Physics for Physiology

 

Principle

Equations

Field

Application

Conservation of Mass (mass is neither created nor destroyed AND amount used = amount in  amount out)

amount (mass) = volume x concentration

amount used = volume in x concentration in - volume out x concentration out

(if volume in is the same as volume out)

amount used = volume (Cin - Cout)

M = CV

C = m/V

Pulmonary

Alveolar Gas Equation

For any substance: Concentration = mass/volume  or

                        C = m/V   (e.g. moles/liter)

        For gases C = Pa  (Henry's law)

        where P is the pressure and alpha is the solubility.

 

      Pa = m/V   or    PV = ma

             The ideal gas law states that:  PV = mRT

              a =  1/RT  

M = V x C    and for gas  M = V x P/RT

amount = volume x concentration 

amount of CO2 in alveolar gas = alveolar volume x concentration

                or CO2, ml = VA, ml air x [CO2], ml/ml air

expressed per unit time

 VCO2, ml /min = VA ml air/min x [CO2] ml CO2/ml air

     

since [CO2] = PCO2 a   and a = 1/RT    (at normal human body temperature RT = 863)

VCO2 = VA x PCO2/RT    =  4315 ml/min x (40/863) = 200 ml/min

       

Rearranged:

VA = (VCO2/PCO2) x RT   using normal values

VA = (200/40) x 863 = 4315 ml/min

 

 

 

 

Pulmonary

   Lung Volumes

Helium dilution.  Helium mass is constant and mass = Conc. x Vol.

A spirometer containing 10% helium has a volume of 2 liters including all the tubing up to the patient's mouthpiece.  The patient is attached to the mouthpiece at the end of a normal expiration (at resting lung volume or FRC) and is instructed to breath normally for several breaths.  The helium concentration is now 5%.  It’s lower since helium is now evenly distributed in both the spirometer and the lungs.

If the spirometer volume is the same at the end of the test, then the following equation applies:   CV initial = CV final    OR

[He]initial  x Vs = [He]final x (Vs + VL)  where Vs is spirometer volume and VL is lung volume

Solving for lung volume, VL = Vs x (([He]i/[He]f)  1))

Example:  VL = 2L x ((10%/5%)  1)) = 2 L

This technique would also measure residual volume is the spirometer is connected at the end of a maximum expiration.

Nitrogen Washout.  Nitrogen mass is constant and mass = CV

Patient is asked to breathe 100% oxygen for 7 minutes.  With each breath, the lungs lose nitrogen and gain oxygen.  The expired gas is collected in an expandable sac.  After 7 minutes the sac contains about 40 liters (about 6L/min for 7 minutes) including all of the nitrogen that was previously in the lungs.

CVlinitial = CVfinal     or CVlung = CVsack

[N2]L x VL = [N2]sack x Vsack

And VL = Vsack x [N2]sack/[N2]lung

Example:  initial N2 = 80%   final N2 = 4%    sack volume = 40L

VL = 40L x (4%/80% ) = 2L  

Area of rectangle is equal to the product of side1 x side2















Volume of rectangle is equal to product of side 1 x 2 x 3

A = side1 x side2




Note: the sum of side1 + side 2 is smallest when the rectangle is a square:

16 = 4 x 4
16 = 8 x 2
16 = 16 x 1

Pulmonary

Cardiovascular

Fick Principle

oxygen used = (oxygen in  oxygen out)

VO2 = (cardiac output x arterial O2)  (cardiac output x venous O2)

VO2 = Q (art. O2  ven. O2)  using normal values

 VO2 = 5000 ml/min (.20 - .15)mlO2/ml blood = 250 mlO2/min.

VO2 = VA (FIO2  FEO2)

VCO2 =  VA (FECO2  FICO2)  since FICO2 = 0

VCO2 = VA (FECO2)

            oxygen used = heart rate x stroke volume x
             (arterial - venous) O2 difference

total amount transported = amount not shunted + amount shunted

amount = vol x conc.

Pulmonary

Cardiovascular

Shunt

Cardiovascular & Pulmonary: amount = volume x concentration

Amount of oxygen transported in arterial blood = vol x conc

Or, amount/min = Qt x CaO2 where Qt = total cardiac output

Amount of oxygen transported in shunted blood = vol x conc

Or, amount/min = Qs x CvO2 where Qs = shunt flow

Amount of oxygen transported in non-shunted blood

= (Qt  Qs) x CcO2 where CcO2 = pulmonary capillary [O2]

QtCaO2 = QsCvO2 + (Qt  Qs)CcO2  and by rearranging

Qs/Qt = (CcO2  CaO2)/(CcO2  CvO2)

amount of substance filtered by kidneys = amount excreted  + amount secreted + amount reabsorbed

 

 

Renal

Renal Clearance

Renal:  amount of substance filtered (M) = M excreted + M reabsorbed + M secreted (the only 3 things that can happen to something that is filtered)

For inulin:  M filtered = M excreted

M filtered = GFR x [In]p

M excreted = Vu x [In]u

so GFR x [In]p = Vu x [In]u

or GFR = Vu x [In]u/[In]p

Ohms Law  in electrical circuits: 

current = voltage/resistance  

Pulmonary

Cardiovascular

Cardiovascular and pulmonary physiology:   blood flow or air flow  =  driving pressure/resistance

 

 

 

 

 

 

Poiseuille’s equation describes these effects  of geometry and fluid  properties on resistance:

 

FLOW = (P1 - P2)/R    where R = 8 hl/pr4


Hydraulic resistors in series:  Rtotal = r1 + r2 + r3  (adding an addition resistance in series always increases total resistance)


Hydraulic resistors in parallel:  1/Rtotal = 1/r1  + 1/r2  +1/r3  (adding an additional resistance in parallel always decreases total resistance) 

This explains why recruitment of pulmonary capillaries cause pulmonary vascular resistance to fall when pulmonary arterial
pressure rises)

Work

WORK = force x distance


pressure = force  x area


W = PA x d


A x d = vol


W = P x Vol

Pulmonary

Cardiovascular

       Pressure = force/area;  Force = PA


Work = PxAxd  =  P x Volume

        CARDIOVASCULAR
Stroke Work =  MAP x Stroke Volume  

 

 PULMONARY
Breathing Work = Inspiratory Pressure x Tidal Volume

Flow                 

 

Osmotic Pressure

Flow =velocity       x area

from ideal gas law

PV = nRT

P = n/V RT

n/V = molarity = i

P = iRT

 

Pulmonary
Cardiovascular

 

Cell Volume

Flow = ml/min or cc3/min =  cm/min x cm2

 

air or blood velocity = flow/area 

 

 

 

 

 

 

 

 

http://dbhs.wvusd.k12.ca.us/webdocs/Solutions/Osmosis-Equation.html