10TH INTERNATIONAL SYMPOSIUM ON PARTICLE IMAGE VELOCIMETRY – PIV13 Delft, The Netherlands, July 1-3, 2013
Influence on fluid-dynamics of the aortic root morphological
modifications induced by Marfan syndrome
Fortini S1*, Querzoli G2, Espa S1, Costantini M3, Sorgini F4, Del Prete Z4, D’Annolfo A5 and Bisegna P3
1.Dipartimento di Ingegneria Civile, Edile e Ambientale - Sapienza Università di Roma, Italy 2 Dipartimento di Ingegneria del Territorio - Università di Cagliari, Italy
3 Dipartimento di Ingegneria Civile - Università di Roma Tor Vergata, Italy
4 Dipartimento di Ingegneria Meccanica e Aerospaziale- Sapienza Università di Roma, Italy
5.Centro per la Sindrome di Marfan - Presidio Regionale - Istituto di Cardiochirurgia Policlinico Tor Vergata,
Roma, Italy
*corresponding author: stefania.fortini@uniroma1.it
ABSTRACT
The Marfan syndrome is a connective tissue disorder inherited as an autosomal dominant trait, characterized by abnormalities involving the skeletal, the ocular and especially the cardiovascular systems. Cardiovascular complications include the aortic valve regurgitation, the dilatation of the proximal main pulmonary artery, the thickening and prolapse of atrio-ventricular valves, the mitral annular calcification, and rarely the dilated cardiomyopathy. However, the main typical sign in Marfan patients is the aortic root dilatation: this is the most common cause of mortality or morbidity since it is correlated with an high risk of aortic dissection or rupture. The interplay and counterplay between morphologic changes and hemodynamics in the development and progression of aortic pathologies are still unknown. The objective of this study is to evaluate the modification on the fluid-dynamics in aortic root of Marfan patients by means of an in vitro study performed in the Pulse Duplicator already used in previous investigations. An 1:1 scale healthy and two Marfan Syndrome aortic root models were designed to analyze the flow in terms of pressure, flow rate, aortic model kinematic behavior and velocity field. The two-dimensional instantaneous velocity fields were measured by means an image analysis technique called Feature Tracking that allowed to reconstruct the particles trajectories; then the Eulerian data was obtained by the interpolating the Lagrangian quantities over a regular grid. The described measurements allowed to underline important hemodynamics alterations between the healthy and Marfan syndrome models, highlighting how the in-vitro analysis may be a valuable support to the early diagnosis and clinical management.
1. INTRODUCTION
Several studies on the fluid dynamics of the large vessels, in particular of the aortic root, are present in literature, primarily motivated by the interest in assessing the hemodynamic performance of prosthetic aortic valves or vascular grafts [1]. The fluid dynamic analysis of such devices, in fact, is crucial in providing any information on the compatibility with the physiological environment, and in evaluating the possible causes for hemolysis or thrombogenic phenomena [2].
The framework of the in vitro study of transvalvular hemodynamics is well established ([3], [4], [5], [6], [7], [8], [9], [10], [11]); on the contrary investigation of the near flow field are reported in more recent studies ([12], [13], [14], [15]). Most of these studies was first focused on the prosthesis’ effects on the fluid-dynamic field immediately downstream the valve and into the proximal portion of the ascending aorta, without considering the possible effects nor morphological variations, neither of the variation of the mechanical properties of the vessels walls. At a later stage both numerical [16] and experimental [17] models take into account the interaction between fluid and wall.
The in-vivo studies found in literature can be very helpful in highlighting the altered blood flow characteristics in common aortic pathologies, showing also how the altered haemodynamics are associated with pathological processes of the vessel wall, leading to the development of atherosclerotic plaques, loss of elastic lamellae, media degradation and the accompanying loss of vessel wall integrity [18]. Kilner et al [19] firstly applied time resolved phase contrast magnetic resonance imaging to investigate the distribution of secondary flows in the aortic arch in healthy subjects. Later the progresses in velocity measurement techniques based on magnetic resonance imaging (MRI) were useful to identify significant changes in the structure of the flow in the case of patients with Marfan syndrome [20]. Bieging et al [21] used the phase contrast MRI to estimate wall shear stress over the vessel surface, for healthy and unhealthy subject. They found that the spatial patterns of wall shear stress in ascending aorta were very different, and they could be associated with atherosclerosis formation and may promote further aneurysm growth.
