U ovom radu razvijen je novi tip srčane pumpe. Originalnost ovog koncepta je da se mehanička energija predaje fluidu trenjem, vrtnjom ravnih diskova koji nemaju lopatice. Primjenom analitičkih, numeričkih i eksperimentalnih metoda definiraju se parametri bezlopatične srčane pumpe (BSP).
Iz Navier–Stokesovih jednadžbi je izveden matematički model strujanja te su određeni glavni geometrijski parametri BSP pumpe. Prilikom određivanja parametara uvedeni su kriteriji koje konstrukcija mora zadovoljiti. Prvi i najvažniji kriterij je da pumpa dobavlja krv unutar zadanih granica protoka i prirasta tlaka da bi se osigurala normalna cirkulacija krvi. Drugi vrlo važan kriterij je visoka hemokompatibilnost te minimalan negativan utjecaj BSP na krv (bez zona zastoja i recirkulacije strujanja, unutar prihvatljivog raspona tangencijalnog naprezanja). Također je bitno postići pumpu minimalnog volumena.
Definiranje parametara konstrukcije centrifugalne bezlopatične srčane pumpe izvodi se u odnosu na referentnu srčanu pumpu HeartMate II (HM2), jer se kroz kliničku praksu pokazalo da uzrokuje najmanje komplikacija i da ima dobru hemokompatibilnost.
Numeričkom simulacijom je, kroz postupna poboljšanja geometrije pumpe; određena konačna konstrukcija BSP pumpe bez recirkulacije i bez zona zastoja strujanja. Za radnu točku određenu sa tlakom Δp = 65 mmHg, protokom Q = 5 l/min i brojem okretaja ω = 6000 o/min određeni su parametri BSP konstrukcije: unutarnji radijus R1 = 12 mm, vanjski radijus R2 = 15 mm, udaljenost između diskova h = 1 mm, i broj diskova n = 6. Iznos tangencijalnog naprezanja u rotoru je u rasponu 46 – 108 Pa, a vrijeme prolaska fluida je 0,0194 sekundi.
Uspoređujući HM2 i BSP pumpe po kriteriju hemokompatibilnosti pri tlaku Δp = 65 mmHg i kutnoj brzini ω = 6000 o/min. Protok kroz HM2 je Q = 5 l/min, dok je za pumpu BSP protok Q = 5,43 l/min. Pumpa HM2 ima tangencijalno naprezanje na zidu u rasponu od 0 do1025 Pa te skalarno smično naprezanje u rasponu od 0,0632 do 3302 Pa. Pumpa BSP ima tangencijalno naprezanje na zidu u rasponu od 0 do 308 Pa, a skalarno smično naprezanje u rasponu od 0 do 667 Pa. U novo razvijenoj BSP pumpi nema recirkulacijskih zona, ni zona zastoja što je sa stanovišta hemokompatibilnosti jako povoljno. Uz to BSP pumpa ima tangencijalno i skalarno smično naprezanje niže nego pumpa HM2 koju možemo smatrati vrlo dobrom izvedbom u smislu hemokompatibilnosti.
|Sažetak (engleski)|| |
The main function of the heart is to ensure continuous blood circulation to support normal body functions. Many life-threatening problems emerge if function of the heart is compromised. Therefore, if the heart is not able to ensure normal blood flow, it is extremely important that the blood flow is ensured by additional pumps called heart pumps. An artificial heart, i.e., a heart pump, is used to pump blood through the body when the heart itself is unable to do so.
Cardiovascular diseases are the most common cause of death in the world. In the European Union countries, 42% of all deaths are due to cardiovascular diseases. Unfortunately, vascular system diseases are the main cause of death in Croatia. In 2016, the share of cardiovascular diseases in total mortality in Croatia was 45%, which means that almost every second person who died in Croatia, died of cardiovascular disease. A reasonable desire is to reduce these numbers, which in turn requires the development of heart pumps. Heart pumps provides the opportunity for people with heart disease to have significantly more time to receive a transplant (so-called bridge to transplantation). Also, heart pumps have the potential to permanently replace the patient heart when transplantation is not possible due to general health of the patient.
In this research, a new type of heart pump is developed. The uniqueness of this pump concept is that the mechanical energy is transferred to the fluid by the rotation of flat discs without blades. Volumetric heart pumps with a diaphragm that provide pulsatile flow and heart pumps with blades that have continuous flow have already been developed. Heart pumps developed so far use shape, i.e., blades or diaphragm to transfer mechanical energy, while use of a bladeless pump as a heart pump is a complete novelty. Analytical, numerical, and experimental analyses are used to define the pump parameters that affect the heart pump hemocompatibility.
