> la1 := -(k01+k21+k12-((k01+k21+k12)^2-4*k01*k12)^.5)*(1/2); > la2 := -(k01+k21+k12+((k01+k21+k12)^2-4*k01*k12)^.5)*(1/2); > a := (k01+k21+la1)/k12; b := k21/(k12+la2); > y1s := rho/k01; y2s := y1s*k21/k12; > x1s := Dose/(tau*k01); x10 := c10*V1; > x2s := x1s*k21/k12; x20 := c20*V1*k21/k12; > > M1 := ((x10-x1s)*b-x20+x2s)/(b-a); > M2 := (x20-x2s-(x10-x1s)*a)/(b-a); > x1tau := M1*exp(la1*tau)+M2*exp(la2*tau)+x1s; > x2tau := M1*a*exp(la1*tau)+M2*b*exp(la2*tau)+x2s; > N1 := ((x1tau-y1s)*b-x2tau+y2s)/(b-a); N2 := (x2tau-y2s-(x1tau-y1s)*a)/(b-a); > > eq1 := N1 = 1.278837*10^3; > eq2 := N2 = 1.310056*10^3; > eq3 := la1 = -6.*10^(-3); > eq4 := la2 = -0.52e-1; > Dose := 2500; tau := 1; rho := 0; c10 := 0; c20 := 0; V1 := 6.655; > solve([eq1, eq3, eq4], [k01, k21, k12]); [[k01 = 0.01054009074, k21 = 0.01785864607, k12 = 0.02960126319]] > eq5 := M1 = -1.82*10^5; eq6 := M2 = -2.602*10^4; > solve([eq5, eq6, eq3, eq4], [k01, k21, k12, V1]); > eq7 := x1s = 30490; 2500 ---- = 30490 k01 > solve([eq7], [k01]); [[ 250 ]] [[k01 = ----]] [[ 3049]] > solve([eq1, eq2, eq3, eq4, eq5, eq6, eq7], [k01]); [] > N1; / // | ||/ | |||/ | 1 |||| |------------------------------------------------------------- |||| | 0.5 |||| |1 1 1 1 / 2 \ |||| |- k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ ||\\ \2 2 2 2 \\ 2500 k21 - ------------------------------------------------------------------- / 0.5\ |1 1 1 1 / 2 \ | k01 |- k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ | \2 2 2 2 / / 2500 k21\ | 1 1 1 + --------| exp|- - k01 - - k21 - - k12 k01 k12 | \ 2 2 2 | | / // 0.5\\ | 1 / 2 \ || | + - \(k01 + k21 + k12) - 4 k01 k12/ || | 2 /| | | | | | / | \ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ 1 1 1 1 / 2 \ | // - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | || 2 2 2 2 | || - -------------------------------------------------------------| + || k12 | || | \\ | / 2500 k21 - -------- k01 k12 / 0.5\\ |1 1 1 1 / 2 \ || 2500 |- k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ || / \2 2 2 2 /| | + --------------------------------------------------------------------| exp| k01 k12 / \ // \ | | | 0.5\| | 1 1 1 1 / 2 \ || | - - k01 - - k21 - - k12 - - \(k01 + k21 + k12) - 4 k01 k12/ || | 2 2 2 2 // | | \ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ \ 1 1 1 1 / 2 \ | | - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | | 2 2 2 2 | 2500| - -------------------------------------------------------------| + ----| k21 k12 | k01 | | | | | / / \ | / | |/ 2500 k21 | ||- ------------------------------------------------------------------- | - || / 0.5\ | || |1 1 1 1 / 2 \ | | || k01 |- k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ | | \\ \2 2 2 2 / / / 0.5\ 2500 k21\ |1 1 1 1 / 2 \ | + --------| |- k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | k01 k12 | \2 2 2 2 / | | / /// / 0.5\\ || | 1 1 1 1 / 2 \ || || exp|- - k01 - - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ || || \ 2 2 2 2 /| || | || | || / || \\ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ \ 1 1 1 1 / 2 \ | | // - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | | || 2 2 2 2 | | || - -------------------------------------------------------------| k12| - || k12 | | || | | \\ | | / / 2500 k21 - -------- k01 k12 / 0.5\\ |1 1 1 1 / 2 \ || 2500 |- k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ || \2 2 2 2 /| + --------------------------------------------------------------------| k21 k01 k12 / /// \ || | || / 0.5\| || | 1 1 1 1 / 2 \ || || exp|- - k01 - - k21 - - k12 - - \(k01 + k21 + k12) - 4 k01 k12/ || || \ 2 2 2 2 // || || \\ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ 1 1 1 1 / 2 \ | - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | / 