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The focus of this research is to determine a mathematical model for the osseointegration process of discretely deposited nano-crystalline (DCD) hydroxyapatite (HAp) onto a titanium implant for bone injury treatments and medical procedures. The research currently focuses on ab initio ground state calculations. The derivative compound of interest is tricalcium phosphate Ca3(PO4)2, which behaves very similarly to HAp. We perform binding energy, geometry optimization, and frequency of vibration calculations between tricalcium phosphate and one atom of titanium in Gaussian 09 computational chemistry package. The basis set used is 6-31G + (d’) and the B3LYP hybrid functional. Calculations involve using mathematical techniques in Functional Density Theory, such as: computationally finding solutions to the Schrodinger equation, functional minimization (in order to calculate the ground energy of HAp), and solutions to differential equations that describe the forces and potential energies involved with the chemical reaction of formation. Since HAp can be crystallographically similar to bone mineral, and since the substance is bioactive and osteoconductive, when a discrete nano-scale layer of HAp is introduced to the micro-topography of the titanium implant, the increase in surface area and biocompatibility results in more space for upregulation of platelet activation and an increase in fibrin retention around the implant. There is a myriad of other advantages of an HAp DCD treated medical implant for bone healing, but perhaps understanding the substance HAp at its most fundamental physical and chemical conditions will shed some light on further improvement of its applications and behavior in non-ideal environments.


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  • Subject
    • Mathematics

  • Institution
    • Gainesville

  • Event location
    • Floor

  • Event date
    • 22 March 2019

  • Date submitted

    19 July 2022

  • Additional information
    • Acknowledgements:

      Dr. Alla Balueva, Dr. Patricia Todebush