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End-stage liver disease due to hepatitis C virus (HCV) infection is the most common indication for liver transplantation in the United States.1, 2 While many patients initially appear to do well following transplantation, graft reinfection as measured by detectable serum HCV ribonucleic acid (RNA) is universal.2, 3
Serum HCV RNA decreases rapidly during and immediately after the removal of the infected liver and the implantation of the new, uninfected one.4–9 This is followed by a steady increase in viral concentrations within days.4–12 Once the new liver becomes infected—presumably by circulating virions that remain2, 6, 12 or from extrahepatic compartments13–19—hepatic viral replication resumes, causing serum HCV RNA levels to rise. Complications of interpretation may arise if the liver is also a major site of virion clearance, as has been suggested in human immunodeficiency virus-1 infection.20 The resumption of viral replication is probably hastened by the immunosuppression that accompanies organ transplantation,6, 8, 12, 16, 21–25 as significant HCV RNA increases have been observed in patients receiving steroids outside the transplantation setting.26, 27
Mathematical models have been successfully used to study the viral dynamics of human immunodeficiency virus-1 infection and responses to antiretroviral therapy.28, 29 Similar models have also been applied to hepatitis B virus infection after initiation of antiviral therapy,30, 31 and these have provided both a greater understanding of the lifecycle of these viruses, and insight into the rationale for therapy. The extension of these models to the study of viral dynamics in chronic HCV infection has been facilitated by the development of sensitive quantitative assays for HCV RNA, which have provided an accurate means of following viral replication and elimination of the virus, particularly during antiviral therapy. Frequent measurements of serum HCV RNA in the initial phases of interferon-based therapy for chronic HCV infection have also allowed mathematical modeling of viral kinetics during treatment, and provided insights into possible mechanisms of interferon resistance and the early, accurate prediction of virologic responses to therapy.32, 33 Taken together, viral kinetics studies may allow the clinician to better select, optimize, and target treatment for those patients with expected poor responses to antiviral therapy.
In the setting of liver transplantation, it is currently unknown whether the evaluation of viral kinetics and viral burden early in the postoperative period following liver transplantation will provide greater insight into disease recurrence and severity, as well as provide a rationale for treating patients according to viral and host factors. Greater understanding of the reinfection time-course, the effects of immunosuppression, the presence of extrahepatic replication as a potential source of reinfection, and the predictive value of serum HCV RNA levels could be used to optimize immunosuppressive and antiviral therapy regimens in liver transplant recipients. A recent report has analyzed in detail the viral decline during the early postanhepatic phase.34 Here we center our analyses on the kinetics of viral resurgence following liver transplantation in 6 HCV-infected patients. We use a model to show that quantitative insights can be gained into the events that follow transplantation. Our study adds new information about the kinetics of reinfection and the level of viremia attained after reinfection, and it estimates how much of the liver needs to be infected before viral resurgence is seen. Our analysis also provides support for the existence of extrahepatic sites of HCV replication.
HCV, hepatitis C virus; RNA, ribonucleic acid.
PATIENTS AND METHODS
Patients and Data Collection
The study population included 6 patients who were undergoing cadaveric liver transplantation for end-stage liver disease due to chronic HCV infection. Baseline characteristics are summarized in Table 1. The study protocol was approved by the institutional review board (Scripps Clinic) and all patients provided informed consent.
Serum samples for HCV RNA levels were collected from peripheral veins in all patients every 2 hours in the preoperative stage, every hour during the preanhepatic phase (during mobilization of the recipient's diseased liver), every 15 minutes during the anhepatic phase (removal of recipient liver), and hourly in the postanhepatic phase (following the insertion of the transplanted liver and unclamping of the porto-caval vessels) until the end of the operation. Thereafter, serum samples were obtained every 4 to 6 hours in the first 2 days postoperatively, and daily until discharge from the hospital. Following discharge, serum for HCV RNA was collected weekly for 10-12 weeks. All patients were given induction immunosuppressive therapy during the immediate preoperative period, and thereafter received an immunosuppressive regimen as indicated in Table 1.
