Understanding early serum hepatitis D virus and HBsAg kinetics during pegylated interferon-alfa therapy via mathematical modeling

Abstract

There is little information on the early kinetics of hepatitis delta virus (HDV) and hepatitis B surface antigen (HBsAg) during interferon-α therapy. Here a mathematical model was developed and fitted to frequent HDV and HBsAg kinetic data from 10 patients during the first 28 weeks of pegylated-interferon-α2a (peg-IFN) therapy. Three patients achieved a complete virological response (CVR), defined as undetectable HDV 6 months after treatment stopped with loss of HBsAg and anti-HBsAg seroconversion. After initiation of therapy a median delay of 9 days (interquartile range IQR:[5;15]) was observed with no significant changes in HDV level. Thereafter, HDV declined in a biphasic manner, where a rapid first-phase lasting for 25 days (IQR:[23;58]) was followed by a slower or plateau second-phase. The model predicts that the main effect of peg-IFN is to reduce HDV production/release with a median effectiveness of 96% (IQR:[93;99.8]). Median serum HDV half-life (t_1/2) was estimated to 2.9 days (IQR:[1.5;5.3]) with pretreatment production and clearance of about 10¹⁰ (IQR:[10^9.8-10^10.8]) virions/day. None of the patients with flat 2^nd phase in HDV achieved CVR. HBsAg kinetics of decline paralleled the second-phase of HDV decline consistent with HBsAg-productive-infected cells being the main source of production of HDV, with a median t_1/2 of 135 days (IQR:[20-460]. The interferon lambda-3 polymorphism (rs12979860) was not associated with kinetic parameters.

Conclusions

Modeling results provide insights into HDV-host dynamics, the relationship between serum HBsAg levels and HBsAg-infected cells, IFN's mode of action and its effectiveness. The observation that a flat second phase in HDV and HBsAg kinetics was associated with failure to achieve CVR provides the basis to develop early stopping rules during peg-IFN treatment in HDV-infected patients.

Introduction

Hepatitis D virus (HDV) is a single-stranded, circular RNA genome that was identified in 1980 as an infectious agent causing hepatitis in persons who are infected with hepatitis B virus (HBV) (1). HDV infection is the most severe form of chronic viral hepatitis in humans (2-4), with an accelerated course of liver disease compared to chronic monoinfection with HBV (5). It is estimated that 15-20 million persons worldwide are chronically infected with HDV, i.e., about 5% of the HBV infected population (6). Hepatitis B surface antigen (HBsAg) encapsidates HDV RNA, forming the viral envelope (7). As such, HDV is a defective virus that depends on HBV envelope protein to enter hepatocytes and assemble new HDV particles. At least 8 different HDV genotypes have been described (8), with genotype 1 being the most common in many areas of the world.

Treatment of HDV infection has been notoriously difficult. Treatment with interferon-based therapies can achieve HDV RNA negativity in approximately 25% of patients (9-12). However, the more definite and durable end point of HDV RNA negativity together with loss of HBsAg, equivalent to HDV eradication, is even more difficult to achieve. Monotherapy with nucleos/tide analogues such as adefovir, lamivudine or ribavirin are not effective in treating HDV and have not been shown to significantly improve complete virological response (CVR) rates when combined with (peg)-IFN compared to (peg)-IFN alone (10, 12, 13).

Mathematical modeling of viral kinetics aims to understand and quantify the biological mechanisms that govern the changes in the viral load and related biomarkers that occur with antiviral therapy. Mathematical modeling provided estimates of key viral and host parameters in viral infections including HIV (14-16), HBV (17-19) and HCV (20) as well as giving valuable insight into the modes of action of antiviral agents. For HCV, which like HDV is a single stranded RNA virus that causes chronic infection and can be eradicated by treatment, viral kinetic parameters showed a high predictive ability for treatment outcome and can be used to individualize treatment duration (21-24).

Here we analyzed data from a clinical trial in which patients with chronic HBV and HDV were treated for up to 260 weeks with peg-IFN. Frequent blood samples were performed in the first 28 weeks following initiation of peg-IFN, allowing for precise characterization of the early dynamics of serum HDV RNA and HBsAg in treated patients. A dual model for HDV and HBsAg was developed to estimate key parameters of HDV and HBsAg dynamics, including peg-IFN effectiveness in blocking HDV production and/or release from infected cells, serum HDV half-life, and HBsAg-infected cell half-life.

