2 research outputs found
Surrogate muscle models based on artificial neural networks with applications in finite element analysis
Biofizički modeli mišića, zasnovani na fiziološkim principima funkcionisanja
mišića, se mogu koristiti da odrede mehanički odziv mišića preciznije nego
fenomenološki modeli, koji su zasnovani na eksperimentalnim merenjima. Međutim,
za razliku od fenomenoloških, biofizički modeli mišića su računski veoma
zahtevni, što otežava njihovu upotrebu u višeskalnim simulacijama. Tipičan
primer biofizičkog modela mišića je Hakslijev model. U ovoj disertaciji, da bi se
omogućila efikasnija upotreba biofizičkih modela, kreirani su surogat modeli
zasnovani na veštačkim neuronskim mrežama takvi da oni imitiraju originalni
Hakslijev model, ali koriste manju količinu memorije i drugih računarskih resursa.
Najbolji rezultati su postignuti zatvorenim rekurentnim jedinicama, koje su dale
najtačnije napone u mišiću od svih konstruisanih mreža. U različitim numeričkim
eksperimentima je pokazano da su predviđeni naponi i trenutna krutost skoro
potpuno isti kao originalni. Pokazano je da je konstruisani surogat model za red
veličine brži od Hakslijevog modela rešavanog klasičnim numeričkim postupkom i
da troši manju količinu memorije. Pored toga, u ovoj disertaciji su prikazane
neuronske mreže podržane fizičkim zakonima, koje su obučavane tako da
aproksimiraju rešenje Hakslijeve jednačine za mišićnu kontrakciju. Pokazano je da
višeslojni perceptron, podržan fizičkim zakonima, bolje generalizuje ponašanje
mišića nego standardni višeslojni perceptron.
U ovoj disertaciji su predstavljene procedure za kreiranje surogat modela mišića,
zajedno sa procedurama za integraciju surogat modela u softverski okvir za analizu
metodom konačnih elemenata. Da bi potencijal surogat modela za korišćenje u
zahtevnim višeskalnim simulacijama bio demonstriran u punom obimu, simuliran je
srčani ciklus leve komore, što bi bilo značajno teže uraditi sa originalnim
Hakslijevim modelom.Biophysical muscle models, which are based on the underlying physiology of the muscles,
can evaluate the mechanical response of the muscles more accurately than phenomenological
muscle models, which are based on experimental measurements. On the other hand,
biophysical muscle models are much more computationally intensive. Biophysical muscle
models are often called Huxley-type muscle models. In this dissertation, to enable the
efficient use of Huxley-type muscle models in multi-scale simulations of the cardiac cycle,
surrogate models were created such that they mimic the original Huxley muscle model but use
less memory and processing power. The best results were achieved with the gated recurrent
units, which produced the most accurate stresses. Stresses and instantaneous stiffnesses
produced by the surrogate model were almost indistinguishable from the original values. The
constructed surrogate model was an order of magnitude faster than Huxley’s muscle model
and used less memory. Additionally, in this dissertation, physics-informed neural networks
were trained to approximately solve Huxley’s muscle contraction equation. It was shown that
the generalization of the physics-informed multilayer perceptron is greater than that of the
ordinary multilayer perceptron.
The procedures for the creation of the surrogate muscle models were introduced in this
dissertation, along with the procedures for the integration of the surrogate models into a finite
element analysis framework. To show the potential of the surrogate models in larger-scale
simulations, the cardiac cycle of the left ventricle model was simulated, which would be much
higher to do with the original Huxley’s muscle model