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A Mathematical Model to Predict Human Microcephaly
1Department of Pediatric Radiology, Faculty of Medicine, Gaziantep University.
Insights
This study developed mathematical formulas to estimate microcephaly (MiC), a condition of smaller-than-normal head circumference (HC). These formulas allow for MiC detection using a calculator, simplifying early childhood health assessments.
Area of Science:
- Pediatrics
- Medical Informatics
- Biostatistics
Background:
- Microcephaly (MiC) is characterized by head circumference (HC) measurements below established normal standards.
- Accurate detection of MiC is crucial for monitoring child development and health outcomes.
Purpose of the Study:
- To develop a mathematical formula for detecting microcephaly (MiC) in young children.
- To provide a simple, accessible method for estimating head circumference (HC) percentiles.
Main Methods:
- Utilized World Health Organization (WHO) head circumference (HC) percentile data for children aged 0-5 years.
- Applied logarithmic regression analysis to define mathematical formulas approximating the 3rd percentile curves for boys and girls.
- Identified models with the highest coefficient of determination (R² = 0.991 for both sexes).
Main Results:
- Derived specific mathematical formulas for estimating HC in girls and boys based on age in months.
- Formulas: HC = 34.025 + 3.283 * ln(age) for girls and HC = 35.475 + 3.14 * ln(age) for boys.
- Acknowledged limitation: formulas cannot calculate HC at birth due to the natural logarithm of zero.
Conclusions:
- Microcephaly (MiC) can be reliably estimated using the derived mathematical formulas.
- These formulas offer a practical alternative to percentile charts, mobile apps, or internet access for HC assessment.
- The method facilitates accessible and immediate screening for potential developmental concerns.
Background:
Microcephaly (MiC) is defined as head circumference (HC) dimensions smaller than the normal standards.
Objective:
To detect MiC with a mathematical formula.
Materials And Methods:
The 0 to 5 years head HC percentile data for girls and boys reported by the World Health Organization were used. To assess early childhood, these growth standards are available on its website for international use. Mathematical formulas best estimating the 3rd percentile curves were defined using basic regression analysis methods.
Results:
The mathematical models obtained as a result of logarithmic regression analysis with the highest coefficient of determination values (R2 = 0.991 for girls; R2 = 0.991 for boys) were identified as the best model. The formulas of HC = 34.025 + 3.283 ∗ ln (age as months), and HC = 35.475 + 3.14 ∗ ln (age as months) were determined for girls and boys, respectively. A limitation of these formulas is that they do not provide the HC at birth (ln (0) = undetermined).
Conclusion:
Microcephaly can be estimated using the mathematical formulas with a calculator without using percentile scales, mobile applications, software, or the Internet.
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