The number of serum HCV RNA measurements ranged from 4 to 9 in the preanhepatic phase, 2 to 4 in the brief anhepatic phase, and 22 to 31 in the postanhepatic phase. All serum samples were separated within 2 hours and stored at −70°C until analysis. Serum HCV RNA was measured by a reverse transcription polymerase chain reaction assay (Superquant; NGI, Los Angeles, CA) with a lower limit of detection of 100 copies/mL as previously described.35 A value of 100 copies/mL was used in all analyses at points where HCV RNA levels dropped below the detection limit. Samples with HCV RNA levels >5,000,000 copies/mL were diluted further and quantified. HCV genotyping was performed using a line-probe assay (Inno-LiPA; Innogenetics NV, Zwijnaarde, Belgium).36
Neumann et al.33 have modeled HCV infection with the following equations:
where T is the number of target cells, I is the number of productively infected cells, and V is the viral concentration in copies/mL of serum HCV RNA. The parameter s denotes the rate at which target cells are produced and d their per capita death rate. The rate constant for de novo infection is β, and the per capita rate at which infected cells are lost is δ. The production of hepatitis C virions occurs at mean rate p per infected cell, and clearance of these virions occurs at rate c per virion.
If we assume that removal of the liver results in a complete lack of productively infected cells (that is, I = 0) during the anhepatic phase and shortly thereafter, before virion production starts in the new liver, then Eq. 3 reduces to
The value of c, then, is given by the slope of the natural logarithm of the serum HCV RNA concentration vs. time. To calculate this value, we used the data during the anhepatic phase and the first 4 hours of the postanhepatic phase, before there was time for viral production to restart.
To model the postanhepatic resurgence in viral concentration, we modified the Neumann et al.33 equations. We assumed that on the time scale of the post-anhepatic viral resurgence, the number of target cells was not substantially changed by new target cell production or death, and thus only the relatively rapid process of infection (as described by the βVT term in Eq. 1) was needed to describe changes in the number of target cells. In this scenario, Eqs. 1–3 reduce to
Using nonlinear least squares regression, we fitted the model given by Eqs. 5–7 to serum HCV RNA measurements during the postanhepatic resurgence. For each fit of the resurgence kinetics, the viral level at the start of resurgence, Vor, was fixed at the patient's final preresurgence measurement, and the clearance rate c was fixed at the value determined from the anhepatic and early postanhepatic decay slope. In patients 1, 5, and 6, we fitted the resurgence beginning with the HCV RNA minimum that followed the postanhepatic decline and immediately preceded the subsequent increase. In patients 2, 3 and 4, who had plateaus in their HCV RNA levels between the decline and increase, we fitted the resurgence starting with the last data point of the plateau.
The data could be fit with δ that was 0 to at least 3 decimal places in all patients, possibly reflecting the effects of immunosuppression on cell-mediated immune responses and the fact that over the 90 days of follow-up, the effects of a small δ are not measurable. Given this result, we removed the δI term from the model to reduce the number of parameters and improve the reliability of our parameter estimates. In addition, from viral load measurements one can not estimate the parameter p. To see this, use the new variables Ĩ = pI and T̃ = pT, and the corresponding model equations:
Fitting the viral load data to this model, we could reliably estimate 2 parameters from the resurgence data: β and pT0r, the initial condition of the new variable T̃. For these fits, the values of V0r and c were fixed at the final preresurgence measurement, as described above for the fits of Eqs. 5–7. The initial number of infected hepatocytes at the start of resurgence (I0r) is given by cV0r/p and thus Ĩ0r = cV0.
