Algebraic Graph Theory and Differential Systems in Predicting Congenital Disorder Progression and Surgical Outcomes in Neonatal Health
Keywords:
Algebraic Graph Theory, Differential Systems, Congenital Disorders, Neonatal Health, Surgical Outcomes, Mathematical Modeling, Disease Progression, Health Networks, Predictive Analysis, Clinical Decision SupportAbstract
Congenital disorders are a significant cause of neonatal morbidity and mortality worldwide. Predicting the progression of these conditions and planning effective surgical interventions require the integration of advanced mathematical frameworks. This paper explores the application of algebraic graph theory and differential systems to model and analyze neonatal health networks, focusing on congenital disorders. Algebraic graph theory provides tools for representing complex interactions among anatomical and physiological systems, while differential systems enable the dynamic modeling of disease progression and response to surgical treatment. By combining these two domains, we present a unified mathematical approach that enhances the prediction of outcomes, identifies critical biomarkers, and optimizes surgical planning. The study also discusses computational implementation, clinical validation, and the potential for integration into neonatal decision-support systems. Our findings suggest that this interdisciplinary methodology offers substantial improvements in the precision and personalization of neonatal care.
Downloads
References
Newman, M. E. J. (2010). Networks: An Introduction. Oxford University Press.
Godsil, C., & Royle, G. (2001). Algebraic Graph Theory. Springer.
Barabási, A.-L. (2016). Network Science. Cambridge University Press.
De Domenico, M., et al. (2013). "Mathematical Formulation of Multilayer Networks." Physical Review X, 3(4), 041022.
Murray, J. D. (2002). Mathematical Biology I: An Introduction. Springer.
Deisenroth, M. P., Faisal, A. A., & Ong, C. S. (2020). Mathematics for Machine Learning. Cambridge University Press.
Holmes, M. H. (2012). Introduction to the Foundations of Applied Mathematics. Springer.
Diestel, R. (2017). Graph Theory (5th ed.). Springer.
Nicosia, V., & Latora, V. (2015). "Measuring and Modeling Correlations in Multiplex Networks." Physical Review E, 92(3), 032805.
Yoon, C., & Cowan, N. J. (2017). "On the Sensitivity of Dynamic Networks to Localized Perturbations." IEEE Transactions on Network Science and Engineering, 4(1), 23–34.
Sporns, O. (2010). Networks of the Brain. MIT Press.
Szymanski, B. K., et al. (2014). "Theory of Multiscale Complex Networks with Application to Neuroscience." IEEE Transactions on Network Science and Engineering, 1(3), 153–167.
Zhang, L., & Wang, Y. (2014). "Modeling and Control of Congenital Heart Defects using PDE-based Methods." Computers in Biology and Medicine, 47, 185–195.
Dedeo, S. (2016). "Information Theory for Complex Systems Science." Springer Handbook of Model Checking, 283–298.
Chen, C. Y., & Lin, C. C. (2020). "Predictive Modeling of Neonatal Sepsis Using Machine Learning on Electronic Health Records." PLOS ONE, 15(6), e0235829.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
You are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
Terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