2 2 2 2 | |1 - -------------------------------------------------------------| |- k12 k12 | \2 | | / \ \// | | | 0.5\| | | 1 1 1 / 2 \ || 2500 k21| | - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ || - --------| | 2 2 2 /| k01 k12 | | | | | | | | / / \ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ 1 1 1 1 / 2 \ | - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | 2 2 2 2 | - -------------------------------------------------------------| k12 | | | / > N1; / // | ||/ | |||/ | 1 |||| |------------------------------------------------------------- |||| | 0.5 |||| |1 1 1 1 / 2 \ |||| |- k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ ||\\ \2 2 2 2 \\ 2500 k21 - ------------------------------------------------------------------- / 0.5\ |1 1 1 1 / 2 \ | k01 |- k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ | \2 2 2 2 / / 2500 k21\ | 1 1 1 + --------| exp|- - k01 - - k21 - - k12 k01 k12 | \ 2 2 2 | | / // 0.5\\ | 1 / 2 \ || | + - \(k01 + k21 + k12) - 4 k01 k12/ || | 2 /| | | | | | / | \ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ 1 1 1 1 / 2 \ | // - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | || 2 2 2 2 | || - -------------------------------------------------------------| + || k12 | || | \\ | / 2500 k21 - -------- k01 k12 / 0.5\\ |1 1 1 1 / 2 \ || 2500 |- k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ || / \2 2 2 2 /| | + --------------------------------------------------------------------| exp| k01 k12 / \ // \ | | | 0.5\| | 1 1 1 1 / 2 \ || | - - k01 - - k21 - - k12 - - \(k01 + k21 + k12) - 4 k01 k12/ || | 2 2 2 2 // | | \ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ \ 1 1 1 1 / 2 \ | | - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | | 2 2 2 2 | 2500| - -------------------------------------------------------------| + ----| k21 k12 | k01 | | | | | / / \ | / | |/ 2500 k21 | ||- ------------------------------------------------------------------- | - || / 0.5\ | || |1 1 1 1 / 2 \ | | || k01 |- k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ | | \\ \2 2 2 2 / / / 0.5\ 2500 k21\ |1 1 1 1 / 2 \ | + --------| |- k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | k01 k12 | \2 2 2 2 / | | / /// / 0.5\\ || | 1 1 1 1 / 2 \ || || exp|- - k01 - - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ || || \ 2 2 2 2 /| || | || | || / || \\ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ \ 1 1 1 1 / 2 \ | | // - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | | || 2 2 2 2 | | || - -------------------------------------------------------------| k12| - || k12 | | || | | \\ | | / / 2500 k21 - -------- k01 k12 / 0.5\\ |1 1 1 1 / 2 \ || 2500 |- k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ || \2 2 2 2 /| + --------------------------------------------------------------------| k21 k01 k12 / /// \ || | || / 0.5\| || | 1 1 1 1 / 2 \ || || exp|- - k01 - - k21 - - k12 - - \(k01 + k21 + k12) - 4 k01 k12/ || || \ 2 2 2 2 // || || \\ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ 1 1 1 1 / 2 \ | - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | / 2 2 2 2 | |1 - -------------------------------------------------------------| |- k12 k12 | \2 | | / \ \// | | | 0.5\| | | 1 1 1 / 2 \ || 2500 k21| | - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ || - --------| | 2 2 2 /| k01 k12 | | | | | | | | / / \ k21 ------------------------------------------------------------- 0.5 1 1 1 1 / 2 \ - k12 - - k01 - - k21 - - \(k01 + k21 + k12) - 4 k01 k12/ 2 2 2 2 0.5\ 1 1 1 1 / 2 \ | - k01 + - k21 - - k12 + - \(k01 + k21 + k12) - 4 k01 k12/ | 2 2 2 2 | - -------------------------------------------------------------| k12 | | | / >