Distinguishing Between Long-Transient and Asymptotic States in a Biological Aggregation Model.

Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the aggregation-diffusion equation with linear diffusion in one spatial dimension. This equation is known to support solutions that involve both single and multiple aggregations. However, numerical evidence suggests that the latter, which we term 'multi-peaked solutions' may often be long-transient solutions rather than asymptotic steady states. We develop a novel technique for distinguishing between long transients and asymptotic steady states via an energy minimisation approach. The technique involves first approximating our study equation using a limiting process and a moment closure procedure. We then analyse local minimum energy states of this approximate system, hypothesising that these will correspond to asymptotic patterns in the aggregation-diffusion equation. Finally, we verify our hypotheses through numerical investigation, showing that our approximate analytic technique gives good predictions as to whether a state is asymptotic or transient. Overall, we find that almost all twin-peaked, and by extension multi-peaked, solutions are transient, except for some very special cases. We demonstrate numerically that these transients can be arbitrarily long-lived, depending on the parameters of the system.

Nonviral Liver Disease Burden in People Living With HIV and Elevated Transaminases: A Cross-Sectional Study.

INTRODUCTION: Because of improved life expectancy in people living with HIV (PLWH), liver disease is increasingly being recognized. We assessed nonviral chronic liver disease burden in PLWH. METHODS: The HIV non-virAL liver disease study (2014-2021) prospectively recruited PLWH with elevated serum alanine aminotransferase levels and negative hepatitis serology. Clinically significant hepatic fibrosis (CSHF) was defined as liver stiffness measurement of >7.1 kPa and hazardous alcohol use as Alcohol Use Disorders Identification Test score ≥ 8. Primary outcome was prevalence/predictors of CSHF. RESULTS: Total recruited were n = 274, 92% male, median age 52 (45-59) years, and 96% having undetectable HIV viral load. Overall, n = 97 (35%) had hazardous alcohol use, n = 72 (26%) had metabolic syndrome, and 17%-27% had exposure to hepatotoxic antiretrovirals. Prevalence of CSHF was 20% (n = 54), prevalence of cirrhosis (liver stiffness measurement > 12.5 kPa) being 7% (19/274). Risk factors for CSHF were hazardous alcohol use in 44% (n = 24), metabolic syndrome in 46% (n = 25), and hepatotoxic antiretrovirals in 56% (n = 30), most having more than one risk factor. Independent predictors of CSHF were serum high-density lipoprotein (odds ratio [OR] 0.220; 95% confidence interval [CI]: 0.061 to 0.790, P = 0.020) (inverse relationship); serum aspartate aminotransferase (OR 1.033, 95% CI: 1.001 to 1.067, P = 0.045), and didanosine use (OR 2.878, 95% CI: 1.228 to 6.774, P = 0.015). Moderate-severe hepatic steatosis was identified in 52% (n = 142). FIB-4 and aspartate aminotransferase-to-platelet ratio index performed poorly in predicting CSHF (positive predictive value 27.3% and 30.6%, respectively) and advanced fibrosis (≥F3) (positive predictive value 17.6% and 5.9%, respectively). CONCLUSION: In this study, 20% of PLWH had CSHF associated with high prevalence of hazardous alcohol use/metabolic syndrome/potentially hepatotoxic antiretrovirals. These potentially modifiable risk factors need addressing.