This studies may offer an overview on the effects that pathological vascular morphology has on the aortic fluid dynamics. However, for the understanding of the origin and development of aortic pathologies, larger studies and further evaluation strategies will be vital. In this context, the in-vitro analysis performed here may be a valuable support to physically based interpretation of the in vivo data.
2. MATERIALS AND METHODS 2.1 Experimental Set-up
Figure 1 shows a sketch of the experimental apparatus.
Figure 1 Sketch of the experimental apparatus: 1.Linear motor, 2.Hydraulic piston, 3.Ventricular chamber, 4.Aortic chamber, R1-R2.Periferic resistances, RC. Compliance flow regulator, C. Compliance, S1. Constant head tank, S2. Atrial tank.
The flow through the aortic bileaflet valve was investigated in a Pulse Duplicator (PD), i.e. a hydraulic loop simulating the human systemic circulation, in both flow rate and ventricular-aortic pressure waves. The anatomic district between the left ventricle outflow tract and the aortic root was accurately reproduced, and the impedance of vascular systemic net was mimicked according to a concentrated parameters approach. A positive displacement piston pump moves accordingly to a given pulsatile time function governing the volume changes of the ventricle (Figure 2). The aortic chamber, which is the core of the apparatus, is made of plexiglass for the required optical access. The aortic root is placed inside the aortic chamber. It is made of silicon rubber, to both simulate the physiological blood vessel elasticity, and also to allow optical access. The prosthetic valve was the pericardial Bioprosthetic aortic valve type ‘St. Jude Medical Biocor Valve’, with nominal diameter of 27 mm and an internal diameter of 25 mm, housed inside the aortic root just upstream of the Valsalva sinuses.
Two piezoelectric sensors (PCB Piezotronics® 1500 series) are located upstream and downstream of the valve, in order to measure, respectively, the aortic (pa) and ventricular pressure (pv), according to the Italian Department of Health prescriptions. Ventricular and aortic pressure tapes are located at 6.25D and 3.5D from the valve housing, respectively. The cardiovascular peripheral resistance is reproduced by two in series shutter taps (R1 and R2, as shown in Figure 1). A third valve controls the flow entering or leaving the compliance chamber. The latter is an air tank and reproduces the compliance of large arteries by allowing storage and release of fluid during the simulated cardiac cycle. The aortic flow
enters the right atrium tank S1 through a nozzle open to the atmosphere, thus closing the systemic circulation. Tank S2 mimics the left atrium, and feeds the left ventricle chamber following a pressure regime completely separated from the aortic one.
Figure 2 Time law of variation of non-dimensional ventricular volume (black line) and flow-rate (blue line)
The aortic root geometric aspect-ratio was 1:1 (§2.2). For the dynamical similarity, equality of both the Reynolds and the Womersley numbers is required between the physiological flow and the experimental one, these parameters being defined as: 2
UD
D
Re
; Wo
ν
Tν
where ν is the kinematic viscosity of the blood analogue fluid, U is the peak velocity through aortic valve orifice at the systolic phase, and T is the period of cardiac cycle. The experiments were performed adopting a solution of sodium chloride in water (9g/l), with viscosity of approximately 1/3 blood viscosity. Hence, to respect the dynamic similarity, an experimental cardiac cycle period equal to 3 times the physiologic one was adopted, for a given physiological stroke volume SV (i.e., the volume ejected from the ventricle in one heart beat).
The tests were performed by changing the stroke volume (SV= 54ml, 64 ml and 80ml) and the period (T=1.8s, 2.4s and 3s). The vertical mid-plane of the aortic root was illuminated by a 12 W, infrared laser. The working fluid was seeded with neutrally buoyant particles with 50 μm average diameter. Images were acquired by a high speed camera (800 frames/s) with a spatial resolution 800x950 pixels. A Feature Tracking algorithm [22] was used to measure the instantaneous velocity field by recognizing particles trajectories. Interpolation of data on a regular 50x51 grid then gave the 2-D velocity matrix. Spatio-temporal resolution (Δxmin= 0.07mm, Δtmin=1/800) was high enough to identify vortex structures in the aortic root, and to follow their evolution during the cardiac cycle.
Each series consisted of 100 runs that have been used to compute the phased averages. The main experiments parameters are listed in Table 1.
