Problem 2 An orthopedic product called “Mend-a-bone” is made of an extracellular

Question

Problem 2 An orthopedic product called “Mend-a-bone” is made of an extracellular matrix extract plasticized with glycerol (MW=92) to help surgeons shape it easily. This product is used to fill defects in bone, such as nonunion fractures. It looks like a sponge—i.e. it is porous and has a high void fraction that can soak up the blood in a defect. Recently, some surgeons have started added marrow to the Mend-a-bone to improve bone healing, but the results are mixed. The product contains 25% by weight glycerol and has a void fraction of ~70%.

In use, some surgeons add marrow directly to the dry Mend-a-bone in a stainless still dish, adding just enough marrow to fill the void space, while others add saline to hydrate the product and then add marrow upon implantation.

Assume Mend-a-bone is at body temperature, 37oC, and is composed of a collagenous substrate with the density of 1 g/cm3 . A surgeon asks you if addition of the marrow directly to the dry product and then letting it sit around for a while causes osmotic shock to the cells. Given the exorbitant cost of malpractice lawsuits, how much money should the “Mend-a-bone” company pay you to keep your mouth shut?

(Note: Osmosis is a term used to describe the diffusion of water through a semi-permeable membrane from a region of higher concentration to a region of lower concentration (of water). Under normal conditions the extracellular fluid is isotonic to the cell cytoplasm meaning the concentration of water in the medium surrounding to the cell is equal to that of the cytoplasm. Osmosis is quantified by the osmotic pressure (OP), the pressure required to stop the osmosis of water across a semi-permeable membrane. Osmotic shock is defined as the rupture of cells in a solution following a sudden change in osmotic pressure. The OP can be given by OP=cRT where R is a gas constant, R=0.08206 (L·atm)/(mol·K), where atm: atmosphere (pressure unit); K, absolute temperature; L, liter; c is the molar concentration of the non-permeable solutes. For the purpose of this problem, we can assume the glycerol is non-permeable.

To solve this problem, we must take into account the void fraction in order to calculate the density of contribution of glycerol.

Explanation / Answer

Glycerol (MW=92)

Mend a bone contains 25% by weight glycerol

And void fraction of 70%

Density of 1 g/cm3

OP=cRT

R=0.08206 (L·atm)/ (mol·K)

atm: atmosphere (pressure unit);

K, absolute temperature; T=37C=310K

L, liter;

c is the molar concentration of the non-permeable solutes

Calculate osmotic pressure that the cells experience

OP=cRT

Calculate the molar concentration of non-permeable solutes

(0.25) x (0.30) x (1g/cm3) = 0.075 g/cm3

(0.075 g/cm3)/(92g/mol)=8.15x10-4=0.815mol/L

OP=cRT

= (0.815mol/L) (0.08206 L.atm/mol.K) (310K)

=20.74atm=1.58x104mmHg

When cells are filled in the dry mend a bone product, cell will experience an osmotic pressure of 15800 mmHg as water leaves the cell.

Obviously cells can’t counterbalance the pressure, so they will implode which finally leads to osmotic shock.

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