I think you question is about the mechanism of the reaction rather than a form of the product or it's histological response. However, the first paper attached by Helen might help you. It presents the reaction equation where you can find how the reaction goes. But the mechanism of the reaction is more complex. It is a crystallization, but the mechanism depends on many variables.
I was trying to find a general mechanism for this kind of reaction, but it is really hard. I found only this paper describing what is happening in this reaction with sodium hyaluronate as a template...
Calcium Phosphate ceramic like Hydroxyapatite is a biocompatible material which is used in orthopedic and dental applications and its Ca/P ratio is 1.67. HAP is a most stable apatite when compared to other calcium phosphate phases. Stoichiometric HAP can be synthesized only when a particular synthesis method and a definite pH conditions were employed.Normally HAP is formed when the pH is maintained at 10 to 11 for the complete process. First the pH of calcium nitrate should maintained at 11 using ammonium hydroxide solution to get ca2+ ions from calcium hydroxide formed. Then pH of ammonium hydrogen phosphate is maintained at 11 to get HPO42- . During the addition of calcium solution to phosphate solution again the pH is maintained at 11, where calcium ions react with phosphate and hydroxyl ion to get a stable HAP.