SV [ml] T [s] U [m/s] Re Wo 54 2.4 0.090 2174 15 64 2.4 0.107 2576 15 80 2.4 0.134 3220 15 64 1.8 0.143 3435 18 64 3 0.086 2061 14
Table 1 Main parameters describing the flow field experiments
The configuration with stroke volume SV 64ml and period T of 2.4s is the reference configuration, reproducing in similarity the same physiological parameters of a subject at rest, as well as the FDA guidelines for valve testing (stoke volume 64ml, hearth rate 75 beats/min).
2.2 AORTIC ROOT MODELS
One of the main focus of this work was to reproduce models with an appropriate geometry and also accordingly with their kinematic behavior.
SHAPE. In order to design (with scale 1:1) the silicon rubber models, an exhaustive literature research was matched. Many studies on ultrasound images based ([20],[23],[24],[25],[26]) allowed to compare the morphologies’ differences between healthy and Marfan Syndrome subjects; the dimensions here chosen have been able to maximize as much as possible the meaningful differences of their fluid dynamics performances. Table 2 summarize the dimension adopted:
an [mm] ra [mm] aa [mm] hs
[mm] ra/an aa/an hs/an
ra/a a HEALTY MODEL 25 45 27,5 20 1,80 1,10 0,80 1,64 MARFAN MODEL 1 25 45 27.5 30 1.80 1.10 1.20 1.60 MARFAN MODEL 2 25 45 27 30 1.82 1.53 1.86 1.19
Table 2 Aortic root models dimensions (an=aortic annulus, ra=aortic root diameter, aa=ascending aorta diameter, hs= height of sinuses of Valsalva)
DISTENSIBILITY. The models’ kinematic behaviors, i.e. their distensibility in the phase between the systole peak and the diastole, have been monitoring by recreating a correct diameter’s variation accordingly with the physiological range. To do so, the air level in the aortic chamber has been properly changed. Figure 3 shows the time diameter variations for all the models tested.
Figure 3 Systolic diameter increases for the healthy root model (left), Marfan model 1 (center) and Marfan model 2 (right) models
Basing on the literature data, the maximum systolic diameter increase (computed as ΔD%=(d-ddias)/(ddiasx100)) for an
healthy and pathological subjects, at rest, must be about 13-15% and 5-8% respectively.
3. RESULTS
3.1 Pressure, Flow-Rate and Distensibility Parameters
Aiming to fully respect the similarity theory, pressures, flow rate curves and the kinematic behavior of the aortic roots wall have been reproduced to match with the physiological one.
PRESSURE
.
The two pressure transducers, located upstream and downstream of the aortic valve, allowed to record the behavior in time of the ventricular and aortic pressure for all the experimental conditions, and then phase-averaged over all the recorded 100 cardiac cycles.The aortic and ventricular pressure waves for the reference condition (SV=64ml, T=2.4s) have been set, both for the healthy and Marfan Syndrome model, by adjusting the compliance and the resistance shutter taps into the hydraulic loop. In addition, it was observed as they changes according to the stroke volume and period variations.
Figure 4 Pressure behavior in time (reference condition, SV 64ml and T 2.4s) for the healthy root model (left), Marfan model 1 (center) and Marfan model 2 (right)
No relevant differences between the healthy and Marfan Syndrome cases have been observed, as found in literature ([20], [26]).
FLOW-RATE
The electromagnetic flowmeter, located upstream the aortic valve, allowed to measure the flow rate for all the experimental conditions (Figure 5). The maximum instantaneous flow rate, for the reference condition, has been obtained at the systolic peak (t/T=0.25). In such condition there is a backflow towards the valve immediately at the end of the systolic phase. This could be related to a delayed and protracted leaflet closure. As expected, no relevant differences exist between the healthy and Marfan Syndrome cases: as well as the pressure waves, the flow rate is directly proportional to the stroke volume and inversely proportional to the cardiac period.
Figure 5 Flow Rate at different stroke volume and simulation period constant (T=2.4 s) in the healthy root model (left), Marfan model 1 (center) and Marfan model 2 (right)
DISTENSIBILITY
The Pulse Duplicator was set under pressure and flow rate physiological conditions. Without changing the compliance and the resistance shutter taps into the hydraulic loop, distensibility measurements have been made and the kinematic behavior in the reference condition was reproduced (Figure 6).
