Recalculation of Lost Information in Neuron with Quadratic Spline Interpolation

Öz

The main function of neurons in a living creature is to transmit information. Neurons carry out information transmission without loss despite environmental and internal noise sources. However, sometimes there may be losses in the transmission of information. This results in diseases such as Alzheimer's, MS, and Epilepsy. In this study, the information lost in neurons is recalculated with the Quadratic Spline Interpolation method. In cases where it is difficult or impossible to calculate a function, the process of calculating the corresponding value of an unmeasured variable is called interpolation. In this study, first of all, three sample neuron behaviours are created with the Fitzhugh-Nagumo model, and the action potential and recovery parameter variables are obtained. Then, some data in the variables are deleted, resulting in unhealthy neuron behaviour. Then, these deleted data are recalculated using the Quadratic Spline Interpolation method. Various error values are obtained by comparing the actual and calculated data. The data lost in the action potential-recovery variable are detected with a very low error rate of 0.2630-0.0524%, 0.2885-0.0165% and 0.2543-0.0781% for the three sample neuron behaviours, respectively. With this study, it has been demonstrated that information lost or incorrectly coded in neurons for any reason can be corrected. It is also understood that this study can be used to prevent losses in real-time measurement results from biological neurons and to recalculate erroneous values.

Anahtar Kelimeler

• Quadratic Spline Interpolation
• Cubic Spline Interpolation
• FitzHugh-Nagumo
• Hodgkin-Huxley
• Neuron Model

İkinci Dereceden İnterpolasyon ile Nöronda Kayıp Bilginin Yeniden Hesabı

Öz

Canlılarda nöronların temel görevi bilgi iletimidir. Nöronlar çevresel ve içsel gürültü kaynaklarına rağmen bilgi iletimini kayıpsız olarak gerçekleştirirler. Fakat kimi zaman bilgi iletiminde kayıplar meydana gelebilir. Bu durum Alzheimer, MS, Epilepsi gibi hastalıklar ile sonuçlar. Bu çalışmada nöronlarda kaybolan bilgi İkinci Dereceden Şerit İnterpolasyon yöntemi ile yeniden hesaplanması sağlanmıştır. Bir fonksiyonun hesaplanmasının zor veya mümkün olmayan durumlarda, değeri ölçülmemiş bir değişkenine karşılık gelen değerinin hesaplanması işlemine interpolasyon adı verilir. Bu çalışamda öncelikle Fitzhugh-Nagumo model ile üç örnek nöron davranışı oluşturulmuş ve aksiyon potansiyeli ile toparlanma parametresi değişkenleri elde edilmiştir. Ardından değişkenlerdeki bazı veriler silinerek sağlıksız bir nöron davranışı sağlanmıştır. Daha sonra İkinci Dereceden Şerit İnterpolasyon yöntemi kullanılarak silinen bu veriler yeniden hesaplanmıştır. Gerçek ve hesaplanan veriler karşılaştırılarak çeşitli hata değerleri elde edilmiştir. Aksiyon potansiyeli- toparlanma parametresinde kaybolan veriler, üç örnek nöron davranışı için sırasıyla %0.2630-%0.0524, %0.2885-%0.0165 ve %0.254-%0.0781 gibi çok düşük bir hata oranıyla tespit edilir. Bu çalışma ile nöronlarda herhangi bir sebepten dolayı kaybolan veya yanlış kodlanan bilgi düzeltilebilir olduğu ortaya konmuştur. Ayrıca bu çalışmanın biyolojik nöronlardan gerçek zamanlı ölçüm sonuçlarındaki kayıpları önlemek ve hatalı değerleri yeniden hesaplamak için kullanılabileceği anlaşılmaktadır.

Anahtar Kelimeler

• İkinci Dereceden İnterpolasyon
• Kübik İnterpolasyon
• FitzHugh-Nagumo
• Hodgkin-Huxley
• Nöron Model

Kaynakça

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