Validation of a Mathematical Model for Green Algae (Raphidocelis Subcapitata) Growth and Implications for a Coupled Dynamical System with Daphnia Magna

Predicting Inter-individual Variability During Lipid Resuscitation of Bupivacaine Cardiotoxicity in Rats: A Virtual Population Modeling Study

Introduction

Intravenous lipid emulsions (ILE) have been credited for successful resuscitation in drug intoxication cases where other cardiac life-support methods have failed. However, inter-individual variability can function as a confounder that challenges our ability to define the scope of efficacy for lipid interventions, particularly as relevant data are scarce. To address this challenge, we developed a quantitative systems pharmacology model to predict outcome variability and shed light on causal mechanisms in a virtual population of rats subjected to bupivacaine toxicity and ILE intervention.

Materials and Methods

We combined a physiologically based pharmacokinetic–pharmacodynamic model with data from a small study in Sprague-Dawley rats to characterize individual-specific cardiac responses to lipid infusion. We used the resulting individual parameter estimates to posit a population distribution of responses to lipid infusion. On that basis, we constructed a large virtual population of rats (N = 10,000) undergoing lipid therapy following bupivacaine cardiotoxicity.

Results

Using unsupervised clustering to assign resuscitation endpoints, our simulations predicted that treatment with a 30% lipid emulsion increases bupivacaine median lethal dose (LD₅₀) by 46% when compared with a simulated control fluid. Prior experimental findings indicated an LD₅₀ increase of 48%. Causal analysis of the population data suggested that muscle accumulation rather than liver accumulation of bupivacaine drives survival outcomes.

Conclusion

Our results represent a successful prediction of complex, dynamic physiological outcomes over a virtual population. Despite being informed by very limited data, our mechanistic model predicted a plausible range of treatment outcomes that accurately predicts changes in LD₅₀ when extrapolated to putatively toxic doses of bupivacaine. Furthermore, causal analysis of the predicted survival outcomes indicated a critical synergy between scavenging and direct cardiotonic mechanisms of ILE action.

Supplementary Information

The online version contains supplementary material available at 10.1007/s40268-021-00353-4.

Prediction of maximum algal productivity in membrane bioreactors with a light-dependent growth model

Algal productivity in steady-state cultivation systems depends on important factors such as biomass concentration, solids retention time (SRT), and light intensity. Current modeling of algal growth often ignores light distribution in algal cultivation systems and does not consider all these factors simultaneously. We developed a new algal growth model using a first principles approach to incorporate the effect of light intensity on algal growth while simultaneously considering biomass concentration and SRT. We first measured light attenuation (decay) with depth in an indoor algal membrane bioreactor (A-MBR) cultivating Chlorella sp. We then simulated the light decay using a multi-layer approach and correlated the decay with biomass concentration and SRT in model development. The model was calibrated by delineating specific light absorptivity and half-saturation constant to match the algal biomass concentration in the A-MBR operated at a target SRT. We finally applied the model to predict the maximum algal productivity in both indoor and outdoor A-MBRs. The predicted maximum algal productivities in indoor and outdoor A-MBRs were 6.7 g·m^-2·d^-1 (incident light intensity 5732 lx, SRT approximately 8 d) and 28 g·m^-2·d^-1 (sunlight intensity 28,660 lx, SRT approximately 4 d), respectively. The model can be extended to include other factors (e.g., water temperature and carbon dioxide bubbling) and such a modeling framework can be applied to full-scale, continuous flow outdoor systems to improve algal productivity.

Characterization of the development stages and roles of nutrients and other environmental factors in green tides in the Southern Yellow Sea, China

Large-scale floating green tides in the Southern Yellow Sea (SYS) caused by the macroalgal species Ulva prolifera have been recurring for 13 years and have become one of the greatest marine ecological disasters in the world. In this study, we attempt to explore the development pattern of green tides and find its key environmental influencing factors. The satellite remote sensing data of the development process of green tides fit the logistic growth curve (R² = 0.93, P < 0.01) well, showing three distinct growth phases (lag, exponential growth, and short plateau phases). Correspondingly, the green tide-drifting area from the coast of Jiangsu to the nearshore waters of the Shandong Peninsula was divided into three sections: the lag phase zone (A), the exponential growth phase zone (B), and the plateau phase zone (C). Zone A in the south of Jiangsu coastal waters had abundant inorganic nutrients that were indispensable to the green tide initiation. Zone B was mainly located out of Haizhou Bay, south of 34.5° N and north of 35.5° N, where approximately 80% of the green tide biomass was generated. The rich bioavailable nutrient sources, suitable temperature, and irradiance in this area were the main promotion factors for the rapid growth and scale expansion of green tides. Wet precipitation in zone B in May and June also played an important role in the final scale of green tides. Zone C had poor nutrients, increasing temperature, and irradiance (high transparency), which limited the continued expansion of green tides, and organic nutrients might be an important support to green tides development in this region. The study based on the growth phases of green tides could help us further understand the eutrophication mechanism in the green tide outbreaks in SYS.