Patients and Methods

Below is a brief description of patients and methods. More details on patients, study design, virological and genetic assays can be found in Heller et al (25).

Patients

Data were obtained from 12 patients (out of 13), with confirmed HDV genotype 1, who participated in a clinical trial (#NCT00023322) of long-term treatment (up to 260 weeks) of HDV with pegylated IFNα-2a (peg-IFN). Baseline characteristics of the study population are provided in Table 1. Patients were treated with a fixed dose of 180 μg of peg-IFN monotherapy weekly during the first 28 weeks of therapy, following which dose increases or reductions (for efficacy or safety, respectively) were allowed (25). Two patients had a treatment interruption, between week 4 and 10 (pt 1) and between week 19 and 21 (pt 8).

Table 1. Baseline patient characteristics.

	Gender	Race	rs12979860 genotype	Liver stage	Age (years)	Time infected (years)	Baseline HDV RNA (logGE/ml)	HBeAg	Baseline ALT (fold the UNL)	Baseline HBsAg (LogIU/ml)	Baseline HBV DNA (Log IU/ml)	Treatment duration (months)
1*	F	C	CC	3	53	27	4.8	Neg	41(2.2)	2.9	3.5	10
2*	M	C	---	3	45	28	6.9	Neg	48 (1.6)	3.2	UD	8
3	F	C	---	3	32	26	6.8	Neg	31 (1.6)	4.2	UD	1
4	M	C	CT	6	44	35	6.2	Neg	296 (9.9)	4.2	<2	70
5*	M	AA	CT	3	48	UN	6.8	Neg	206 (6.9)	4.0	2.7	60
6**	M	C	CT	4	58	34	4.5	Neg	42 (1.4)	2.6	UD	20
8**	M	C	CC	3	20	UN	7.3	Neg	84 (2.8)	4.3	<2	65
9	M	C	CT	4	47	UN	6.5	Neg	506 (16.9)	3.8	2.5	62
10	M	C	CC	3	46	25	6.9	Neg	107 (3.6)	4.3	UD	92
11	M	C	CC	3	44	7	8.0	Pos	59 (2.0)	4.0	2.9	35
12	M	C	CT	4	18	UN	7.6	Pos	185 (6.2)	4.3	2.1	62
13	M	C	CC	6	49	14	8.5	Pos	172 (5.7)	3.5	4.9	12
Mean± SD					42 ±12	24 ±9	6.7 ±1.1		148 (5.1) ±134 (4.4)	3.8 ±0.6	2.6 ±0.9	41±29

^*Complete virological response, CVR;

^**Viral response and breakthrough; UNL, upper normal limit of ALT (19 U/L for women and 30 U/L for men); C, Caucasians, AA, African Americans; UN, unknown; UD, less than 95 IU/ml.; Liver Stage –Ishak scale (0-6) for baseline biopsy. Note that patient no. 7 who was infected with non-genotype-1 HDV was excluded here.

Virological and genetic assays

HDV-RNA levels were measured by a real-time PCR assay (National Genetics Institute, Los Angeles, CA) with a lower limit of quantification (LOQ) of 100 genome equivalents per ml (GE/ml). HBsAg levels were measured with the Roche Cobas HBsAg quantitative assay, with a lower limit of detection of 0.055 IU/ml. The interferon lambda 3, IFNL3 (formerly called IL28B) associated single-nucleotide polymorphism, SNP, rs12979860 was determined in 10 patients using TaqMan genotyping assay (Table 1).

Blood samples

Frequent HDV-RNA, HBV-DNA, ALT and HBsAg levels were measured at times 0, 6h, 12h and 18h during the first day of peg-IFN treatment, at days 2, 3 and 7 and at weeks 2, 3, 4, 8, 12, 16, 20, 24 and 28. The viral kinetic analysis was limited to the first 28 weeks of treatment.

