A Time-Dose Model to Quantify the Antioxidant Responses of the Oxidative Hemolysis Inhibition Assay (OxHLIA) and Its Extension to Evaluate Other Hemolytic Effectors

Table 2

Short review of different mathematical methodologies from related fields of study, such as the hemolytic bioassays, antioxidant, and dose-response theory.

Reference	Type*	Use**	Description
From related hemolytic analytical techniques
[39]	M	OMT	Sophisticated mechanistic model to evaluate the erythrocyte lysis analyzed with a scanning flow cytometer in isotonic solution, obtaining several parameters (volume, surface area, hemoglobin concentration, elasticity. and critical tension of membrane, etc.) that allow us to evaluate the lysis.
[40]	E	OMT	A mathematical model based on the Gaussian distribution function to measure the degree of osmotic fragility to test the degree of resistance of red blood cells to hemolysis was developed. It provides parameters that define the midpoint, the dispersion, and maximum hemolysis, respectively.
[38]	E	OMT	Demonstrating the suitability of the Weibull survival distribution to study the surfactant-induced erythrocyte hemolysis (osmotic fragility test) connecting its parameters to blood properties.
[28]	E	PHA	Developing a toxicological dynamic model, applying in equivalent form the Weibull and Logistic equation, to describe the hemolysis of erythrocytes by palytoxin and its inhibition by ouabain, allowing us to detect this potentially nonprotein marine toxin.
From the antioxidant field
[41]	E	DAA	A bivariate model was proposed. It allows us to obtain the simultaneous solution of a series of oxidation kinetics of a dose-response of antioxidants. Its application is simple, provides parametric estimates which characterize oxidative process, and facilitates rigorous comparisons.
[42]	E	DAA	A kinetic approach to evaluate the efficiency of antioxidants in scavenging the radical generated in the -carotene, DPPH, and the superoxide anion radical methods. The authors highlighted the need of approaches to estimate the rate of the antioxidant reactions.
[43]	E	DAA	A general mathematical model for lipid oxidation in food systems based on the logistic equation. A simple method was described for the evaluation of the model parameters. Variations of these numerical values were also associated with varying pretreatment and storage conditions.
From the dose-response theory
[44]	E	DDRA	A general bivariate method to describe the time-dose-response curves for physiological and pharmacological studies. The method permits rigorous statistical analysis, provides a basis for pooling of information from separate experiments, and determines characteristics shared by curves.
[45]	E	DDRA	A review to describe the importance of the time dimension on dose-responses for toxic chemicals. In many situations, the effect of a toxic chemical on a biological system depends on both the intensity and the duration of exposure.
[46]	E	DDRA	The suitability of several common descriptive models for the study of dose-response relationships is discussed, and changes are introduced that improve their suitability, generalize their application, and lead to their possible application for multivariable analysis.
[47]	E	DDRA	A review of various properties of the Hill equation which is widely used in many pharmacokinetic-pharmacodynamic models to describe nonlinear drug dose-response relationships. The main mechanistic aspect and multivariate potential applications are also discussed.

Model type: mechanistic (M); empirical (E).
Use: Osmotic fragility test (OFT); palytoxin hemolytic activity (PHA); different antioxidant assays (DAA); different dose-response approaches (DDRA).