Aort kapağı kan akımının katı-sıvı etkileşim yöntemiyle sayısal incelenmesi
Numerical investigation of the aortic valve blood flow using fluid-structure approach
Yazar: ARMİN AMİNDARİ
Danışman: PROF. DR. KADİR KIRKKÖPRÜ
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Makine Mühendisliği Bilim Dalı
Derece: Doktora, 2022
Konu: Biyomühendislik = Bioengineering ; Makine Mühendisliği = Mechanical Engineering ; Mühendislik Bilimleri = Engineering Sciences
Dizin: Akışkanlar mekaniği = Fluid mechanics ; Aort kapağı = Aortic valve ; Doku mühendisliği = Tissue engineering ; Katı-sıvı etkileşimi = Solid-liquid interaction ; Modelleme = Modelling ; Sonlu elemanlar yöntemi = Finite element method

Özet:
Günümüzde, insan ölümlerinin başlıca sebebi kalp hastalıkları olup bu hastalıkların çoğu ise kapak kusurları ile ilgilidir. Bu kusurların tedavisinde uygulanacak tedavinin kararlaştırılmasında, kusurun karakterize edilmesi ve hastalığın ciddiyetinin belirlenmesi hayati önem taşımaktadır. Günümüzde bu teşhisler, tıbbi görüntüleme temellidir ve teşhisi yapan hekimin tecrübesine bağlı olarak özel biçimde yapılmaktadır. Bununla birlikte, ileri seviyede hastalıklarda aort kapaklarının mekanik ve prostetik kapaklarla değişimi sağlanmaktadır. Yapay kapakların tasarımı ve
kullanılan malzemenin, gerçek aort kapak fonksiyonunu yerine getirecek şekilde belirlenmesi için, aort kapak dinamiği ve malzemesinin mekanik özelliklerinin doğru bir şekilde anlaşılması gerekmektedir. Bu tez, aort kapağının elastisitesi ve geçen kan akışının sayısal ortamda modellenmesi ile ilgilidir. Çalışma kapsamında, aort kapağında gerçekleşen kan akışı ve kapak elastodinamiğinin sayısal olarak modellenmesi için bir metodoloji oluşturulması hedeflenmiştir. Bu metodoloji ile kapak kusurlarının kan akışı üzerinde oluşturduğu etkiler doğru ve hassas şekilde modellenebilecektir. Aort kapak yapısı, kan akışının oluşturduğu dinamik basınçlar altında deforme olarak kalpten bütün vücuda doğru tek yönlü kan akışını sağlamaktadır. Bu sebepten kan akışı ve aort kapak yapısı güçlü bir etkileşim içindedir. Kan akışı ve kapak elastodinamiğini gerçeğe yakın ve doğru bir şekilde modellemek için her iki çözüm alanı olan kan akış alanı ve aort kapağı katı alanının eş zamanlı ve birlikte çözülmesi gerekmektedir. Bu tez çalışması kapsamında, ileri bir mühendislik tekniği olan katı-sıvı etkileşim metotları kullanılarak, kan akışı ve aort yapısal alanlarının eş zamanlı çözülmesi için
bir modelleme metodolojisi oluşturulmuştur. İlk aşamada iki boyutlu ideal aort kapak modelleri oluşturularak aort kapak üzerinde meydana gelen kireçlenme probleminin kapak dinamiği üzerindeki etkisi incelenmiştir. Bir sonraki aşamada ise farklı hastalık grupları belirlenerek gerçek ve hastaya özel üç boyutlu katı-sıvı etkileşim modelleri oluşturulmuştur. Sayısal sonuçlar gerçek ölçüm sonuçlarıyla karşılaştırılmış ve metodolojinin hassasiyeti değerlendirilmiştir. Tezin son bölümünde ise aort kapak malzemesinin doğrusal olmayan mekanik özelliklerinin kan akışı ve kapak dinamiği üzerindeki etkisi incelenmiştir. Bu aşamada, üç farklı malzeme modeli kullanılarak farklı katı-sıvı etkileşim kontrol modelleri
oluşturulmuştur. Bu şekilde, kapak malzemesinin doğrusal olamayan özelliklerinin kapak stabilizasyonu ve ayrıca kireçlenme riski üzerindeki ektisi detaylı ve sayısal olarak incelenebilmiştir. Yapılan hesaplamalara göre kolajen fiberlerinin kapak kapanış evresindeki titreşimini düşürüp, kapağın kararlılığını artırdığı gözlemlenmiştir. Ayrıca, kolajen fiberlerinin çevresel yöndeki konumlanması, aort kapağın başlangıç pozisyonuna daha hızlı ve rahat şekilde dönmesini sağladığı ve bu şekilde kapak boyunca tek yönlü akışın sağlanmasında önemli rol üstlendiği gözlemlenmiştir. Öte yandan, malzemenin doğrusal olmayan elastisite özelliği sebebiyle kireçlenme problemini ciddi derecede azaldığı ve bu sebepten stenoz riskinin azaldığı sonucuna varılmıştır.