Mathematical modeling of viral kinetics

Serum HDV RNA levels declined during the first 28 weeks of peg-IFN therapy in a biphasic manner similar to what has been observed during antiviral therapy in some HBV monoinfected patients (19, 26) and HCV-infected patients (22, 27) treated with IFN-based therapy. In addition, serum HBsAg kinetics was associated with the 2^nd phase kinetics of serum HDV RNA (see Results). Based on these observations we developed a dual model that coupled HDV RNA and HBsAg kinetics:

$$\{\begin{array}{c}dI/\mathit{dt}=\beta (1-\theta )V{T}_0-\delta I\\ dV/\mathit{dt}=p(1-\varepsilon )I-cV\\ dH/dt=p_{H}I-c_{H}H\end{array}$$ (Eq.1)

where t is time elapsed since treatment initiation, I represents HBsAg-infected cells, i.e., cells that can synthetize HDV virions, V is serum HDV level and H is serum HBsAg level. T₀ is the number of target (or susceptible) cells, namely HBsAg-productive cells that could be infected with HDV. Similar to previous modeling efforts (26), we assume that T₀ was constant during the first 28 weeks of therapy and equal to its pre-treatment steady state value cδ/βp. Parameter p is the daily rate of HDV virion production per infected cell, and c and δ are the clearance and loss rates of serum HDV RNA and productively HBsAg-infected cells, respectively. HBsAg-infected cells produce, on average, p_H HBsAg particles per day and are cleared from the serum with rate constant c_H. Treatment is assumed to be effective after a time t₀ and slows viral production and/or release with an effectiveness noted ε, i.e., during treatment the viral production/release can be reduced from p to p(1- ε). Of note, IFN may also act by limiting cell infection with effectiveness θ. However this mode of action, if it occurs, has only a minimal effect on viral decline as long as ε>0.9 and cannot be estimated (20). Thus for simplification we set θ=0. Importantly HDV RNA viremia was previously found to be stable with minor fluctuations over periods of weeks to months in the absence of treatment (28). Assuming that HDV and HBsAg are in equilibrium before treatment initiation, the model can be simplified and p_H=p·H₀/c·V₀ where H₀ and V₀ are the initial levels of serum HBsAg and HDV, respectively. Additional information on model parameters and data fitting is provided in the Supplementary Material File.

Statistical Methods

Statistical analysis was performed with IBM SPSS V.21. Continuous variables were compared using the non-parametric Mann-Whitney U-test. Categorical variables were compared using a 2-tailed Fisher exact test. The non-parametric Spearman Test was used assess the relationship between continuous variables. In all cases a p-value ≤0.05 was considered significant.

Results

Patients' baseline characteristics

Most patients were male (10/12), non-Hispanic white (11/12), between 40 and 60 years old (9/12) and had negative HBeAg (9/12) (Table 1). All patients had detectable and high levels of baseline HDV RNA with mean 6.7±1.1 log₁₀ GE/mL. The mean baseline ALT level was 148±134 U/L with 5 patients having levels greater than three times the upper limit of normal. The mean baseline HBsAg level was 3.8±0.6 log₁₀IU/mL. HBV DNA was <5 log₁₀ IU/ml in all patients and below the LOQ in 6 patients. Five patients had rs12979860 CC genotype and 5 had CT genotype.

Treatment outcome

Treatment was administrated for a mean duration of 142±105 weeks, median 111 [range 6–260] weeks (Table 1). Three patients achieved CVR: two patients (patients 1 and 2) had a rapid virologic and biochemical response and were treated for less than a year (41 and 32 weeks, respectively) while in one patient (patient 5) undetectable HDV was achieved after 3.5 years of treatment with an overall treatment duration of 4.5 years. Patient no. 6 achieved undetectable HDV RNA at week 20 but experienced an on treatment breakthrough 4 weeks later; Patient no. 8 achieved HDV negativity after 4 years of treatment without loss of HBsAg. More details on treatment outcome can be found in (25).

Early HBV DNA and biochemical response to treatment

All 6 patients having a baseline ALT greater than three times ULN had a reduction of ALT to less than three times ULN by week 8. The HBV DNA kinetic data were limited, precluding a joint HDV and HBV modeling approach (see Fig. S2). Of the 12 patients in the study, at baseline 6 had HBV-DNA below quantitation limit, another 4 had HBV-DNA < 1×10³ IU/ml and only 2 had HBV-DNA > 1×10³ IU/ml. Of the latter, one patient became non-quantifiable 24 hours after starting IFN and remained so for the duration of the study, while the single patient with HBV-DNA > 1E4 (Pt13) was started on tenofovir at the same time (Fig. S2).