Figure 6 Distensibility behavior in time at different stroke volume and simulation period T constant (T=2.4 s) in the healthy root model (left), Marfan model 1 (center) and Marfan model 2 (right)
The diameter variation has the same trend of the flow rate (Figure 5), simulating the aortic physiological function of windkessel, i.e. the aortic silicon models expand during the systolic phase, and recoil its initial position at the end of the diastolic phase.
It can also be observed that the systolic diameter increase has the same reaction of pressures and flow rate curves to stroke volume changes. Distensibility increases when the stroke volume increases, and vice-versa, for all the root models, according to the lower aortic deformation reproduced for the pathological models.
The table 3 summarizes the values of aortic pressure, flow-rate and distensibility parameters adopted during the tests. The highest peak flow rate correspond to highest aortic pressure values which, in turns, correspond to greatest diameter increase.
Table 3 Pressure, flow-rate and distensibility parameters
3.2 Velocity field
Figures 7 describes the salient instants during the cycle of the analyzed phenomenon in the reference condition.
On the bottom of each plot, the non-dimensional time is reported and the corresponding point on the flow rate graph is represented by a red dot on the lower-left corner of the graphs.
During the systole (first row) series of vortices are shed from the leaflets of the valve. On the side of the sinus of Valsalva (right-side of the color maps) the vorticity accumulates in the sinus forming a nearly steady vortex, whose size is increased in dilated aortic root. This behavior is similar in all the three test cases. A different behavior is observed on the side of the commissure. In the healthy root (left panel), the vortices released on that side are advected downstream, thus partially obstructing the aortic lumen and deflecting the mean jet flow which impinge the vessel wall on the side of the sinus. Conversely, in the dilated root models 1 and 2 (center and right panel), the vorticity finds room to accumulate in a steady vortex also on the side of the commissure, and it is not advected downstream. At the same time, the dilated sinus hosts a larger vortex which tends to deflect the main jet flow which impinge the vessel wall on the opposite (commissure) side. The alteration in the systolic flow leads to different patterns in the residual flow during the diastole (second row). The healthy root exhibits an overall counterclockwise circulation (left panel), whereas the circulation is clockwise in both the Marfan dilated roots 1 and 2 (center and right panels). In particular, the flow is well organized in a single vortex residing in the sinus in the right panel (Marfan model 2, right column). It is worth notice that the variations in the flow pattern could affect the feeding of the coronaries, which take place during this phase of the cycle.
Figure 7 Streamlines graphs onto absolute velocity values color map. The plots referring to two instants in the reference condition (SV 64ml T2.4s), in the healthy root (left column ) Marfan model 1 (center column ) and Marfan model 2 (right column)
3.3 Viscous shear stress
It is known that forces exerted on the blood elements are likely related to thrombus formation and hemolysis ([28], [29]). Moreover, it has been recognized that shear stresses can cause platelet activation [30]. Therefore, when evaluating the blood flow, the description of the forces that the flow induces on its constituent cells is also needed. Even if the investigation of the mechanisms causing blood cell damage is not easy. In any case, it is possible to think that the stress tangential component is the most relevant.
Obviously, it depends on the orientation of the surface that one considers, but the surface of a blood cell is closed, so it assumes all orientations. Therefore, one can be sure that, somewhere, the surface is exposed to the maximum possible shear stress. Since in the present experiment only two components of velocity have been measured on a plane of symmetry, we can considered only the 2-D case, but similar results can be obtained also in 3-D. Using the constitutive equation for Newtonian fluids, such as the blood flowing in large vessels, the maximum shear stress, τmax is [22]:
2 1 max 2 1
(
)
=
(
)
2
e
e
where τi and ei are the eigenvalues of the stress tensor and the strain velocity tensor, respectively, and the expression is in their common, principal reference frame.
As reported in literature [31], dilated ascending aorta is associated with alteration in shear stress distribution due to the changes in flow pattern and velocities; viscous shear stress values are similar between healthy and Marfan Syndrome cases, what is different is the spatial distribution.
Figure 8 shows the non-dimensional viscous shear stress averaged over the measuring region, during the cardiac cycle, for all the root models in the reference configuration. The magnitude of the average shear stress is more or less of the same order in the healthy and Marfan cases.
