Answers.

Filtration rate (Jv)=L_pA[(P_c-P_i)-s(p_c-p_i)]

Diffusive flux (J_sdiff)=PA(C_p-C_t)

Convective Flux (J_sconv)=Jv(1-s)C_p

1.a) Jv=0.16x10^-7cm.sec^-1.mmHg^-1 x 100cm².g^-1x[(20mmHg-0mmHg)-0.9(25mmHg-5mmHg)]

=10 x10^-7cm.min^-1.mmHg^-1 x 10000cm².100g^-1x[(20-19)mmHg]

=0.01 cm³.min^-1.mmHg^-1.100g^-1x1mmHg

=0.01ml.min^-1.100g^-1

The value is positive, so fluid flows out of the vasculature

b) for a 70kg person fluid volume is 7ml.min^-1

For the whole day fluid turnover is 7ml.min^-1 x 60min/hr x 24hr/day

= 9.68 litres.day^-1. Blood volume is 5l, Hct is 0.45, so plasma volume is 2.75l.

9.6868 litres.day^-1/2.75 litres = 3.5 x plasma volume turns over per day.

c) With no swelling lymph flow = filtration rate = 0.01ml.min^-1.100g^-1 tissue, or 9.68 litres per day.

2. Flow limited solutes such as glucose and oxygen, are flow limited because the microvascular wall is permeable to the solute. (i.e. the solutes are small relative to the pores in the microvessel wall, and/or they have a high oil:water partition coefficient). Diffusion limited solutes such as albumin are limited because the microvascular wall has a low permeability to such solutes, because the solutes are large relative to the pores in the wall, and they are water soluble.

b) Under flow limited conditions, the plasma solute concentration goes down, and the interstitial solute concentration goes up, so reducing the plasma to tissue concentration gradient. There is not necessarily any change in surface area or permeability.

3. NOTE 1mM=1mmol.l^-1 = 1mmol.1000ml^-1=1µmol.ml^-1

For glucose

Js=[0.08ml.sec^-1.100g^-1 x (5-4.7mmol.l^-1)] +[0.01 ml.min^-1.100g^-1 x (1-0.1) x 5mM]

=[0.08ml.sec^-1.100g^-1 x (0.3umol.ml^-1)] +[0.01 ml.min^-1.100g^-1x(0.9)x5 umol.ml^-1 ]

=[0.024umol.sec^-1.100g^-1] +[0.045 umol.min^-1.100g^-1]

=[1.44umol.min^-1.100g^-1] +[0.045 umol.min^-1.100g^-1]

Diffusive Convective

=[1.485umol.min^-1.100g^-1] , of which 97% is diffusive.

1mol=180g, 1umol=180ug

=263ug.min^-1.100g^-1.
 
 

b) For albumin

Js=[1.2x10^-4ml.min^-1.100g^-1 x (60mg.ml^-1-10mg.ml^-1)]+[0.01 ml.min^-1.100g^-1 x (1-0.95) x 60mg.ml^-1]

=[1.2x10^-4ml.min^-1.100g^-1 x (50mg.ml^-1)] +[0.01 ml.min^-1.100g^-1x(0.05)x 60mg.ml^-1 ]

=[0.006 mg.min^-1.100g^-1] +[0.03 mg.min^-1.100g^-1]

Diffusive Convective

=6.3ug.min^-1.100g^-1 , of which 84% is convective.

6.3ug albumin (molecular weight 50,000) = 0.72nmol.min^-1.100g^-1

Molar flux is 2000 fold greater for glucose than albumin, but permeability is 40,000 fold greater.

P, A and C_i will all vary between tissues. eg. Liver has a very high P, brain has very low P. Lung has a high A, skin has a low A, C_i for glucose will be higher in tissues which are not particularly metabolically active, and low in exercising skeletal muscle. C_i for albumin will be higher in tissues with a high permeability, and low in tissues with low permeability. Plasma concentration is unlikely to change a great deal from tissue to tissue, although it will be higher in arterial blood than venous blood.

Part 3.

4.

1. Arterial glucose concentration , No change,
2. Decreased interstitial glucose concentration - Up to 10 fold,
3. Increased blood flow - more than 20 fold, and increases A up to 4 fold as a result,
4. Filtration rate - Increases, but does not greatly affect glucose delivery directly,
5. Permeability doesn't change,
6. Lymph flow increases, but does not affect glucose delivery.

5.

pore density, Ps increase, Lp increase, s no change

path length, , Ps decrease, Lp decrease, s no change

radius, Ps increase, Lp increase, s decrease

ratio of large to small pores-, Ps for albumin will increase, Lp no change, s decrease

blood flow, Ps no change, Lp no change, s no change

6. Click on table to get a better view