Early HDV RNA kinetics

In the ten patients for whom HDV kinetics could be characterized (see methods), a delay of several days was observed in all patients before HDV RNA load declined significantly from baseline levels. HDV RNA declined in a biphasic manner with an initial rapid viral decline followed by a slower second phase of viral decline (Fig. 1).

Figure 1. Data fitting using the dual model for HDV and HBsAg (Eq. 1).

Black and grey circles represent observed HDV RNA and HBsAg, respectively, and black and grey lines represent the best curve fits of the dual model.

HBsAg kinetics

In the aforementioned ten patients serum HBsAg kinetics were monophasic (i.e., linear) during the first 28 weeks of treatment. In seven cases (patients 4, 5, 8, 9, 11, 12 and 13) the slope was extremely slow or flat, i.e., HBsAg remained at approximately baseline levels (Fig. 1 and Table S1). In the three remaining patients, a significant decline of HBsAg was observed after a delay of several days following treatment initiation (patients 1, 2 and 6). In all 10 patients, HBsAg kinetics paralleled the second phase slope of HDV DNA (Fig. 1).

Significant association between death/loss of HDV producing cells and serum HBsAg decline

The relation between HBsAg kinetics and the HDV 2^nd phase was evaluated by fitting HDV and HBsAg to uncoupled biphasic and monophasic models, respectively (Eqs. S3 and S4, respectively, Table S1). The estimated slope of the HBsAg decline, η, was significantly associated with the rate of the 2^nd phase of the HDV RNA decline, λ₂ (P=0.0002; Fig S1).

Modeling HDV and HBsAg kinetic parameter values

The relation between η and λ₂ suggests that the reduction of both HBsAg and HDV (during the second phase of HDV kinetics) is due to the progressive decrease in the number of HDV producing cells (or HBsAg-infected cells). This association can be captured using the viral kinetic model Eq.1 in which HDV and HBsAg kinetics are coupled and simultaneously fitted. The model fits the observed HDV RNA and HBsAg kinetics (Fig. 1, solid lines) as described in the following section.

HDV and HBsAg kinetic parameters estimation

A median pharmacological delay, t₀, of 8.5 days (with interquartile range, IQR: [5-15 days]) was estimated before peg-IFN led to a visible decline of HDV RNA level. Thereafter, a first phase rapid decline of HDV RNA, λ₁, with a median slope value equal to 0.73 log/mL/week (IQR: 0.4; 1.4) and lasting for a median duration of t_r=25.2 days (IQR: 22-57) was estimated (Eq. S2). The median effectiveness of peg-IFN in blocking HDV production and/or release, ε, was estimated as 96.2% (IQR: 93-99.8). Further, the median serum clearance rate of HDV, c, was equal to 0.24 d^-1 (IQR: 0.1-0.5), which translates into a viral half-life, t_1/2, of ln(2)/0.24=2.9 day (IQR: 1.5-5.3), with pretreatment production and clearance of about 10¹⁰ (IQR:[10⁷-10¹⁰]) virions/day (Table 2).

Table 2. HDV RNA and HBsAg kinetic parameter estimates obtained using 28 weeks of treatment data.

