The system of equations shown below in Figure 1 describes bulk-degrading microsphere drug delivery and can be used to describe the release of CaO2 from the design microspheres for the proposed solution [1]. In the context of the proposed design, the variables of Equation (1) are defined as follows [1]:
1) Mt = Mass of released CaO2 at a given timepoint 2) C0 = Microsphere CaO2 concentration at time=0 3) Cs = CaO2 solubility limit 4) D = CaO2 diffusion coefficient 5) r = PLGA microsphere radius 6) t = time Furthermore, since the PLGA microsphere of the proposed design is degradable, its diffusion coefficient (D) varies according to Equation (2) over time (Note: D=Dt). The variables for Equation (2) include [1]: 1) Dt = time t diffusion coefficient 2) D0 = initial diffusion coefficient 3) c = constant term 4) Mw,t = time-dependent molecular weight for the PLGA making up the microsphere The Mw,t term Equation (2) is defined by Equation (3). For this equation, the right-hand side terms are as follows [1]: 1) Mw,0 = Molecular weight of the PLGA microsphere at time=0 2) k = PLGA reaction (degradation) rate Collectively, these equations can model the amount of CaO2 released from the microspheres over time [5.1]. These equations therefore can indirectly provide insight into oxygen delivery to the wound. Lastly, these equations can be used to model microsphere degradation (and therefore CaO2 release) for a range of PLGA microspheres to further confirm that the oxygen delivery to the DFU is sufficient.
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