The design parameters of a centrifugal bladeless heart pump are defined in relation to the reference heart pump. The HeartMate II Left Ventricular Assist Device from Thoratec Corporation (HM2) was selected as the reference heart pump. Through clinical practice, it was shown that HM2 causes the least complications and has good hemocompatibility. As part of this thesis, a bladeless heart pump (BSP) is designed. Hemocompatibility parameters of the BSP are equal to or better than HM2. Experimental analysis of the HM2 heart pump was performed in the interdisciplinary Laboratory for Artificial Cardiovascular Circulation, Faculty of Mechanical Engineering and Naval Architecture. For this purpose, an open-loop MOCK circulatory system was made for testing heart pumps. The MOCK circulatory system is made of Plexiglas and consists of a large tank, control valves, straight pipes of circular cross-section, a heart pump holder and a Venturimeter. In the experimental measurements, the prescribed standards for testing pumps defined by the ISO 9906: 2012 standard are met. The measured values are flow, pressure increase in the pump and suction pressure in the pump. All measuring chains were calibrated before the measurement and the measurement uncertainty of each individual measuring chain was assessed, according to ISO GUM standard. Measurements were performed with two different fluids: water and a solution of glycerol and water used as a substitute for blood. Based on the experimental results, the h – Q characteristic curves of the HM2 pump for both fluids are presented. The estimation of the total measurement uncertainty was performed based on the measurement uncertainty of each measuring chain and the deviation of the measured values of the h – Q curve from the regression curve.
For the purposes of numerical calculation of the HM2 pump, it is necessary to know its geometry. Therefore, in the Laboratory for Precise Length Measurements, a cloud of points was obtained by precise CT scanning of the HM2 heart pump. The pump was scanned with a high-resolution detector (4000 x 3000 pixels), with a maximum CT scan resolution of 54 μm. After the described data collection, the 3D volume of the HM2 pump was reconstructed.
Numerical analyses of HM2 was made in ANSYS Fluent 15.0. A 3D design of HM2, that was obtained by CT scanning, was used. The computer domain was divided into 6,4·106 control volumes, with the aim of achieving quality simulation. The mesh was refined in the boundary layer and near the joints and details. k – ω SST model was used to model turbulence. The rotation of the rotor was modeled using the Moving Reference Frame method. All numerical calculations were performed with a second order scheme of accuracy, until the result convergence and sufficient accuracy of the observed parameters was achieved. Shear stress magnitudes were calculated numerically. The Δp – Q characteristic curve for the HM2 pump was also calculated in the scope of the simulation.
Quality of the numerical analysis settings was assessed by comparison of experimental and numerical results. Selected simulation settings were to be used for all further numerical calculations within this thesis. Different ranges of shear stress for which acceptable numerical hemocompatibility is achieved are reported in the literature. In this thesis, the narrowest range of 30 – 140 Pa was used for the reference shear stress range. Since these ranges are general, shear stress ranges for which hemocompatibility has been clinically confirmed have been taken from the numerical simulation of the reference heart pump HM2. The stated ranges of shear stresses need to be achieved in the numerical simulation of a bladeless centrifugal heart pump. This ensures the necessary condition of acceptable hemocompatibility for the new heart pump design.
The flow inside the BSP can be divided into two parts, the flow inside the pump rotor and the flow in the connecting pipes. Energy transfer from the pump to the fluid is performed inside the rotor (active part of the pump). As the geometry of the BSP rotor is simple, it is possible to analyze the flow using Navier – Stokes equations. Although blood is a multiphase non-Newtonian fluid, the theoretical analysis introduced the assumption of blood as a single-phase Newtonian fluid with a density of 1050 kg/m3 and a dynamic viscosity coefficient of 0,0035 kg/(m s). Stationary flow was assumed, although there is a non-stationary velocity profile at the pump inlet resulting from active part of the heart. The relative Reynolds number is lower than the critical Reynolds number for the flow between the two plates, and laminar flow in the rotor was assumed. In addition to the above assumptions and limitations, a mathematical model of the flow in the BSP rotor was derived using the Navier – Stokes equations. The initial assumption was made for the rectified flow model. After that, the Navier – Stokes equation in cylindrical coordinates was solved.
Algebraic expressions for the pressure field, velocity field, shear stress distribution on the disc, torque and force required for rotor rotation are derived. Furthermore, Δp – Q characteristic curve of the BSP pump was derived. Using the above terms and data obtained from the analysis of the HM2 pump, the main geometrical parameters of the BSP pump were determined.
