A mathematical model of hepatitis C virus dynamics in patients with high baseline viral loads or advanced liver disease

Abstract

Background & aims: Patients with baseline hepatitis C virus-RNA levels (bHCV-RNA)>6 log IU/mL or cirrhosis have a reduced probability of a sustained-virologic response (SVR). We examined the relation between bHCV-RNA, cirrhosis, and SVR with a mathematical model that includes the critical-drug efficacy (epsilonc; the efficacy required for a drug to clear HCV), the infection-rate constant (beta), and the percentage of HCV-infected hepatocytes (pi).

Methods: The relation between baseline factors and SVR was evaluated in 1000 in silico HCV-infected patients, generated by random assignment of realistic host and viral kinetic parameters. Model predictions were compared with clinical data from 170 noncirrhotic and 75 cirrhotic patients.

Results: The ranges chosen for beta and the viral production rate (p) resulted in bHCV-RNA levels that were in agreement with the distribution observed in US patients. With these beta and p values, higher bHCV-RNA levels led to higher epsilonc, resulting in lower SVR rates. However, higher beta values resulted in lower bHCV-RNA levels but higher pi and (epsilonc), predicting lower rates of SVR. Cirrhotic patients had lower bHCV-RNA levels than noncirrhotic patients (P=.013), and more had bHCV-RNA levels<6 log IU/mL (P<.001). Even cirrhotic patients with lower bHCV-RNA levels had lower SVR rates. An increase in beta could explain the results observed in cirrhotic patients.

Conclusions: Our model predicts that higher bHCV-RNA levels lead to higher epsilonc, reducing the chance of achieving SVR; cirrhotic patients have lower SVR rates because of large pi values, caused by increased rates of hepatocyte infection.

Figure 1. The distribution of baseline HCV-RNA levels

(A) The predicted baseline viral load distribution from one thousand simulated patients with a range of p=0.1–6 virions/day and β=1×10⁻⁹–1×10⁻⁸ ml/day/virions (black bars) is close to the observed baseline HCV-RNA distribution in the U. S. (red line), digitized from Nainan et al.. (B) With a larger range of p=0.1–45 virions/day and the same β=1×10⁻⁹–1×10⁻⁸ ml/day/virions the predicted HCV-RNA distribution (blue bars) is skewed right from the actual distribution (red line), and with a range of p=0.1–6 virions/day and a higher infectivity rate constant, β=1×10⁻⁷–1×10⁻⁶ ml/day/virions (green bars) it is skewed to the left due to increased rates of infected cell death, δ, and HCV clearance, c (Table 3). All other model parameters (Table 1) did not significantly change the distribution of HCV-RNA values in (A) and (B) (not shown). (C) Distribution of baseline HCV-RNA in cirrhotic (brown bars) and non-cirrhotic (gray bars) patients, from the University of Illinois at Chicago.

Figure 2. Critical-drug efficacy, baseline HCV-RNA level and infection-rate constant, β

We randomly chose one thousand parameter sets within the ranges given in Table 1, except p=0.1–6 virions/day (see Figure 1). We then calculated the critical-drug efficacy (ε_c) and virus steady-state level (V̄) using Eqs. (2) and (Eq. S3 in online supplemental material), respectively, for different ranges of the infection rate constant, β. These different ranges affect the percentage of hepatocytes that are HCV-infected, as shown in Table 3, - high fraction of infected cells (filled squares), moderately-high fraction of infected cells (filled circles), and moderate fraction of infected cells (filled triangles)). Here we plot the median ε_c in groups of in-silico patients that have baseline viral loads that differ by 0.5log₁₀ HCV-RNA IU/ml, and found that this median increases as a sigmoid function of baseline viral-load. Thus, higher baseline HCV-RNA levels correlate with higher median ε_c.