Time-kill Behavior

By investigating into the time-kill behavior of bacteria, we will be able to predict when the bacteria die out and therefore able to decide the dose and frequency of administration. In this part we used the model proposed by Roland R.Regoes regoesModelRoland R.Regoes et al., Pharmacodynamic Functions: a Multiparameter Approach to the Design of Antibiotic Treatment Regimens. Antimicrobial Agents and Chemetherapy 48, 3670-3676 (2004).

Bacteria Growth in Tumor

It has been validated that bacteria grow enormously in tumor zone than the other human tissues bacteriaDistMinoru Fujimori, Bifidobacterium longum as a gene delivery system for cancer gene therapy. Gene Therapy and Molecular Biology 6, 195-200 (2001). From their study, the bacteria growth rate in tumor zone is estimated.

Time-kill Model

Following the model of Reagoes regoesModel, the following equation set are implemented in the model: $$ \eqalignno{ \Psi(\alpha) &= \Psi_{max} - \frac{(\Psi_{max}-\Psi_{min})(\alpha/zMIC)^{\kappa}}{(\alpha/zMIC)^{\kappa}-\Psi_{min}/\Psi_{max}}\\ \frac{dx}{x} &= \Psi(\alpha(t))dt }$$

where:

• $\Psi_{max}$ is the maximum growth rate in the absense of the drug
• $\Psi_{min}$ is the maximum die-out rate in the high concentration of the drug. It is present as a negative rate
• $\alpha$ is the antibiotic concentration
• $zMIC$ is the MIC value under which the net growth rate of bacteria is zero
• $\kappa$ is the Hill coefficient and measures the steepness of the curve.

Data Acquisition

$\Psi_{max}$ is estimated from the study of Fujimori bacteriaDist by fitting the following function into the curve from tumor: $$ \eqalignno{ x=ae^{\Psi_{max}t+t_0}\\ }$$ where:

• $a$ is the amplification factor
• $\Psi_{max}$ is the maximum bacteria growth rate
• $t_0$ is the time offset

Result

References