During the transplant surgery patients lose blood, and are given compensatory amounts of fluid and cells. Fluid balance was monitored for each patient during the surgery and we used the patient's chart to correct the viral concentration for blood loss and fluid input, assumed to occur mostly during the anhepatic and postanhepatic phases. Consider the total number of viral particles (VT) and total fluid volume (F) in a patient, then these quantities change according to
where ι is the fluid input rate and λ is the blood loss rate, which we assume constant during the anhepatic and postanhepatic phases. That is, we use the patient's charts to calculate the total fluid intake and blood loss and then divide these by the duration of the anhepatic and postanhepatic phases, assuming that 20% of the fluid exchanges occur between the start of surgery and the time the liver is removed, and that 80% of the fluid exchanges occur during the anhepatic and postanhepatic phases. In general, these values will differ from patient to patient, but we use this approximation because the exact times of blood loss and fluid infusion are not available. Fluid input does not change the total body viral burden, but can lower the virus concentration through dilution. Furthermore, loss of blood containing virus does not change the virus concentration but leads to a reduction in total viral burden at rate λVT. We assume V, the viral concentration, is the same in serum and other extracellular fluids and hence is given by V = VT/F. Taking into account the fluid exchanges, the viral concentration changes according to
From Eq. 12, F = F0 + (ι − λ)t, where F0 is the total body fluid at baseline, which we calculated based on the patient's weight and assuming that a 70 kg patient has a normal extracellular fluid volume of 15 L.37 As before, we assume that during the anhepatic phase the viral production term is 0, and solving Eq. 13 shows that the natural logarithm of V decreases approximately with slope −(c + ι/F0), instead of just c. The input of fluid includes the volume of plasma, cryoglobulins, saline/dextrose solution and 40% of the volume of packed red cells given to the patient. Input of cell-saver units was assumed to include virus at the same concentration as found in blood, and thus to not change the concentration of virus. We used our estimates of ι and F0 to calculate c from the viral decay slope during the anhepatic phase. It was this value of c that we used as a fixed parameter in our model fits (Eqs. 8–10).
We used linear regression to assess the relationships between continuous variables. Viral concentration slopes were calculated by linear random effects regression with HCV RNA measurements expressed in natural logarithm using SPlus (Insightful, Seattle, WA). The elimination half-life of hepatitis C virions during HCV RNA decline and HCV doubling time during periods of increase were calculated as ln(2)/slope, where ln(2) represents the natural logarithm of 2. Confidence intervals (95%) were obtained with bootstrap resampling using 500 simulations. Results are presented as mean ± standard deviation.
In most patients, HCV RNA levels decreased rapidly during and after transplantation and subsequently began to increase—reaching above pretransplantation levels in all but 1 patient (patient 5)—within a few days of the procedure (Fig. 1). During the anhepatic phase, which ranged from 28 to 53 minutes, and early graft reperfusion (less than 4-hour postanhepatic phase), serum HCV RNA levels decreased in all 6 patients by an average of 1.0 log10 ± 0.52 log10. The mean decay slope during this phase was −0.99 ± 0.18 per hour (Table 2). We then estimated the clearance rate, c, by correcting these slopes for the average fluid input rate during this period (see Patients and Methods). The mean value of the virion clearance rate (c) was estimated as 0.87 ± 0.15 per hour (mean t1/2 = 0.82 hours) (Table 2).
Table 2. Slopes and Half-Lives/Doubling Times of Serum HCV RNA Changes
Serum HCV RNA concentration continued to decline rapidly up to 23 hours into the postanhepatic phase (Table 3), with a mean decrease of 1.6 log10. The mean decay slope during this period was −0.23 ± 0.08 per hour, and the mean viral elimination half-life was 3.4 ± 1.3 hours (Table 2). In patients 2 and 4, this decline was followed by a plateau in serum HCV RNA levels before they began to rise again; in these patients, serum HCV RNA slopes were nearly 0 for 6 to 34 days after the postanhepatic decline ended (Fig. 1; Table 3). Similarly, patient 3 experienced a plateau between days 2 and 7, although this plateau followed a brief initial increase in HCV RNA levels after the decline (Fig. 1).
Table 3. Duration of the Different Postanhepatic Phases and Estimated Viral Load and Infected Cell Percentage at Steady State
HCV RNA concentration increases following the initial postanhepatic decline were dramatic, ranging from 1.4 log10 to 6.0 log10, and reached a steady state higher than the pretransplantation level in patients 1, 2, 3, 4, and 6 within 4 to 82 days (Fig. 1; Table 3). These new steady states were between 1.4 and 450 times higher than the mean preanhepatic serum HCV RNA levels. Interestingly, patients with higher baseline viral loads reached the posttransplantation steady state faster (p = 0.04). During the postanhepatic viral resurgence, the mean slope was 0.77 ± 0.64 per day, and the mean HCV RNA doubling time was 2.0 ± 2.0 days (Table 2). If we consider only those patients with at least a 2 log10 increase during the first week after transplantation, as has been done previously,6 we obtain a doubling time of 18.6 ± 11.8 hours.
