Multidimensional Population Balance Modeling for Pathological Calcium Pyrophosphate Dihydrate Crystals in the Presence of Amino Acids

A multidimensional population balance model was applied to elaborate the effects of amino acids on the crystallization mechanisms of calcium pyrophosphate dihydrate crystals. Breakage and growth terms defined in the model were expressed in two dimensions depending on the sizes. The exponential hyperbolic function based on the particle sizes was selected for expressing the growth. The model was resolved by using the finite differences method. It was detected that in the non-additive media, the growth along the length-1 is extremely dominant against both the growth along the length-2 and the breakage. However, it was discovered that the amino acids made the crystals more fragile, and the breakage at certain size ranges and certain concentrations of amino acids was the dominant mechanism. In any case, it was proven that both growth and breakage are suppressed considerably in the amino acid-containing media.