Pat #	V0 [LogGE/ml]	H0 [Log IU/ml]	t0 [d]	c [d-1]	ε [%]	δ [d1]	HDV Production& [GE/day]	λ1 [log/mL/week]	λ2 [log/mL/ week]	tr [d]
1*	4.6 [4.4-4.7]	2.9 [2.8-3.0]	10 [0-19.6]	0.21 [0-0.47]	93.0 [87.2-98.8]	0.042 [0.038-0.046]	108.03	0.65	0.12	22.3
2*	6.7 [6.31-7.03]	3.2 [3.0-3.3]	6.3 [0-14.8]	0.23 [0.09-0.37]	99.9 [99.7-100]	0.069 [0.063-0.075]	1010.16	0.70	0.21	44.7
4	6.1 [5.95-6.21]	4.1 [4.1-4.2]	15	0.25 [0.03-0.47]	87.0 [80.8-100]	0.001#	109.6	0.76	0.003	22.6
5*	7.1 [6.91-7.23]	4.0 [3.9-4.1]	14.8 [11.2-18.3]	0.34 [0.02-0.66]	93.0 [88.8-97.2]	0.0065 [0.0025-0.010]	1010.72	1.03	0.018	22.4
6**	4.6 [4.3-5.0]	2.7 [2.4-2.9]	26.5 [0-71.3]	1.44 [0-30]	87.0 [65-100]	0.046 [0.026-0.066]	108.91	4.40	0.12	27.8
8**	7.4 [7.1-7.7]	4.70 [4.4-5.0]	14.5 [0-45.9]	0.092 [0-0.18]	99.9 [99.8-100]	0.014 [0.004-0.024]	1010.51	0.28	0.043	98.8
9	7.4 [7.3-7.6]	3.8 [3.7-3.9]	4.71 [0-16.3]	0.092 [0.058-0.13]	99.8 [99.6-100]	0.0030 [0.001-0.005]	1010.51	0.28	0.009	73.8
11	8.4	4.0 [4.0-4.1]	1.5	4.30 [0-9.0]	96.3 [85-100]	0.001#	1013.15	13.07	0.003	2.3
12	7.1	4.4 [4.3-4.5]	5.0	0.11 [0.09-0.13]	99.8 [99.7-99.9]	0.001#	1010.26	0.33	0.003	61.5
13	7.6 [7.1-8.0]	3.4 [3.3-3.6]	7.0	0.5	96 [89.6-100]	0.0037 [0-0.018]	1011.38	1.52	0.011	13.4
Median (IQR)	7.1 (6.2-7.4)	3.9 (3.2-4.1)	8.5 (5.3-14.7)	0.24 (0.13-0.46)	96.2 (93.0-99.8)	0.0051 (0.0015-0.035)	1010.4 (109.82-10108)	0.73 (0.41-1.40)	0.015 (0.005-0.098)	25.2 (22.3-57.5)

^*CVR patients;

^**, Viral response and breakthrough; IQR: interquartile range Q1-Q3;

^#minimal fixed value;

^&, see supplementary material for the estimation of HDV production; t₀, delay before HDV declined from baseline levels; c, HDV RNA clearance rate in serum; ε, peg-IFN effectiveness in blocking production and/or release of HDV from infected cells; δ, death/loss rate of HBsAg-infected cells; HDV RNA decline is biphasic with slopes λ₁ and λ₂ whereas HBsAg decline is monophasic with slope λ₂ (Eq. S1); t_r: time of transition between the 1^st and 2^nd phase of HDV decline (Eq. S2); V₀, baseline HDV level, H₀, baseline HBsAg levels; [ ], 95% confidence interval; where confidence interval is not shown, for the sake of identifiability the parameter was fixed to the best fit. Note that kinetic data from patient no. 3 who discontinued treatment at week 6 and patient no. 10 who was a complete non responder (<0.5 log10 HDV reduction from baseline), were not fit to Eq. 1 (Fig. 1).

The long-term viral and HBsAg decline slope, λ₂, was modest with a median value of 0.015 log/mL/week (IQR:0.0050-0.098). This decline was due to the progressive reduction of infected cells that are lost at a rate δ with a median value of 0.0051 d^-1 and large interpatient variability (IQR: 0.0015-0.035). This translates into a median HBsAg-infected cell half-life of about 135 days (IQR:20-460).

Finally, mean parameters t₀ (8.25 vs 13.2 d in CC and CT patients, respectively), c (0.36 vs 0.25 d^-1), ε (96.1% vs 93.0 %), and δ (0.0089 vs 0.0030 d^-1) were not significantly (all P-values >0.3) different between patients with IL28B CC allele (n=4) and patients with IL28B CT allele (n=5).

Early kinetics and treatment outcome

We examined whether HDV and HBsAg early kinetics were predictive of treatment outcome. The five patients (1, 2, 5, 6, and 8) who reached HDV negativity had significantly (p=0.008) faster HBsAg decline slope, λ₂, compared to the remaining patients who did not reach HDV negativity (median 0.102 vs 0.003 log/mL/week, respectively). Among the three patients who had a λ₂ > 0.1 log/mL/week, two achieved CVR after less than a year of treatment (patients 1 and 2). This rapid second phase of viral decline was mostly due to a high loss rate of infected cells rather than to a high antiviral effectiveness (Table 2). Interestingly three patients (patients 8, 9 and 12) had greater than 99% effectiveness in blocking viral production (see parameter ε in Table 2) but yet did not achieve a rapid second phase of viral decline or CVR, which reflects the lack of association between ε and λ₂ (or δ; not shown). None of the 5 patients with extremely slow (or flat) 2nd phase slope of HDV ie., λ₂<0.018 log/ml/week (i.e., patients 4, 9, 11, 12 and 13) achieved CVR; λ₂<0.018 had 60% positive and 100% negative predictive values for CVR (with 100% sensitivity and 71% specificity).