Our model of posttransplantation HCV dynamics, given by Eqs. 8–10, provided a good description of the postanhepatic viral resurgence, as illustrated by the fit of each patient's resurgence data to the model (Fig. 2). We fixed c at the values estimated above, and used the posttransplantation data to estimate, via nonlinear least-squares regression, the de novo infection rate constant (β) as 1.5 × 10−6 ± 2.6 × 10−6 mL/virion/day, with relatively small 95% confidence intervals for each patient obtained from bootstrap resampling (Table 4). As explained in Patients and Methods, the other parameter estimated was the product pT0r. The number of virions produced per infected cell (p) is not known in humans. But the difficulty in detecting HCV replication intermediates in the liver, by immunoblot, in situ immunochemistry, and other techniques, indicates that p should be small.38 In addition, a recent study of HCV primary infection in chimpanzees also estimated small values for p (range 0.1-300 virions/cell/day) in this animal model.39 If we assume that p = 100 virions/cell/day, then we can estimate that the number of hepatocytes susceptible to infection (T0r) is about 7 × 1010 and the corresponding number of infected hepatocytes (I0r) is 2.6 × 107, before resurgence (Table 4). These results are consistent with the results in Table 3, where, by solving Eqs. 8–10, we estimate that essentially all these target cells are infected at steady state. We note, however, that in the model given by Eqs. 8–10, steady state is reached when all target cells are infected. It is important to note that although the sum of infected and target cells estimated by our model (mean 6.8 × 1010) at the beginning of resurgence (Table 4) is smaller than the total number of hepatocytes estimated to be in the average liver (2 × 1011),40 it is likely that only a fraction of hepatocytes are susceptible to HCV infection.40 Thus, we would expect the model estimate to be smaller than the total number of liver hepatocytes. With p = 100 virions/cell/day, we can estimate that the number of target cells (i.e., infected cells at steady state), based on the donor liver's weight,40, 41 can be anywhere between 0.2 and 90% of total hepatocytes, with an average of 19% (Table 3).
Table 4. Initial Serum HCV RNA Concentration and Estimated Parameters for Postanhepatic Resurgence
NOTE: T0r and I0r = cV0r/p calculated for p = 100 virions/cell/day.
Mean ± SD
7031 ± 12265
68 ± 131
26 ± 44
15 ± 26
An important result of our model, however, is that since pT0r must be constant, if p is smaller than 100 then T0r has to be proportionally larger. At most, all hepatocytes are potential targets for infection and p is then at a minimum. From our average value for liver size and average c, we can calculate that the minimum estimate for p consistent with our data is approximately 18 virions/cell/day. For this minimum p, and the estimated values of c and measured V0r, we calculate that the average maximum I0r (=cV0r/p) is 1.5 × 108 hepatocytes; that is, about 0.06% of the hepatocytes in the liver are infected at the time viral resurgence is observed to begin. Correspondingly, at steady state the whole liver would be infected.
The patterns of viremia decline and increase observed in the current study are consistent with previous studies in liver transplant recipients.4–12 Viremia dropped rapidly during and after transplantation, and then began to rise as early as 1 day later (15 hours in patient 1). The mean anhepatic decline of 1.0 log10 ± 0.52 log10 was larger than previously reported.6 We were interested in the decay of viral load before the new liver started producing virions, and as such we calculated the decay over the first 4 hours of anhepatic phase and graft reperfusion, whereas in the previous report the authors considered only the anhepatic phase.6 The subsequent mean decline of 1.6 log10 during the first 2 to 23 hours of the postanhepatic phase was similar to the decrease of 1.5 log10 observed by Garcia-Retortillo et al.6 during the first 8 to 24 hours after transplantation.
