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Serum osmolarity is the effective solute concentration of blood serum and is measured in osmoles. Blood serum includes everything in blood except red blood cells, or erythrocytes. This measurement is an important tool in medicine because osmotic pressure can affect all cells in the body, due to the power of osmosis and cell wall permeability to water but not to many solutes.
Osmolarity is the measurement of how many solute molecules are contained within a certain volume of liquid, and it indicates the molecular molarity of a solute dissolved in solution. One reason that this is an important measure when working in biological systems is the fact that water moves through osmosis, being attracted through diffusion and concentration gradients to areas with a higher ionic or solute density, rather than areas with lower solute densities. Osmosis can force water into cells or draw it out of them, depending on the relative concentration of ions and solutes inside cells to the concentration of solutes in extracellular fluid like blood serum.
Cell walls function as, among other things, semi-permeable membranes. While there are some channels in cells called "aquaporins" that allow water to pass freely in and out, ion concentrations inside cells are regulated with channels, gates, and ion pumps. Sodium, calcium, and potassium are common ions found inside cells that are heavily regulated in concentration.
If serum osmolarity is too high, that indicates that the solute concentration of blood serum will tend to leach water from inside cells due to the effects of osmosis. Water will be attracted to the extracellular space, where solute concentration is higher due to osmosis. This can cause cell shrinkage and, in extreme cases, necrotize some cells.
Too low osmolarity indicates a lack of sufficient ions or solutes in blood serum, which creates a problem of hypotonicity. When this happens, cells draw too much water in due to the relative solute concentration gradients across the cell membrane. In extreme cases, this can cause cell death through apoptosis.
Serum osmolarity can be used to diagnose dietary deficiencies or dangerously high intakes of certain foods or minerals. Too few ions or solutes in blood serum can be dangerous, which is why it's important to drink electrolytic fluids during periods of heavy water loss through sweating. Measurements can also be used as indicators for other health anomalies, like an inability or deficiency in the ability to process sugar.