Figure 8 Average non-dimensional maximum viscous shear stresses during the cycle, in the reference condition (SV 64ml T2.4s), for the healthy root (blue line), Marfan model 1 (red line) and Marfan model 2 (black line)
Figure 9 shows the non-dimensionalised (by means the scale ρU2) maximum shear stress at two main instants; the
velocity vectors are plotted over a viscous shear stress color map.
As already discussed in the velocity fields description, the spatial distribution of the vortical structures are different in the root models: this determines different location of the shear stress higher values, that are generally localized at the boundary of the axial jet and in the recirculating region. At t/T=0.158, just before the systolic peak, in the healthy model (left column) maxima values are at the right wall, due to the central axial jet that deflects the flow on the wall on the sinus side. At this instants, in the Marfan models the flow is constricted towards the left aortic wall due to the large sinus vortex. Correspondingly, in those models elevated shear stress values are along the left wall, in particular at the level of the sinus ridge, and on the right, along the boundary of the axial jet, due to the high velocity gradient values between the recirculating region in the Valsalva sinus and the jet itself. At the systolic peak (t/T=0.218), no many differences in the spatial distribution are visible between the healthy model and the Marfan model 1 (respectively, left and center columns) except that the flow in the dilated root is skewed on the left, causing moderated shear stress level on the walls. In the Marfan model 2 (right column) higher values are in proximity of the prosthetic valve.
Figure 9 Velocity field (white vectors) onto viscous shear stress color map. The grafts referring to two instants of the flow field in the reference condition (SV 64ml T2.4s), in the healthy root (left column ) Marfan model 1 (center column ) and Marfan model 2 (right column)
4. CONCLUSIONS
An in-vitro study has been performed to allow a comprehensive characterization of the fluid-dynamics in the aortic root in Marfan syndrome patients, aiming to identify potential hemodynamic alterations, which may lead to aneurysmatic remodeling. The human circulatory system has been reproduced thanks to a Pulse Duplicator simulating the cardiocircolatory system. Three aortic root models were designed to reproduce both the anatomical geometry and the physiological kinematic behavior. Several tests have been carried out by changing the period and stroke volume; for each condition, pressure, flow rate, distensibility have been monitored. Each measurements series consisted of 100 runs, used to compute the phase-averaged quantities.
To analyze the velocity field the working fluid was seeded with tracer particles, the vertical symmetry-plane of the interesting region was illuminated by a laser light sheet, and the images were recorded by an high speed camera. From the recorded images, the Feature Tracking algorithm allowed to measure the instantaneous velocity field by recognizing particles trajectories, and so the Langrangian velocity. This Langrangian data have been then interpolated on a regular grid to give the Eulerian velocity fields, which have been used to compute the vorticity and viscous shear stress distribution for both the models.
The described measurements allowed to underline important hemodynamics alterations between the healthy and Marfan syndrome models. In particular, the healthy model showed mainly undisturbed flow pattern. At the valve opening, two small vortical structures, immediately downstream the aortic valve, were generated and disappeared during the following instants. The axial jet was skewed on the right aortic wall, due to the commissure swirling region which move from the aortic root toward the ascending aortic tract. The axial jet peak velocity was about 1.3m/s.
In Marfan Syndrome models, already in early systole, large vortices were formed on each side of the axial jet, clockwise on the left and anticlockwise on the right side. The sinus vortex on the right was larger than that at the commissure and skewed the jet on the left side, with peak velocity of up 0.9m/s. The vortices lasted through systole, and during the deceleration phase the sinus vortex took up a large fraction of the available aortic lumen.
The viscous shear stress distribution reflected the flow fields alterations, with high values on the right for the healthy model, on the left for the Marfan Syndrome models. Whereas, the magnitude of the average shear stress was of the same order both in the healthy and Marfan case.
The irregular blood flow patterns could be associated with aortic root dilation, aneurysm formation and vessel wall dissection. These flow disturbances could induce pathologic shear forces at the vessel wall, which could affect endothelial function, and thus promote disease progression by creating areas at increased risk for vascular remodeling. Thus, such geometrically triggered changes in blood flow characteristics may be a useful clinical marker regarding the severity and progression of the disease, and may help to identify patients at risk for aortic dissection and rupture. The results illustrate that pathological flow features, rather than pure geometrical parameters, may be an important clinical marker for future treatment planning, in particular they may be useful in determining the appropriate time for intervention
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