The fact that HCV RNA falls to ∼1% of its initial level (i.e., declines by ∼2 log10) 24 hours postanhepatic phase (Fig. 1) suggests that at least 99% of HCV is produced in the liver. However, if we take into consideration the dilution effects of fluid input during the anhepatic and postanhepatic phases, we estimate HCV RNA falls to about 4% (a decline of 1.8 log10) of its initial value due to lack of viral production, indicating that a minimum of approximately 96% of this production occurs in the liver. However, the observation that HCV RNA does not simply continue to decline and become undetectable indicates that either infection of the new liver starts extremely rapidly or that virus production by extrahepatic sources or leakage from extrahepatic reservoirs, such as the surfaces of follicular dendritic cells,42 provides a continuing low level of HCV RNA. In 3 patients (patients 2, 3, and 4) there was a plateau in HCV RNA levels before viral resurgence occurred (Fig. 1A; Table 3), consistent with a low rate of viral production, possibly extrahepatic. Indeed, Dahari et al.34 found, by modeling the early postanhepatic phase, that any extrahepatic compartments would be responsible for approximately 3% of virus in circulation. The exact nature of these extrahepatic sites is unknown, but peripheral blood mononuclear cells have been suggested as likely candidates.43, 44
From the kinetics of viral decline, we estimated that the free virion half-life was 0.8 ± 0.2 hours during the anhepatic and early postanhepatic phase, much faster than the 2.2-hour estimate of Garcia-Retortillo et al.6 and the estimate of 2.7 hours obtained under interferon treatment.33 Our estimated free virion half-life is also faster than the fastest half-life obtained by plasma apheresis (1.7 hours).45 This observation may indicate that the initial viral decay in plasma after the liver is grafted and reperfused is partially due to liver uptake of virions; however, this has to be confirmed in a larger sample of patients. Consistent with this observation, experiments following the fate of radiolabeled simian immunodeficiency virus injected into rhesus macaques indicated that the liver was a major site of virion deposition.20
After this rapid initial decline, viral clearance slows, possibly due to the filling of absorption sites in the newly grafted liver. The calculated post-anhepatic decline slope of −0.23 ± 0.08 per hour and elimination half-life of 3.4 ± 1.3 hours are quite similar to the −0.34 per hour slope and 3.4-hour half-life reported by Garcia-Retortillo et al.6 By comparison, Fukumoto et al.4 reported a longer half-life of 4.0 hours; however, this half-life was calculated from decay in both the anhepatic and postanhepatic phases.
Our results provide further evidence that HCV can replicate rapidly in the posttransplantation, immunosuppressed patient. Analyzing the kinetics of viral resurgence, we estimated that the mean HCV RNA doubling time was 2.0 ± 2.0 days. However, if we consider only the first week posttransplantation and those patients with at least a 2 log10 increase, we obtain a doubling time of 18.6 ± 11.8 hours, consistent with the 13.8 hours reported by Garcia-Retortillo et al.6 for the same time period and patient group. Interestingly, the HCV doubling time in the early phase of primary infection, measured in chimpanzees, was about 12 hours in one study,39 in agreement with the early reinfection kinetics in the setting of liver transplant, but it was slightly faster (6-9 hours) in another study.46
We found in all but one patient (patient 5) that posttransplantation viral concentrations exceeded pretransplantation levels within 4 to 55 days of transplantation, in general agreement with previous reports.4, 7, 21 Within the context of our model, one possible explanation for the higher posttransplantation viral concentration is that the number of hepatocytes in the damaged, pretransplantation liver might be lower than in the new liver. This is consistent with the estimated sizes of the donor livers, which were 4 to 131% larger than the explants (Table 1). Under these circumstances, the new liver should be able to support higher levels of viral replication. Additionally, as immunosuppression has been shown to increase viral levels in HCV patients,26, 27 it is possible that the higher posttransplantation levels are partly attributable to the immunosuppressive therapy given following transplantation.