Discussion

The current study provides the first detailed kinetic analysis of HDV during peg-IFN therapy and provides new information about HDV infection and treatment. After a delay of several days, HDV RNA levels decline in a biphasic pattern with a first rapid viral decline phase lasting for 2 days to 14 weeks, followed by a slower second phase decline or a new lower viral plateau. In contrast, HBsAg had a monophasic linear decline (or plateau) with a slope that paralleled the second phase of HDV RNA decline (or plateau). Interestingly, in patients who had a 2^nd phase of viral decline (not a plateau) the decline in HBsAg began approximately at the time the 2^nd phase HDV decline started.

The kinetic data were fit to a viral dynamic model inspired by previous studies of HBV and HCV (17-19, 29). This approach provided new insights into the host/viral interactions. Frequent sampling of HDV and HBsAg allowed for the estimation of HDV-host-drug parameters using mathematical modeling. Novel insights into HDV dynamics during treatment included the peg-IFN effectiveness in blocking HDV production/release (median ε=96%) and of the serum HDV clearance rate, c. We found a median value for c of 0.24 d^-1, corresponding to a half-life of HDV particles in serum of about 2.9 days. The estimated virus half-life implies a production and elimination of about 10¹⁰ virions per day during HDV-chronic infection. This rate is somewhat lower than the 10¹¹-10¹² virions produced and cleared in individuals with chronic HBV monoinfection, HIV or HCV (14). Previous data regarding HDV kinetics are limited. A study by Manesis et al. included only monthly measurements of HDV RNA and HBsAg, precluding a detailed kinetic analysis (30).

The finding of the current study that the decline of HBsAg paralleled the second phase of HDV RNA kinetics suggests a common mechanism of clearance. Here we obtained a very good fit to the data by assuming in the model that HBsAg-productive infected cells were the main site of HDV RNA production. This assumption is consistent with the fact that HDV is a defective virus that requires HBV envelope proteins to enter hepatocytes and assemble new HDV particles. In the framework of the model, the effectiveness of Peg-IFN rapidly reduces HDV RNA viremia during the first phase of viral decline. With less virus in circulation, there is less de novo infection of susceptible hepatocytes during treatment than at pre-treatment baseline, and thus the HDV productive infected cells that are naturally lost with rate δ (median 0.0051 d^-1 corresponding to a mean half-life of 135 days) are not efficiently replaced. Our model suggests that the slow but progressive elimination of HDV-productively infected cells may cause both the decline in HBsAg levels and the 2^nd phase of HDV decline. Of note the estimated rate of loss of HBsAg-infected cells is about 10 to 20 times lower than what was found in HBV or HCV infected patients treated with IFN, with mean values of 0.051 d^-1 (31) and 0.14 d^-1 (29), respectively. The IFNL3-associated SNP rs12979860, is strongly associated with response to IFN therapy in patients with chronic hepatitis C. Both IFN effectiveness and death/loss of HCV-infected cells were shown to be higher in patients with rs12979860 CC genotype compared to non-CC(32), and furthermore, the febrile response to IFN, an extra-hepatic manifestation of IFN-response was shown to be higher in CC patients (33). In contrast, Martin et al. (34) showed that IFNL3 polymorphism (rs12979860) did not determine outcomes of other chronic viral infections such as HBV or HIV. Similarly, in the current study, rs12979860 was not associated with HDV kinetics during IFN therapy although the number of subject in the study may be too small to demonstrate an effect.

