CASE STUDY 1c | Kill Curves and Antiblotic Effectiveness 385 CASE STUDY 1c Kill Curves and Antibiotic Effectiveness Recall that in this case study we are exploring the relationship between the magnitude of antibiotic treatment and the effectiveness of the treat- ment. One of the most important components of our analysis is the antibiotic concentration profile, which is a plot of the antibiotic concentration as a function of time. In the simple model of Case Studies la and lb we modeled a single dose of antibiotic using the equation de dr for some positive constant k. From this we saw that the concentration as a function of time is where co is the concentration at 0. (See Figure 1.) 1.5 0.5 FIGURE 1 Antibiotic concentration profile 20 30 t(hours) 10 modeled by the function c(r)- withd, Time 1.2 ㎍/mL and k-0.175 Three of the most common measures of the magnitude of antibiotic treatment are (1) the peak antibiotic concentration divided by MIC, denoted by p: (2) the duration of time for which the antibiotic concentration remains above MIC. denoted h r. and < the area under the antibiotic concentration profile divided by MIC, denoted by a. These are shown in Figure 2. In Case Study la you derived expressions for the first two. agimL.) a- area A MIC MAC FIGURE 2 Three measures of the magnitude of antibiotic treatment Time (hours) 1. Find an expression for α in terms of k, co and MIC, using Equation 2. The area t centration profile should be calculated from -0 to co, under the con We saw in Case Study la that, for a given antibiotic and bacteria species (in other words, for a given value of k and MIC), all three quantities p, T. and α increase with one another. In other words, it is not possible to have a high value of a without also having high values of ρ and T. Here you will show that we can break this dependency if we