Question

The net filtration across relaxed skeletal muscle capillaries is about 0.005 mL/min per 100 g of tissue. Assume the following values: the density of muscle is 1.08 g/cm3; the length of the capillaries is 500 μm and their cross-sectional density is 250 capillaries/mm2. Their average radius is 4 μm. Pressure at the arteriolar end of the capillary is 40 mm Hg and it decays linearly to 15 mm Hg at the venule end. The oncotic pressure of plasma is 25 mm Hg. Interstitial fluid pressure in relaxed muscle is -1 mm Hg and intersitial fluid oncotic pressure is 5 mm Hg
a. Calculate the surface area of the capillaries per 100 g of muscle. (Hint: calculate the mass of muscle 250 mm2 in cross-section and 500 um long)
b. Does the capillary filter fluid along its entire length, or does it reabsorb fluid at the venule end? Support your answer with calculations based on the givern information.

Answer 1

Answer:

0.58 m²/100 g

Explanation:

Let us consider a chunk of muscle with a cross-sectional area of 1 mm² and which 500m long. If this chunk contain 250 capillaries and each with 4m radius long .

Now if we calculate the muscle slab weight along with the surface area of capillaries in the muscles. To calculate the surface area per unit weight of muscle we will neee to divide the surface area of capillaries that are there in the muscle to the area by the mass of the muscle long.

This slab of muscle contains 250 capillaries with a radius of 4m each. We calculate how much this muscle slab weighs,

how much surface area of capillaries there are in the muscle,

and then we will divide the area by the mass of the muscle to find the surface area per unit weight of muscle

The volume of the piece of muscle is;

=1 mm²  x 500 x 10⁻⁶ m

= 1 mm²  x 0.5 mm

= 0.5 mm³

Now  since 1cm = 1000mm

Therefore, the volume will be equal to

= 0.5 x 10⁻³ cm³

And its mass is 0.5 x 10 ⁻³ cm³ x 1.08 g cm⁻³

= 0.54 x 10⁻³ g

surface area of a single capillary is = 2B × r × l

where;

r = radius, l = length

∴ surface area = 2 B x 4 x 10⁻⁶ m x 500 x 10⁻⁶ m

= 12566 x 10⁻¹² m²

Now for 250 capillaries the total surface area is 250 x 12566 x 10⁻¹² m²

= 3141500 x 10⁻¹² m² in a mass of muscle that weighs 0.54 x 10⁻³ g.

So the surface area of capillaries is 3.1415 x 10⁻⁶ m²/ 0.54 x 10⁻³ g

= 5.818 x 10⁻³ m² g⁻¹ x 1 g /100 g

= 0.58 m²/100 g