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A Mathematical Approach with Fractional Calculus for the Modelling of Children's Physical Development

Nisa Özge Önal¹, Kamil Karaçuha¹, Göksu Hazar Erdinç¹

¹Informatics Institute, Istanbul Technical University, Istanbul 34467, Turkey.

Computational and Mathematical Methods in Medicine

|October 16, 2019

Insights

Tracking children

Area of Science:

Pediatrics and Child Health
Biostatistics
Mathematical Modeling

Background:

Monitoring child development is crucial for effective healthcare.
Identifying factors influencing physical development (weight, height, BMI) aids in better child care.
Existing methods may lack precision in continuous developmental tracking.

Purpose of the Study:

To develop a novel mathematical approach for analyzing children's physical development.
To create a continuous model for tracking weight, height, and body mass index (BMI) from birth to 18 years.
To improve the accuracy of children's growth assessment using advanced mathematical techniques.

Main Methods:

Utilized discrete data from Turkey's Percentage Chart for weight, height, and BMI across 7 age groups.
Applied the least squares method to generate a continuous growth curve for children aged 0-18 years.
Developed a new mathematical model incorporating fractional calculus theory for enhanced analysis.

Main Results:

Successfully created a continuous curve for analyzing children's physical development data.
Enabled precise determination of a child's percentile and position within growth charts.
Demonstrated superior performance of the fractional calculus model over linear and polynomial models.

Conclusions:

The developed fractional calculus model offers a more accurate and reliable method for assessing child development.
This approach facilitates the prediction of future developmental values based on historical data.
The study provides a valuable tool for pediatricians and healthcare providers in monitoring child growth.

Read full analysis

Abstract:

From birth to now, it is getting more and more important to keep track of the children development, because knowing and determining the factors related to the physical development of the children would provide better and reliable results for children care. In this study, we developed a mathematical approach to have the ability of analysing and examining factors such as weight, height, and body mass index with respect to the age. We used 7 groups for weight, height, and body mass index in Percentage Chart of Turkey. We developed a continuous curve which is valid for any time interval by using discrete weight, height, and body mass index data of 0-18 years old children and the least squares method. By doing so, it became possible to find the percentage and location of the children in Percentage Chart. We advanced a new mathematical model with the help of fractional calculus theory. The results are quite successful and better compared to linear and Polynomial Model analysis. The method provides the opportunity to predict expected values of the children for the future by using previous data obtained in the development of the children.

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