not exactly true in humans as eqm is not quite reached, but approx is good. ABP increase increases P_{cap} and decreases p_{cap} so increases GFR Blockages ÝPbc à ßGFR ÝBP à thick basement membrane ßK_{f} 

Respiratory and Cardiovascular 




Henry’s Law 
[X] = S_{X} · P_{X} 
[X] = concentration mMoles S_{X} = solubility Kp mM/mmHg P_{X} = partial pressure mmHg 
Kp solubility at 37degrees ~0.03 


Fick Principle F = removal [a][v] 
Net flux = D[X]·A ·d d _{. }where d µ ÖMW^{1}_{} Q = P_{X }· S_{X }· A · d d 
Q = net flux
P_{X} = partial pressure of X S_{X} = solubility coefficient of X A = exchange surface area D = diffusion pathway distance d = diffusion
coefficient of X 
S_{X} · d = k (diffusion constant)
Use to calculate rate of flow of substance down conc. Grad S_{X} in
mmol · l^{1} · mmHg^{1} 


Reynaud’s Number 
Re = r·D·V h 
Re = Reynaud’s number r = density of fluid D = diameter of tube V = velocity of flow h = viscosity of
fluid 
If Re > 2000, turbulence certain If Re < 200, turbulence does not occur 


Law of Laplace 
P µ T (capillaries) R 
P = pressure in tube T = tension in wall of tube r = radius of tube 
T = P_{T} r if not infinitely thin! u (P_{T} = transmural pressure, u = wall thickness) 


Laplace in a sphere 
P = 2T (alveoli) R 
As surface tenstion = 2 p r · T Opposing = p r^{2} · P 
Relevant as surfactant reduces surface T à less P so prevents atelectasis 


Poiselle in glass tubing
(any fluid) 
Flow = DP · p · r^{4} 8 · h · l and Flow = DP R 
Flow = rate of flow of fluid DP = pressure gradient p = 3.14159265358979… r^{4} = radius to 4^{th} power h = viscosity (eta) l = length of tube 
Resistance = DP = 8 · h · l F p · r^{4} Distributing vessels minimise resistance withour creating
turbulence (cf Reynauld). Capillary apparent reduction in viscosity
due to bolus flow 


Flow 
R = A · v 
A = area v = velocity 
Same vol of fluid passes per unit time Smaller tube faster flow 


Bernoulli or Venturi principle 
P + ½ rv^{2} + rgh = c
Pressure, kinetic and potential energy total is always constant 
C = constant P = hydrostatic pressure r = density v = velocity g = 9.8 h = height Respiratory: during snoring small gap high speed. 
Cardiovascular: Kinetic energy rarely significant in the blood, perhaps in pulmonary circulation, during exercise, and at entry to the heart KE helps filling. Pot. energy works against venous return. 


Einstein 
v = Ö [2E/m] Distance = Ö (2
· d · t) therefore t µ d^{2} 
V = diffusion velocity E = kinetic energy m = mass of particle 
a) The heavier the particle, the slower the particle diffuses in air. b) Diffusion only efficient over small d 


Dead space 
V_{D}=V_{T }·(P_{A}CO_{2} – P_{E}CO_{2}) P_{A}CO_{2} 
V_{D} = dead space volume V_{T} = tidal volume P_{A}CO_{2} = alveolar PCO_{2} P_{E}CO_{2} = expired PCO2 
Derived from V_{T} · P_{E}CO_{2} = P_{A}CO_{2} · V_{A} And V_{A} = V_{T} – V_{D} 


Total lung capacity (Bohr equation) 
TLC = – P_{FRC} · DP DV 
TLC = total lung capacity (l) P_{FRC} = pressure after exhaled DP = change in pressure (Pa) DV = change in volume (l) 
Pressures measured at mouth DV change in body box volume FRC = RV + IRV 


Prediction of partial pressures 
P_{A}CO_{2} = k · VCO_{2} V_{A}
P_{A}O_{2} = P_{I}O_{2} – P_{A}CO_{2} +F RQ 
RQ = CO_{2} exhaled/O_{2} taken up (Normally ~ 0.8) A = alveolar I = inspired V = rate of ventillation 
K = a constant F = small correction factor of 13 mmHg 


Transport Factor 
TF = Q . t ·DP
requires endinspiration alveolar gas sample 
TF = transport factor Q = quantity of CO transferred across epitheliunm (alveoli) t = time (minutes) DP = pressure gradient of CO 
Single breath of CO and He, as He does not dissolve dilution measures alveolar volume therefore P_{ACO }(=DP) and Q/tDP can be calculated 


Compliance 
C = DV =
1 . DP elastance 
C = compliance P = pressure, V = volume 
Compliance decreases in fibroses and therefore Ý RV and TLC but ßFVC 


van’t Hoff 
pV=s(nRT) 
p = osmotic pressure (Pa) V = volume (l) s = relative permeability (10) n = amount of
solute (mol) R = molar gas
constant (8.314) T = temperature (K) 
From perfect molar gas equation PV = nRT
1kPa = 10cmH_{2}O = 7mmHg 


HendersonHasselbach 
pH = pK_{a} + log_{10} [A^{}]
[HA] 
pH = log [H+] pK_{a} =
log K_{a} [A^{}] =
base concentration [HA] = acid
concentration 
Blood pH = 6.1 + log [HCO3^{}] [H_{2}CO_{3}]
6.1 composite Pka of both reactions 


Bernuille principle 
E = PE + KE (or Venturi) 
Pressure Energy Kinetic Energy
(½mv^{2}) 
As airway narrows, kinetic energy increases,
pressure drops 


Resistance in parallel 
1 =
1 + 1 + 1 + 1… R_{T} R_{1} R_{2} R_{3} R_{n} 
Total Resistance
of multiple (n) airways or blood vessels 
Small airway disease
local R but cannot detect
total airway R 


D’ Arcy’s
Law (simplified version) 
ABP = CO x. TPR 
ABP = arterial blood pressure CO = cardiac output TPR = total peripheral resistance 
Simplified version of D’ Arcy’s Law 


Nerves 





Nernst equation 
E = RT ·
ln (C_{O}/C_{I}) nF or at 37 degrees
C: E = 61mV · log
(Co/Ci) 
E = voltage
across membrane R = gas constant
8.3 T = temperature n =
charge/valency F = faraday’s
constant 96,500 
C_{O}/C_{I} is the concentration gradient across the membrane, from Outside to Inside (for something more concentrated on the inside gradient will have the opposite sign to n) 


GHK equation E = 
RT · ln P_{K}[K]_{O} + P_{Na}[Na]_{O} F
P_{K}[K]_{O} + P_{Na}[Na]_{O} 
P_{X} =
relative permeability of x 
Note: if permeability of only one ion is significant,
GHK = Nernst 


Charge 
Q = Q_{0} · (1  e^{T/RC}) 
T_{½} = RC ln2 
As RC is time taken to fall to 63% 

