1. A Pharmacodynamic Model for Cefprozil against Haemphilus influenzae in an in vitro Infection Model across Multiple Regimens Olanrewaju O. Okusanya, Pharm.D, BCPS University at Buffalo, School of Pharmacy and Pharmaceutical Sciences

2. Co-Authors Alan Forrest, Pharm.D Brent M. Booker, Pharm.D Pamela Kelchin,BS Patrick F. Smith, Pharm.D University at Buffalo, School of Pharmacy and Pharmaceutical Sciences, Buffalo, NY

3. Introduction/Objectives Adequately characterizing the pharmacodynamics of β-lactams can give insight into avenues to optimizing the use of this class of drug and reduce the incidence of resistance development Serial samples of bacterial CFU to track the time course of drug effect is difficult to obtain in human trials. Modeling concentration vs. rate and extent of kill and/or re-growth using in vitro PK/PD models (IVM) can provide important insights into concentrations needed to optimize outcomes in man We have used a mathematical pharmacodynamic model to characterize bacterial rates of replication and death and the effect of cefprozil on these processes when administered using different regimens

4. Methods MICs of 2 β-lactamase (-), and 1 β-lactamase (+) H.flu strains were determined in triplicate following NCCLS criteria A 1 compartment IVM consisting of a central compartment containing bacteria in Log-phase growth ( 10 7 CFU/mL) and bacterial growth media was used for the experiment Drug free media was delivered into the central compartment using a high precision computer driven pump and bacterial growth media removed to a waste flask Bacteria were exposed to cefprozil administered into the central compartment with changing concentrations consistent with that seen in humans, similar free drug concentrations, with an approximate half-life of 2 hrs The once daily (QD), twice daily (BID), and continuous infusion (CI) regimens were simulated to obtain %T>MIC ranging from 6.6% - 100+% with appropriate growth control for each strain and regimen Serial samples were obtained over 24 hours to determine bacterial CFU in duplicate with a lower limit of detection of 10 2 CFU/mL

5. Pharmacodynamic Model BacteriaCFU/mL Pop 1 Pop 1 Pop2 Pop2 Pop3 Pop3 Pop4 Pop4 KDKD Replication EC 50 Drug (+) (-) Figure 1: Pharmacodynamic model. CFU/mL, bacteria colony forming units/mL; Pop1-4, bacteria sub-populations; K D, first-order bacterial death rate constant (hr -1 );EC 50, drug concentration of 50% inhibition of growth or acceleration of death (µg/mL) CFU i - CFU/mL of the ith population VGmax - maximum velocity of growth (CFU/mL/hr) CFU mi - CFU/mL associated with ½ maximal growth CFU TOT - sum of all subpopulations Kd – 1 st order rate constant for bacterial death (hr -1 ) Imax - maximum effect (Conc/MIC) - approx inverse serum inhibitory titer (SIT) H is Hill’s constant, SITmi is the SIT associated with 50% of maximum drug effect

6. Methods Cefprozil was modeled as either enhancing Kd or inhibiting replication Each curve was fit individually and later simultaneously regardless of regimen for each strain using maximum likelihood and then MAP Bayesian estimation Each inoculum modeled was allowed to have up to 4 sub- populations AIC, Sum of Squares residuals, and visual inspection was used for model discrimination, to determine the number of subpopulations, and parameters that would be allowed to vary between sub-populations

7. Strain X219 CI regimen Strain X219 BID regimen Strain X208 QD regimen Strain X208 BID regimen Results

8. r 2 =0.94 Obs=1.00x Fit-0.0 Strain X219 CI regimen BID regimen Strain X208 QD regimen BID regimen Strain X204 QD regimen r 2 =0.94 Obs=1.01x Fit-0.23 r 2 =0.89 Obs=1.00x Fit-0.28

9. Results The MICs of the β-lactamase (+) strain (X208) was 2 mg/L and was 2 mg/L and 4 mg/L for the β-lactamase (-) strain (X219 & X204) Drug effect was best modeled as inhibiting replication (up to 100%) The model required 1-2 sub-populations with the VGmax allowed to vary between sub-populations The fit of the pharmacodynamic models for each strain was excellent accommodating all regimens studied

10. Results ParameterX204X219X208 Average VGmax (CFU/mL/hr)9.02x10 8 1.18x10 9 4.95x10 8 CFUm (CFU/mL)3.89x10 8 8.00x10 8 2.43x10 8 T ½ d (hr)1.001.531.11 cVGmax--0.7090.694 Imax1.000.9920.999 Hill’s Constant2.002.171.00 SITm 1 0.3610.6121.78 % POP 110099.699.9 SITm 2 --115636 % POP 2--0.3710.061 VGmax: maximum velocity of growth (CFU/ml/hr), CFUm: CFU/mL associated with half the maximal growth, T1/2d: half life of bacteria giving no replication, Hill’s constant of sigmoidicity, SITm i serum inhibitory titer term associated with 50% enhancement of bacterial death, POPi is the estimated % of the ith population present in the initial inoculum

11. Discussion Drug effect gradually increases with increasing concentration causing total inhibition of bacteria replication The 2 nd population was clearly seen by the inability of the drug to have little to no effect on bacteria replication even at its highest dose The poor effect on the 2 nd population is reflected by the high SITm 2, and the presence of re-growth at peak concentrations of 86.5XMIC for the X219 strain and 173.3XMIC for the X208 strain

12. Discussion Regrowth at high doses indicate the need for unsustainable concentrations for substantial effect against the 2 nd sub- population The velocity of growth of the resistant population were 0.69X and 0.71X that of the sensitive sub-population for the X208 and X219 strains respectively indicating reduced fitness In- spite of β-lactamase activity, there is still a population that is susceptible to cefprozil, is essentially ineffective against the 2 nd sub-population

13. Conclusion Cefprozil can be best modeled by inhibiting the replication of H. flu The X204 strain can be best described by 1 sub-population, and the X208 and X219 strains, by 2 sub-populations Cefprozil at adequate concentrations causes complete inhibition of the bacteria replication Multiple regimens of ceprozil against H. flu could be well described (comodeled) using a mathematical model

14. Questions ?