By characterizing viral dynamics during the postanhepatic resurgence, we were also able to determine the infected-cell fraction at the viral steady state that occurs after the graft has been infected, Iss. This estimate depends on our choice of p, the viral production rate, but for p = 100 virions/cell/day, we estimate that an average of 19% (range of 0.2-90%) of hepatocytes are productively infected at steady state. This is consistent with, but perhaps slightly smaller than, estimates of 6 to 95% obtained previously by immunohistochemistry or in situ hybridization in liver transplant patients.47, 48
In all 6 patients, viral decline ended within 24 hours posttransplantation. In 3 patients, viral resurgence began during this first day, and in 2 of the remaining 3, resurgence began within the first week. All but one patient (patient 2) reached a postanhepatic viral steady state within 55 days, and in all but one patient (patient 5), the posttransplantation viral load exceeded the pretransplantation level. These results, in addition to our estimate that viral resurgence begins when much less than 1% of the engrafted liver's hepatocytes are infected, suggest that antiviral therapy should begin soon after, or before, transplantation in order to prevent or delay reinfection.
Our estimated values of the rate constant for de novo infection, β, varied considerably among patients (Table 4), possibly reflecting host factors or the presence of different viral quasispecies in different patients. It is interesting that patient 4, who seems to be an outlier having a very small β = 7 × 10−9 mL/virions/day and, by far, the largest percentage of infected cells at steady state (90%), is also the patient with the highest level of posttransplantation virus at steady state (8.6 × 107 virions/mL). Significantly, our estimated values for the infection rate were of the same order as those estimated in the chimpanzee model during primary infection.39 We also estimated that the loss rate of infected cells, δ, during the postanhepatic viral resurgence was 0, suggesting that immunosuppressive therapy prevented cell-mediated immune responses against the newly infected liver. This conclusion needs to be tempered by the observation that in the model used to estimate δ (Eqs. 5–7), a postresurgence viral steady state can only occur if δ = 0. Thus, in the context of this model the observation of a postresurgence steady state supports the conclusion that little infected cell loss occurs with immunosuppressive therapy. However, if the full Neumann et al.33 model or similar models49 that include a source of uninfected cells are used, then a postresurgence steady state can be obtained with δ ≠ 0. Thus, if, as seen in primary infection of chimpanzees,39 liver regeneration or noncytolytic cure of infected cells were a substantial factor during the postanhepatic resurgence period, our conclusion that δ = 0 would need to be reevaluated.
There are a few limitations in this study, including the small number of patients and resulting variability in parameter estimates. Additionally, parameter estimates obtained from our model are most realistic if the HCV RNA level in blood is indicative of the replication events occurring in the liver. Finally, since we have used a single-compartment model, which does not separately account for liver and extrahepatic sites of viral replication, any contribution of virions from the latter has not been considered. Others have reported that a 2-compartment model is needed to describe the preresurgence viral plateaus and slower viral declines in the postanhepatic phases,34 as observed in some patients (e.g., our patients 2, 3, and 4). Nevertheless, the rapid HCV RNA decline in the anhepatic phase, followed by the postoperative increase observed in several patients of this study and others, suggest that the liver is the primary site of viral replication, with at most small contributions from extrahepatic sites. Additionally, our single-compartment model provided a good description of the postanhepatic resurgence—whether or not it is preceded by a plateau—as well as the anhepatic and postanhepatic declines.
In summary, we have described HCV kinetics during and after cadaveric liver transplantation. In both the anhepatic phase and the postanhepatic resurgence, our model described viral dynamics well, and allowed us to estimate fundamental viral-kinetic parameters. We used the model to estimate at less than 4% the contribution to viral load of any putative extrahepatic source, in agreement with previous estimates.34 In addition, we estimated the number of infected and target cells at the start of the posttransplantation viral resurgence, as well as the number of infected hepatocytes at the subsequent viral steady state. Our analysis also suggests that loss of infected cells is negligible during the 3-month postanhepatic follow-up period, consistent with immunosuppression effectively preventing an immune response against infected liver cells. Continued work toward elucidating extrahepatic replication, the time-course of reinfection, the effects of immunosuppressive therapy, and the relationships among viremia, infection, and liver damage will be beneficial in optimizing treatment for HCV patients undergoing liver transplantation.
R.M.R. thanks R. May for comments on the manuscript and the Department of Zoology, University of Oxford, South Parks Road, Oxford, UK, for generous hospitality during parts of this work.