Table 1.

Observed plasma HCV RNA kinetics and mathematical models.

Viral kinetic pattern	Viral kinetic definition	Model name	Comments	Model predictions	Model concerns/limitations	Ref. #
Biphasic	The typical viral decline seen under daily IFN or DAAs: consists of a rapid first phase (0.5 – 2 days) of viral decline followed by a slower 2nd phase decline	Biphasic (Eq.1)	Uninfected hepatocytes are at steady state during the period of analysis	High ε and δ have been shown to be important for treated patients to achieve an SVR	(i) Explain only biphasic viral decline pattern (ii) may underestimate viral clearance rate, c, and loss/death rate of infected cells, δ	[4, 11, 59•, 60, 97, 98]
		Extended (Eq. 2)	Includes both uninfected and infected hepatocyte proliferation rates.	Low rate of SVR in subjects with high baseline viral load and/or advanced liver disease. With high ε~1, second phase viral decline is close to δ	Many unknown parameters that can only be calculated after model parameters are estimated; hepatocyte proliferation rate in HCV infected patients is not known. May underestimate viral clearance rate, c.	[19, 20, 23]
		ICCI model	Explains why 2nd phase is enhanced under DAAs	Above a certain level of effectiveness, vRNA is not reduced to a new steady state but rather is declining exponentially in a treatment effectiveness dependent manner	Many unknown parameters. Lack of intracellular data	[61•]
		Colombatto et al. model	Includes serum ALT levels to improve the understanding of infected cells dynamics and its relationship with treatment outcome. Allows for the simulation of the viral kinetics during the whole treatment course.	Estimate the number of infected cells at the end of therapy and accordingly the chance to achieve SVR based on ALT and HCV kinetics during the first month of SOC	Many parameters are assumed and not computed. Lack of experimental data to fully establish the relationship between the infected cells death rate and serum ALT levels	[99, 100, 106]
Triphasic	first phase (0.5 – 2 days) with rapid virus load decline followed by a shoulder phase (4 – 28 days) – in which virus load decays slowly or remains constant – and a third phase of renewed viral decay	Herrmann et al.. model	Model assumes that IFN and RBV have a delayed immunomodulatory effect	Shoulder phase is explained by very long half life of infected cells (δ~0)	Lack of frequent viral kinetic data in common clinical practice	[101]
		Extended (Eq. 2)	Includes both uninfected and infected hepatocyte proliferation rates.	Assumes a large fraction of HCV-infected susceptible hepatocytes at baseline	Same as above	[18•, 20]
Null response or flat-partial response	Less than ~2 log decline throughout treatment	Extended (Eq. 2) or (Eq. 1) with non constant level of target cells	The definition of these viral kinetic patterns varies among studies (explained in main text)	Existence a critical drug effectiveness, εc, These viral kinetic patterns are predicted in cases that total drug effectiveness is lower than εc.	Same as above	[19, 20, 102]
Late partial virologic response or viral breakthrough	After weeks of continuous viral decline during SOC viral load spontaneously rebounds from nadir viral load above or below assay limit, respectively.	Extended (Eq. 2) with PEG-IFN pharmacodynamic features	Hepatocytes proliferation rate constant, r, was assumed very low compared to other viral kinetic studies	The model demonstrated excellent positive (99%) and negative (97%) predictive values for SVR.	Hard to distinguish between spontaneous viral rebounds dose reductions or suboptimal drug adherence	[30•]
Repeated transient viral rebounds	Repeated oscillations in viral load that fall in all the above viral kinetic patterns	Eq.1 or Eq.2 with the assumption that drug effectiveness, ε, is not constant	Valid for modeling viral rebounds due to change in drug concentrations in serum	Estimate differences in pharmacodynamic parameters among individuals with different race/ethnicity and/or IL28B polymorphism	Lack of frequent drug and viral load concentration data in common clinical practice	[18•, 80•, 103, 104]
Rapid emergence of resistance HCV- variants	First phase (0.5 – 2 days) with rapid virus load decline followed by viral increase of resistant virus strains during monotherapy with HCV protease inhibitors	Extension of Eq.1 to two or several viral strains	Several strains of resistant virus are modeled and compete for new cell infection	The resistance emergence is supported by the rapid death of infected cells and the similarly rapid proliferation of new susceptible	Assume rapid hepatocyte turn over to support the early and rapid emergence of resistant HCV strains	[22••, 62]
		ICCI model	Assumes that viral resistant and wild-type strains competition occurs also intracellularly	Viral mutants preexist intracellularly in most infected hepatocytes; resistance related viral breakthrough are not necessarily a marker of treatment failure; can be followed by a renewed viral decline	Same as above; the effect of deterministic and mean-field approximations is not known	[61•]