Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Let S(t) and R(t) represent the number of cells that are sensitive or resistant to imatinib. During imatinib exposure, assume zero growth and a death rate δ for sensitive cells, µ << δ as the rate at which sensitive cells mutate to resistance, and no death and a growth rate β for resistant cells. The two cell populations then follow:
Nested in optimizations performed to estimate the parameters β, δ and µ, these equations were integrated numerically using lsoda of the R package odesolve. The parameters were estimated in exponentiated forms to constrain them and their confidence intervals (CIs) to positive values (see Table 1). CIs were estimated from Hessians (matrices of second derivates) of the SSEs (sum of squared errors) evaluated at the optimum (minimum SSE) using the function optim in R: Hessians were divided by 2, inverted, multiplied by SSE/(N - P) where N and P are the number of data points and parameters, and square roots of the main diagonal were then be multiplied by 1.96 to form the 95% Wald CI (in Table 1).
Table 1. Parameter estimates of fit in Fig. 1. Units: rate constants=1/day, cells numbers=104.
CANCER RESEARCH 59, 4770–4775, October 1, 1999
Tumor Development under Angiogenic Signaling: A Dynamical Theory of Tumor Growth, Treatment Response, and Postvascular Dormancy
Philip Hahnfeldt, DipakPanigrahy, Judah Folkman, and Lynn Hlatky
Model building datasets
Model validation data
V follows setpoint/carrying capacity K
With lambda2 fixed to zero and all else fitted to all of the data simultaneously, the fit was
initial final opt CI95prct
lambda1 1.92e-01 1.92e-01 TRUE (0.185, 0.202)
lambda2 0.00e+00 0.00e+00 FALSE not fitted
b 5.85e+00 5.78e+00 TRUE (5.47, 6.11)
d 8.73e-03 8.73e-03 TRUE (0.00823, 0.00919)
eT 1.30e+00 1.43e+00 TRUE (0.317, 6.42) ** 20 fold
clrT 1.01e+01 1.02e+01 TRUE (3.22, 32.1) ** 10 fold
eE 6.60e-01 5.84e-01 TRUE (0.228, 1.5)
clrE 1.70e+00 2.07e+00 TRUE (0.814, 5.26)
V0 1.80e+02 1.90e+02 TRUE (178, 202)
V0valid 3.00e+02 2.81e+02 TRUE (200, 395)
K0 6.25e+02 7.93e+02 TRUE (742, 846)
Initital SSE = 2,314,351; Final SSE=750,720.4 Note that the nice initial fit in Endo
at 20 mg/kg is sacrificed for a better final fit in endo at 4mg/kg (next page).
Initial values take from here
Fits of initial parameter values (i.e. those given in Cancer Res. 1999)
initial parameter value drug time courses
Fits of final parameter values
Fits when data and model are normalized by the mean of the data
The problem here is that the initial K0 is less than V0
initial final opt CI95prct