Contents 1 Time-kill Behavior 1.1 Bacteria Growth in Tumor 1.2 Time-kill Model 1.3 Data Acquisition 1.4 Result 1.5 References

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

Data Name	Data Value	Source
$\Psi_{max}$, maximum growth rate of bacteria	0.207	the study from Fujimori bacteriaDist
$\Psi_{min}$, maximum die-out rate of bacteria	-6	the study from Speciale GCVanalogA. Speciale et al., Minimal inhibitory concentrations and time-kill determination of moxifloxacin against aerobic and anaerobic isolates. International Journal of Antimicrobial Agents 19, 111-118 (2002)
$zMIC$, minimal inhibitory concentration	0.03	the study from Speciale GCVanalog
$\kappa$, the hill coefficient	1	the study from Speciale GCVanalog

Result

Taking the result of PBPK model as the input of time-kill function(). The GCV is administered once a day for 5mg/L intravenously.

The bacteria growth rate is shown in . The negative value means that the number of bacteria is decreasing. The integration of bacteria growth rate is the time-kill curve in .

The comparison between different doses every day is in below. When the dose is 1 mg/L, the bacteria continue to grow. When the dose is 9 mg/L, the bacteria die out too fast. It shows that 5 mg/L is a proper dose.

References

The source code of all models can be found here.