Abstract:
The human heart is the key component of the cardiovascular system. The heart pumps the oxygenated blood to the whole body through the aortic valve (AV) which lies at the junction of the left ventricle and the aorta. The AV is normally comprised of three luminal leaflets. However, in some cases it is found that the AV has congenitally only two cusps. The cusps are anatomically restricted to open in one direction to ensure the unidirectional flow of the blood flow through the aortic valve. Therefore, the efficient transport of blood cells to the whole body relies on the proper function of three cusps. Any structural abnormality of the leaflets can lead to serious diseases associated with high mortality and morbidity unless treated properly. The narrowing of the AV opening during the systole phase which is the most prevalent
of all valve disorders is called aortic stenosis. Aortic stenosis may be caused by a congenital heart defect or by other conditions such as the accumulation of calcium deposits on the AV leaflets. Aortic valve regurgitation is yet another serious leaflet dysfunction, which is associated with diastolic backflow of the blood from aorta to the left ventricle.
The severity of AV diseases is evaluated by several test standards. Depending on the severity of the disease different treatment plans can be adapted by physicians. Since AV disease is a structural dysfunction, it can be managed only using mechanical treatments. For mild conditions, some medications can be prescribed to control the symptoms and the complications. These medications help open blood vessels or tame the heart rhythm. In moderate cases, the narrowed aortic valve can be repaired using balloon valvuloplasty. In this Procedure, a balloon is guided through artery up to the aortic valve. By the inflammation of the balloon, the stenosed valve is stretched. However, the procedure does not provide a permanent treatment, and the valve narrows again by the time. For patients with severe AV diseases, aortic valve replacement is the most effective treatment standard, in which the AV is replaced with a mechanical or biological one. Through the different options for valve replacement operations, transcatheter aortic valve replacement is known to be less invasive and traumatic. However, the valve which is used for the replacement should offer proper hemodynamic performance and lifelong durability quality. Disturbed hemodynamics can lead to serious conditions like hemolysis which is associated with high shear stresses. The valve tissue should guarantee perfect physiological hemodynamics and be safe for blood-material reactivity. By this means, efforts to create stronger durable valves using tissue engineering are rising between researchers. Although bold steps have been made toward creating functional valve tissue, the developed materials still need better biocompatibility and bi-functionality. The successful evaluation of the aortic valve disease severity and development of the functional artificial valve tissue solely relies on an accurate and detailed investigation of the natural human valve structure. However, the current medical imaging techniques including the echocardiography and Doppler velocimetry have limited accuracy and are not sufficient for a detailed and quantified evaluation of the valve problem. Moreover, more accurate measurement methods such as angiography is an invasive
procedure which can lead to severe complications. As an alternative to medical imaging procedures, numerical methods can be adopted to investigate the dynamics of the aortic valve and the blood flow. However, realistic and accurate modeling of the valve deformations using numerical models comes with many challenges. The blood flow and the leaflet structure are in strong interaction with each other. The blood flow exerts hydrodynamic pressure on the leaflets and leaflets
are deformed elastically under these pressure variations between the downstream and upstream of the aortic valve. Thus, solving these fields separately will neglect this interaction and may lead to incorrect results. On the other hand, the aortic valve leaflets are complex thin structures which made up of a various networks of cells and microstructures. Various compositions of these molecules through the thickness of the leaflets form distinctive layers. Each layer
contributes to enensuring optimal hemodynamic and mechanical environment without any abnormal hemodynamic disturbance. The deformation of the aortic valve tissue under blood flow forces is highly non-linear due to these distinctive layers.
