Tıp ve Diş Hekimliği Alanlarında Fraktal Analiz Yöntemi
Özet
Fraktal geometri, doğadaki ve insan vücudundaki klasik Öklid geometrisiyle açıklanamayan karmaşık, pürüzsüz olmayan ve öz benzerlik gösteren yapıların matematiksel olarak haritalanmasını ve fraktal boyutunun (FB) hesaplanmasını sağlar. Tıp ve diş hekimliği alanlarında fraktal analiz; damarlar, nöronlar, akciğerler, sinyaller (EKG, EMG, EEG) ve trabeküler kemik gibi karmaşık dokuların yapısını ve fizyolojik parametrelerini nicel olarak değerlendirmek amacıyla yaygın şekilde kullanılmaktadır. FB hesaplamalarında, uygulama kolaylığı nedeniyle en sık kutu sayma yöntemi tercih edilir. Sağlıklı bireylerde bu dokuların karmaşıklığı ve FB değerleri daha yüksekken, yaşlanma ve hastalık durumlarında (osteoporoz, diyabet, bruksizm, kalp yetmezliği vb.) FB değerinde belirgin bir düşüş ve karmaşıklık kaybı gözlenir. Buna karşın, malignitelerin incelendiği histolojik kesitlerde, karsinom yapılarında ve yüksek dereceli tümörlerde normal dokulara kıyasla daha yüksek bir FB ve karmaşıklık saptanmaktadır. Sonuç olarak fraktal analiz; radyografi, MRG, ultrason ve mikroskop görüntüleri üzerinden non-invaziv bir biyobelirteç olarak hastalıkların teşhisinde, iyileşme süreçlerinin takibinde ve klinik gidişatın öngörülmesinde güçlü bir araçtır.
Fractal geometry enables the mathematical mapping and calculation of the fractal dimension (FD) of complex, non-smooth, and self-similar structures in nature and the human body that cannot be explained by classical Euclidean geometry. In the fields of medicine and dentistry, fractal analysis is widely used to quantitatively evaluate the structure and physiological parameters of complex tissues such as vessels, neurons, lungs, signals (ECG, EMG, EEG), and trabecular bone. Among FD calculation methods, the box-counting method is most frequently preferred due to its ease of application. While the complexity and FD values of these tissues are higher in healthy individuals, a significant decrease in FD values and a loss of complexity are observed during aging and disease states such as osteoporosis, diabetes, bruxism, and heart failure. Conversely, in histological sections where malignancies are examined, higher FD and complexity are detected in carcinoma structures and high-grade tumors compared to normal tissues. Consequently, fractal analysis serves as a powerful tool in diagnosing diseases, monitoring healing processes, and predicting clinical courses as a non-invasive biomarker using radiographs, MRI, ultrasound, and microscopic images.
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