Aims: Models for CD4 count and viral load have long been crucial in antiretroviral drug development , and have increasingly been used in long-term pharmacometric studies [2,3]. However, the basic model has the following problems when fitting long-term data: mathematical instability and oscillatory behavior; not accounting for CD4 Tcells division in the periphery; no clear method to scale for size and age (normal CD4 T cell count drops 3-fold over the first 5 years of life); incorrect attribution of multi-phasic viral decline due to very rapid free virion clearance and insufficient circulating latent reservoir to give multiple phases (< 1% of circulating cells are infected ); assumption of steady-state so cannot account for disease progression. These problems extend to more complex models with latently and quiescently infected compartments. We aimed to develop a new model which is mathematically simple but incorporates biological prior knowledge to address these problems. Focus in this work will be scaling for size and age.
Methods: Starting with the basic model we removed the infected CD4 T cell compartment, adding a viral-dependent CD4 loss term. The zero order CD4 production rate was assumed to come directly from thymic output, and densitydependent proliferation and loss terms were added. Considering scaling for size, Ki67 (a marker for proliferation) expression decreases with age  suggesting proliferation (and loss assuming homeostasis) is higher in younger patients. Upon reanalysis we show size is a more plausible explanation, the proliferation and loss allometric exponent estimate being 0.77. Thymic output inferred from thymic epithelial space volume, or more accurately by T cell receptor excision circle expression, falls with age according to a well characterised relationship : this scaled our thymic output term. Virion production and loss were set equal, with loss assumed to slow with decreasing viral load using a logistic Michaelis-Menten-like term. We have fitted this model to adult and paediatric data but confine this work to two paediatric studies ARROW and PENTA11. Briefly, ARROW was an open-label RCT in 1206 antiretroviral naive children followed up for 3-5 years. PENTA11 randomised 109 children already on antiretrovirals, to either continue treatment or have periods of treatment interruption. Importance sampling implemented in NONMEM 7.3 was used for parameter estimation; the M3 method was used for viral load datapoints below the detection limit.
Results: System-related parameters were similar for both ARROW and PENTA studies indicating mechanistic parameters have been captured: for example the proportion of expected thymic output being 0.10 and 0.18 respectively, which is in agreement with recent work suggesting the Bains estimate  to be high. Various extensions have been explored including a model for viral rebound in the ARROW data (time to rebound 408 days, IIV 89%CV).
Figure 1: VPC for CD4 T cell count and viral load in PENTA (treatment interruption) (A,B) and ARROW (responders) (C,D)
Conclusion: A new HIV model has been developed with a priori scaling for size and age. Future work will involve inclusion of PK data and adding genetic determinants of viral resistance.
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