In this thesis, it was aimed to solve the aortic valve structure and the blood flow fields simultaneously using an iterative implicit method. This fluid-structure interaction method will ensure that the interaction between the flow fields and structure fields will be captured accurately. Using this method in each time step the flow and structure
fields are solved simultaneously with separate computational fluid dynamics and finite element methods solvers. At the end of each time step, the information regarding the pressure field of the blood flow and the deformation of the leaflets are shared between solvers using an iterative method. At first, the iterative implicit method for fluid-structure interaction analyses was studied in detail. A general procedure for employing the interaction between the blood flow and the structure fields was created. Any potential errors or stability problems and available solutions within this method were studied for ensuring accurate results during simulations. Afterwards, two-dimensional aortic valve geometries were generated based on real echocardiography images of a patient. The interaction between the blood flow and flexible leaflets was employed using itterative implicit fluid-structure interaction method. Valve inlet velocity, measured from Doppler echocardiography from the patient was used as a velocity boundary condition in the model. The results of the numerical simulations were compared and verified with real valve movements. Later, three different two-dimensional models with varying leaflet stiffness values were developed to represent healthy, mild and severe aortic stenosis. The velocity contours, streamlines, and vectors were plotted to investigate and compare the blood flow characteristics in each model. In the next part, patient-specific three-dimensional models were developed for the patients with normal tri-leaflet valves, stiffened stenosed tri-leaflet valves and congenital bicuspid valves. The dimensions of the aortic valve and the blood flow velocities were captured using real medical measurements of the patients. For each model, the peak pressure difference, velocity profiles, vortex formation downstream of the valve, and peak shear stress levels on the leaflets were evaluated in detail. The deformations of the leaflets through simulations were compared to echocardiography movies for validation. In addition, pressure catheterization data were used to verify the numerical models. The results were in good agreement with experimental pressure catheterization data and the numerical approach was verified. In the last part of the thesis, it was aimed to investigate the effect of AV material
properties on the valve deformations, by implementing different non-linear properties of the AV leaflets in three different material models. By comparison of the iterative implicit simulation results of these three models, the effects of material non-linearity and anisotropy on the valve deformations were studied in detail. To evaluate the calcification risk, the mechanical stress levels on different parts of the leaflets were calculated. While the calculated mechanical stress in the free edges area was near zero, high-stress regions were observed in coaptation and leaflet roots. The
results suggested that the calcification patterns on the leaflets first initiate from the coaptation and leaflet root surfaces. The comparison of stress levels between models shows that the non-linear aortic valve model is prone to slightly lower mechanical stresses distribution on the leaflets. This suggests that, the non-linear character of the
aortic valve reduces the risk of calcification. Furthermore, for an accurate and quantitative comparison of the performance of each control model, the time-dependent orifice area profiles for each control model were captured by processing the images created by simulation results. The orifice area profiles revealed the fact that the material nonlinear properties have a dominant effect on the aortic valve dynamics. The results show that the collagen fiber orientation in the circumferential direction has a noticeable effect on stabilizing the valve deformations, which leads to lower oscillations and fewer flutters of the leaflets. Similarly, the orifice area profiles also revealed that the closing phase of the AV leaflets is also affected strongly by the collagen fibers. By this means, the role of the
added rigidity in circumferential direction became more apparent for helping the leaflets to retain their closed shape.