A multi-scale spatial model of hepatitis-B viral dynamics

Abstract

Chronic hepatitis B viral infection (HBV) afflicts around 250 million individuals globally and few options for treatment exist. Once infected, the virus entrenches itself in the liver with a notoriously resilient colonisation of viral DNA (covalently-closed circular DNA, cccDNA). The majority of infections are cleared, yet we do not understand why 5% of adult immune responses fail leading to the chronic state with its collateral morbid effects such as cirrhosis and eventual hepatic carcinoma. The liver environment exhibits particularly complex spatial structures for metabolic processing and corresponding distributions of nutrients and transporters that may influence successful HBV entrenchment. We assembled a multi-scaled mathematical model of the fundamental hepatic processing unit, the sinusoid, into a whole-liver representation to investigate the impact of this intrinsic spatial heterogeneity on the HBV dynamic. Our results suggest HBV may be exploiting spatial aspects of the liver environment. We distributed increased HBV replication rates coincident with elevated levels of nutrients in the sinusoid entry point (the periportal region) in tandem with similar distributions of hepatocyte transporters key to HBV invasion (e.g., the sodium-taurocholate cotransporting polypeptide or NTCP), or immune system activity. According to our results, such co-alignment of spatial distributions may contribute to persistence of HBV infections, depending on spatial distributions and intensity of immune response as well. Moreover, inspired by previous HBV models and experimentalist suggestions of extra-hepatic HBV replication, we tested in our model influence of HBV blood replication and observe an overall nominal effect on persistent liver infection. Regardless, we confirm prior results showing a solo cccDNA is sufficient to re-infect an entire liver, with corresponding concerns for transplantation and treatment.

Mathematical Modeling for Hepatitis B Virus: Would Spatial Effects Play a Role and How to Model It?

“…In silico modeling efforts aimed at hepatic drug perfusion demonstrate a subtle impact of different spatial distributions for hepatocyte steatosis over initial phases of treatment (Schwen et al, 2016). By constructing representative sinusoidal regions over the whole liver organ, blood-flow is modeled through sinusoidal spaces and corresponding variations of hepatic metabolic processing with one-dimensional advection equations coupled to systems of ordinary differential equations assigned to individual hepatocytes (Schwen et al, 2016;Cangelosi et al, 2017). In effect, the representative suites of sinusoid models are distributed over the liver tissue with varying physiologicallybased pharmacokinetic (PBPK) models-instead of the entire liver organ (Schwen et al, 2016).…”

“…Differing densities for immune cells (Kupffer, NK) at key spatial locations as well as cell-level transporter distributions (e.g., the NTCP) are natural inclusions for investigation. With a continuum model for fluid transport and tissue-level dynamics (e.g., a convection-diffusion equation for the sinusoidal flow) and discrete cell models (e.g., cellular dynamics models of ordinary differential equation systems) over a suite of spatially heterogeneous sample regions, a multi-scaled, detailed and computationally tractable model of the hepatic HBV-immune dynamic is possible (Cangelosi et al, 2017;Franiatte et al, 2019). Low densities of innate immune cells at key spatial locations (e.g., Kupffer near portal-triads), the polarity of cellular distributions of sinusoid-facing transporters (e.g., NTCP), and metabolic roles along the portal-central axis (e.g., hepatic zones I-III) have yet to be investigated for their impact on the HBV infection dynamic.…”

“…Low densities of innate immune cells at key spatial locations (e.g., Kupffer near portal-triads), the polarity of cellular distributions of sinusoid-facing transporters (e.g., NTCP), and metabolic roles along the portal-central axis (e.g., hepatic zones I-III) have yet to be investigated for their impact on the HBV infection dynamic. The model in Cangelosi et al (2017) was interrogated with spatial distributions of NTCP activity, metabolic influence on HBV and a rather simplistic immune response to HBV infection. Nevertheless, substantial spatial heterogeneities remain to be investigated, particularly including above noted immunity response aspects.…”

“…Additionally, dependence of chronic or acute manifestations on the sheer number of HBV suggests an optimal invasion population strategy for HBV (Asabe et al, 2009), presumably evading detection but sufficient for colonization. Unfortunately, direct study of the initial HBV-immune dynamic in patients is difficult or simply not possible, hence the attention given to animal and mathematical models (Murray and Goyal, 2015;Cangelosi et al, 2017).…”

Modeling the dynamics of hepatitis B infection, immunity, and drug therapy

“…Mathematical models have been developed and used for insight into the hepatitis B infection, treatment, and progression. Some studies investigated the mechanisms behind progression from acute to chronic disease in humans and animal models . Others estimated the efficacy of mono‐ and combination drug therapy, the virological‐immunological mechanisms associated with the therapy, and the role of immune responses in HBV DNA removal .…”