When determining the parameters, additional criteria were introduced that the structure must meet. The first and most important criterion is that the pump supplies blood within strict limits to ensure normal blood circulation throughout the body. The designed operating point Δp = 65 mmHg, Q = 5 l / min was selected for the construction of the BSP pump. Another very important criterion is high hemocompatibility and minimal negative impact of BSP on the blood (minimal thrombosis and hemolysis). The acceptable shear stress is within the range of 30 – 140 Pa. The third criterion is to achieve a minimum pump volume. The fourth criterion is the high efficiency of the pump due to the longer autonomy without charging the batteries. The first parameter selected in the theoretical analysis is the angular velocity. This parameter is independent, and all other parameters will depend on it. The designed operating point is defined at ω = 6000 rpm. From the condition that the shear stress is within the given limits, the inner radius of the disc is defined. Considering the criterion of the minimum pump volume, the outer radius of the disc and the number of discs are defined. Using the equations derived by solving the Navier – Stokes equations, the following were calculated: shear stress on the disc, pump power and torque required to rotate the rotor. Main parameters of the BSP pump were defined using theoretical analysis: pressure Δp = 65 mmHg and flow Q = 5.43 l/min at the designed operating point, angular speed ω = 6000 rpm, six discs 1 mm thick with 1 mm disc spacing, internal disc radius R1 = 12 mm, outer disc radius R2 = 15 mm. The range of shear stresses is from τϴz = 115 Pa at the bottom of the disc, to τϴz = 92 Pa at the top of the disc. The power of the pump is P = 1,324 W. The analytical equation Δp = Δp (Q) was derived from which the Δp – Q characteristic curve of the BSP pump was determined.
Although all the main parameters required for the construction of a BSP pump have been derived by the theoretical analysis, it is impossible to design the geometry of the pump without numerical analysis. The ANSYS Fluent 15.0 program was used for flow analysis. The pump was analyzed as five identical computer domains. The domain consists of the space between two discs with the addition of a flow separator, and part of the domain of the inlet and outlet connecting pipes. In order to achieve a quality simulation, the domain was approximated with 1,1·105 control volumes. The mesh was refined in the boundary layer as well as near the junction of the flow separator and the connecting pipes. Turbulence was modeled with k – ε and k – ω SST turbulence models. In the thesis, gradual improvements of the pump shape are presented, up to the final fifth version of the pump shape, with which flow without stagnation and recirculation zones was achieved.
The Δp – Q characteristic curve of the final version of the BSP pump design was calculated using numerical simulation. A comparison of the curves obtained by theoretical and numerical analysis shows that both curves are linear and coincide. The numerical Δp – Q characteristic curve was calculated considering the flow in the computation domain (with flow separator and connecting pipes), while the theoretical Δp – Q characteristic curve was calculated only for the rotor, i.e., the space between the disks. Therefore, resulting in incomplete coincidence between theoretical and numerical Δp – Q characteristic curves. Three parameters were used to assess the quality of the structure on hemocompatibility: wall shear stress (WSS), scalar shear stress (SSS) and residence time. The WSS in the rotor is in the range of 46 to 108 Pa, which is lower than the required value of the maximum WSS. The residence time of the fluid in the BSP pump is 0.0194 s. There is a small area (5% of the total volume) at the flow separator in which the values are higher than allowed (108 – 308 Pa). Exposure time in the area in question is short, in order of 5·10-4 s. According to the Hellums diagram for fluid residence time of 5·10-4 s, the allowable WSS is 700 Pa which is significantly higher than the calculated stress. During the numerical analysis, the SSS field was calculated, which determines the stress of the particles inside the fluid. 10% of the total volume was exposed to high linear stress in the fluid (SSS ˃ 100), 10% of the total volume was exposed to medium SSS (10 <SSS <100), and the remaining 80% of the fluid volume was exposed to low SSS (SSS <10).
Comparison of the HM2 and BSP pumps regarding the hemocompatibility was performed for angular velocities ω = 6000 rpm. The flow through HM2 pump is Q = 5 l/min while the flow through BSP pump is Q=5.43 l / min. The HM2 pump has a WSS in the range of 0 to 1025 Pa and a SSS in the range of 0.0632 to 3302 Pa. The BSP pump has a WSS in the range of 0 to 308 Pa and a SSS in the range of 0 to 667 Pa. In the newly developed BSP pump, there are no stagnation or recirculation zones, which is very favorable from the hemocompatibility viewpoint. In addition, the BSP pump has WSS and SSS parameters lower than the HM2 pump, which can be considered a very good performance in terms of hemocompatibility.
All hypotheses of the doctoral thesis were confirmed:
• Hemocompatibility of the heart pump is acceptable when the shear stresses are in the range of 30 – 140 Pa and when there is no stagnation and recirculation zones.
• The shear stress on the blood is proportional to the pump head, the angular velocity and the distance between the discs, and inversely proportional to the diameter of the discs.