Duration of an intermittent episode of viremia

Bulletin of Mathematical Biology 67 (2005) 885–900 www.elsevier.com/locate/ybulm Duration of an intermittent episode of viremia Michele Di Mascioa,b, Jerome K. Percusc, Ora E. Percusc, Martin Markowitzd, David D. Hod, Alan S. Perelsona,∗ a Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA b National Institute of Allergy and Infectious Diseases, NIH, Bethesda, MD 20892, USA c Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA d Aaron Diamond AIDS Research Center, Rockefeller University, New York, NY 10016, USA Received 4 December 2003; accepted 17 November 2004 Abstract HIV-1 infected patients after being treated with potent combinations of antiretroviral drugs for 2–6 months typically reach a state in which virus can no longer be detected within their blood. These patients with undetectable virus occasionally have viral load measurements that are above the limit of detection of current assays. Such measurements are called blips. Here we examine the possibility that such blips represent infrequent measurements taken during a period of time in which there is a transient elevation of virus in the patient’s blood, i.e., a so-called transient episode of viremia. By analyzing time series of blips from a large number of patients, we conclude that transient episodes of viremia exist and that on average they extend for a period of about 3 weeks. Published by Elsevier Ltd on behalf of Society for Mathematical Biology. Introduction In HIV-1 infected patients treated with highly active antiretroviral therapy (HAART), viral levels measured in plasma are generally suppressed below the limit of detection of current clinical assays. However, during this period of suppression, viral blips, defined as viral load (VL) measurements over the threshold of detection, are occasionally observed. ∗ Corresponding address: Theoretical Division, MS K710, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. Tel.: +1 505 667 6829; fax: +1 505 665 3493. E-mail address: asp@lanl.gov (A.S. Perelson). 0092-8240/$30 Published by Elsevier Ltd on behalf of Society for Mathematical Biology. doi:10.1016/j.bulm.2004.11.003 886 M. Di Mascio et al. / Bulletin of Mathematical Biology 67 (2005) 885–900 Since viral blips are relatively rare events, little is still known about their etiology. In principle, increases of HIV RNA levels above a threshold of detection may represent assay variation or may result from laboratory errors in specimen processing, identification, or reporting. However, a viral blip may also be an indicator of what has been called an “intermittent episode of viremia”, defined as a sustained but transient increase of plasma viral load over the threshold of detection. Because viral load measurements are made infrequently, it is difficult to distinguish between a “blip” and a transient episode of viremia. Interestingly, it has been reported that an increased frequency of blips correlates with slower decay of latently infected cells (Ramratnam et al., 2000), whose persistence has been proposed as the major hurdle to HIV-1 eradication (Ho, 1998). With viral load data collected from a relatively large set of patients successfully treated with HAART, we have recently shown that the variability in the number of viral blips observed in HAART treated patients during the period of viral load suppression below threshold cannot be explained by assuming a common probability distribution of VL amplitudes among patients (Percus et al., 2003). This argues against the hypothesis that viral blips simply represent assay variation, and leads to the conclusion that patients have different tendencies to show viral blips. Here we use these same data to examine whether viral blips are true blips or more accurately represent transient episodes of viremia which are only characterized as blips due to poor sampling. The data we analyze consist of viral load measurements from a group of 123 patients treated with 8 different regimens of HAART, obtained with an HIV-PCR assay that detects HIV-1 in plasma with a lower threshold of 50 copies/ml. After 2–6 months of antiretroviral therapy, the viral load in these patients is reduced to a value below the threshold of detection (50 copies/ml). After this period, patients usually showed VL values below threshold for a long period with occasional viral loads over the threshold, i.e., what we have defined as viral blips. This period, in which viral loads largely remain undetectable, is referred to as a period of sustained viral load suppression. We define the period of sustained viral load suppression as starting when two consecutive VL measurements below threshold occur. In most patients this period lasts for the entire period they were under observation. In the few cases in which patients show a rebound of viremia, the rebound has been eliminated from the analysis and the period of sustained suppression terminates at the last measurement preceding the onset of viral rebound. Patients were observed during the period of sustained viral load suppression for 810±468 days, sampled on average every 34±15 days for a total number of VL measurements per patient of 26 ± 15. Thus, the average time between two consecutive VL measurements is approximately 1 month, but this time is characterized by a certain variability, due to multiple unrelated logistic and clinical factors that do not affect the probability of showing blips (Di Mascio et al., 2003). However, because of this variability in the time scheduled between two consecutive VL measurements, the present analysis on the duration of an intermittent episode of viremia becomes possible. In a more recent study, we have presented an analysis of the dynamics of viral blips showing that viral blips occur substantially at random, viral blip frequency does not change with longer periods of observations and that this frequency correlates inversely with the CD4+ T cell count at the time of therapy initiation, i.e., with host specific factors