A long delay, t₀ (median 8.5 days), was estimated before peg-IFN had an effect in reducing pretreatment HDV RNA levels. Previous studies in HBV or HCV-infected patients treated with (peg)-IFN found a shorter delay of about 20 (31) and 10 hours (27, 35), respectively. Interestingly in the 6 patients who had detectable HBV, HBV tended to decline from baseline earlier than HDV. The longer delay with HDV compared to HBV might be partly explained by in vitro findings that HDV inhibits alfa interferon signaling (36), however it is yet to be shown if there are specific interferon-stimulated gene products against HDV and whether their induction is delayed. Alternatively, if IFN mainly blocks HDV RNA synthesis with little effect on HDV assembly and secretion, a large pool of intracellular HDV RNA might sustain pre-treatment progeny HDV formation and secretion rates during the observed delay. Under this assumption, it is expected that the long delay would be significantly shortened with anti-HDV drugs that inhibit HDV assembly. Interestingly, using a mouse model of HDV production, Bordier et al. (37) showed that prenylation inhibitors that inhibit HDV assembly led to approximately 85% reduction in serum HDV RNA titer within 2 days from initiation of treatment. The long and variable pharmacological delay observed for HDV should be further investigated in future HDV viral kinetic studies in order to refine the estimates of kinetic parameters, especially for drug effectiveness and viral clearance.

The present study focused on the first 28 weeks of treatment. Afterwards a variety of viral patterns were observed, such as rebound to steady state or oscillations (25), which cannot be predicted with the model developed here. In addition, HBV DNA kinetics were not modeled in conjunction with HDV because most patients had low or undetectable HBV DNA levels. More complex models and larger datasets will be required to characterize the relation between HBV DNA and HDV kinetics and to fit long-term on treatment data such as models that consider hepatocyte proliferation (17, 38), HBV/HDV dynamics (38, 39) and/or the immune responses (40). Recently proposed complex models that predict HBV and HDV dynamics during infection and treatment (38, 39) require revision to account for the long delay and biphasic HDV decline pattern observed, for the first time, in this study. Major limitations in validating the complex models include the lack of quantifiable HBV kinetic data during therapy (as in the present study) and the practical barriers to performing frequent liver biopsies in patients to obtain hepatocellular kinetic data. However it is anticipated that small animal models may partly overcome these limitations_(41). Nevertheless, an important insight gained from models that include hepatocyte proliferation is that suboptimal drug effectiveness may lead in some cases to a slower/flat second/final phase viral decline or rebound which is not necessarily caused by a low elimination rate of infected cells (42). Thus more potent drugs may lead to enhanced decline of both viral kinetic phases as found for HCV (22).

Viral kinetic models, as in the case of HCV (21, 23), could provide useful predictors of treatment outcome. Here 2 of the 3 patients who achieved CVR had a rapid second phase of viral decline, attributed in the model to a high loss rate of infected cells (δ>0.04 d^-1). However the third patient (patient 5) who achieved CVR did not differ in kinetic parameters from non-CVR patients. Notably, none of the 5 patients with 2^nd phase in HDV viremia (<0.018 log/wk) reached CVR. Larger studies are needed to verify these prediction parameters and suggest stopping rules.

Three patients who were HBeAg positive (patients 11, 12 and 13) had a flat second phase (or extremely low HBsAg-infected cell loss/death rate δ). Interestingly, δ was lower in HBeAg positive patients than in HBeAg negative patients (p=0.08). This pattern of results is similar to what was previously estimated in HBeAg positive monoinfected HBV IFN-treated subjects who had a lower δ compared to HBeAg negative subjects with an active HBV-specific immune response (31). The fact that here HBeAg positive patients had very low HBV levels with low δ may reflect the capacity of HDV to suppress HBV replication in patients without an active HBV directed immune response (43).

Recently, Ouzan et al. suggested discontinuation of treatment with peg-IFN when HBsAg levels reach undetectable levels (<0.5 IU/ml) (44). Interestingly the authors reported that based on this treatment stopping rule, all 4 patients in their study (who were male and HBeAg negative) achieved CVR. Our finding that HBsAg-productive infected cells are the main source of production of HDV is consistent with the use of HBsAg kinetics to optimize HDV treatment duration.

In summary, modeling early HDV dynamics provides new insights into HDV-host dynamics, the relationship between serum HBsAg levels and HBsAg-infected cells, IFN's mode of action and its effectiveness against HDV. The observation that a flat 2^nd phase in HDV and HBsAg kinetics was associated with failure to achieve CVR provides the basis to develop early stopping rules during peg-IFN treatment in HDV patients. Further data will be needed to confirm these results and evaluate the predictive ability of treatment outcome using early kinetics for the treatment of HDV.