- Email: [email protected]
The carotid sinus acts as a mechanotransducer of shear oscillation rather than a baroreceptor
Medical Hypotheses 134 (2020) 109441
Contents lists available at ScienceDirect
Medical Hypotheses journal homepage: www.elsevier.com/locate/mehy
The carotid sinus acts as a mechanotransducer of shear oscillation rather than a baroreceptor
T
⁎
Andrew John Iskandera, , Rotem Naftalovichb, Xiaolei Yangc a
Department of Anesthesiology, Westchester Medical Center, 100 Woods Road, Valhalla, NY 10595, United States Department of Anesthesiology, Rutgers-New Jersey Medical School, Newark, NJ 07101-1709, United States c Department of Civil Engineering, Stony Brook University, Stony Brook, NY 11794-2300, United States b
A B S T R A C T
The carotid sinus is a dilated area at the base of the internal carotid artery of humans and is located immediately superior to the bifurcation of the internal and external carotid arteries. It is widely accepted, in the fields of medicine and physiology, to function as a baroreceptor in its central control role. This paper presents a hypothesis challenging this paradigm - that the carotid sinus functions by detecting oscillations at the vessel wall which result from shear stress due to vortical flow. This is contrary to conventional thinking which presumes that the carotid sinus responds to blood pressure or wall pressure. Our hypothesis is based on anatomy, physiology and physical properties of fluid which make the sinus the area of highest vorticity. Utilizing magnetic resonance angiograms of undiseased carotid vessels, we computed the oscillatory shear index (OSI) via a computational fluid dynamics simulation of flow. This region of highest OSI coincides with the area where the nerve to the carotid sinus lies within the vessel wall. Accordingly, the hypothesis is that the carotid sinus acts as a mechanotransducer of wall shear stress oscillation and not as a baroreceptor.
Introduction Every medical student learns about the baroreceptor reflex whereby baroreceptors in the carotid sinus sense increased arterial pressure and in response increase parasympathetic tone and subsequent negative feedback to the heart (e.g. via the sinoatrial node). The carotid sinus is important because of its role in autonomic control and homeostasis regulation. This relevance is significant for treatments of recalcitrant hypertension, heart failure, and fluid status optimization [1]. The carotid sinus anatomical location is unique; it is the only location within the vasculature with a dilation immediately distal to a bifurcation. It acts as a physiologic aneurysm in which there is a separation of flow [2]. The site of dilatation provides room for the energy of the blood flow to create a region of vorticity or flow reversal. This, in turn, leads to secondary flows as the forward flow and reverse flow interact within the base of the internal carotid at the opening into the sinus. This results in velocity oscillation inside a region of relatively low wall shear stress [3]. Hypothesis We hypothesize that the carotid sinus detects oscillations of shear forces created by the flow reversal rather than detecting pressure as a barometer. This hypothesis implies that it is not coincidental that the nerve innervation, the link between the vascular and nervous system, of ⁎
this anatomical area is at a dilatation just distal to the carotid bifurcation; rather, it is a product of evolutionary reasoning given that this is the area where shear forces are enhanced due to more vortical flow. Blood pressure or arterial pressure is a surrogate to shear forces; higher blood pressures would typically produce greater curling of flow at this site with a concomitant increase in velocity and shear oscillation. The dilation of the carotid sinus combined with its anatomical location immediately distal to a bifurcation makes it the area of highest vorticity. Vorticity causes shear oscillation [3]. Given that this area is the region understood to be the site of innervation of the carotid sinus, we further hypothesize that the carotid sinus transduces shear oscillation. Since it is easier to measure blood pressure than oscillations, it is understandable why the carotid sinus has long been referred to as a baroreceptor. This hypothesis can be tested in silico by simulating carotid shear stress at different areas of the carotid. It can be tested using a mechanical model, as well as in animals or humans by modifying parameters that alter vorticity (i.e. blood flow speed via heart rate and contractility, blood volume, or blood viscosity) and correlating these changes with shear oscillation measurements. Empirical evidence In this study, numerical simulations of blood flow in normal human carotid bifurcations were carried out to evaluate the wall shear
Corresponding author. E-mail addresses: [email protected] (A.J. Iskander), [email protected] (R. Naftalovich), [email protected] (X. Yang).
https://doi.org/10.1016/j.mehy.2019.109441 Received 27 August 2019; Received in revised form 12 October 2019; Accepted 17 October 2019 0306-9877/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Medical Hypotheses 134 (2020) 109441
A.J. Iskander, et al.
Fig. 1. The flow rate of blood over one cardiac cycle utilized for the simulations, corresponding to a heart rate of 60 bpm.
characteristics in the region where the carotid sinus nerve (CSN) is noted to insert into the wall adventitia. As this example is in a larger vessel rather than a capillary, the blood is assumed to be incompressible Newtonian fluid. The Virtual Flow Simulator (VFS) code [4] is employed to simulate the blood flow in the carotid bifurcation. In VFS the blood flow is governed by the following incompressible Navier-Stokes equation and continuity equation:
Fig. 2. An example of a wall shear stress (WSS) map rendered for the carotid angiograms. This is carotid 1 in Fig. 3.
OSI =
T τw dt ⎞ ∫0 → 1⎛ 1 − T → 2⎜ ∫0 | τw | dt ⎟⎠ ⎝
→
∂v + v·∇v⎞ = −∇p + μ∇2 v + , ∇ ·v ≠ 0, ρ⎛ ⎝ ∂t ⎠
where τw represents the WSS vector and T represents the period of the cardiac cycle (Fig. 3). It is a metric that depicts how aligned the vector of greatest WSS is with the primary flow. An OSI of 0 suggests no change of direction between the WSS and the primary flow. An OSI of 0.5 corresponds to zero net forward flow with only oscillation present in that region. It quantifies the magnitude of change in WSS direction. On visual inspection, the WSS results for the six carotids chosen resulted in WSS patterns that isolated the region where the CSN is understood to insert into the adventitial layer of the carotid artery. In the area of recirculation where the base of the internal carotid dilates, the change in direction of the flow results in WSS patterns that resulted in regions of shear that are consistent with less laminar flow, an example of which is depicted in Fig. 2. As the direction of flow is directed away from the endothelium, the WSS decreases as the vectors of flow are directed away from vessel wall. Qualitatively, when OSI is tabulated for the six carotids, the areas of greatest change in WSS or flow directionality overlap with the regions understood to comprise the carotid sinus. Values for OSI in areas outside the sinus region were largely at or near zero. The region at the origin of the internal carotid where the vessel is dilated has the highest values for OSI, with values at or near 0.2 (Fig. 3). This was seen in all six carotids. The areas of highest OSI correlate with the carotid sinus which is the area of nerve insertion.
where ρ is the fluid density, v is the blood velocity, t is the time, p is the pressure, μ is the dynamic viscosity. In the present work, μ = 0.0037 Ns / m2 , and ρ = 1050 Kg / m3 . The geometry of the carotid is represented using the immersed boundary (IB) method [5]. The wall of the carotid is assumed to be rigid. The velocity boundary condition with the waveform from Holdsworth et al. [6] (Fig. 1) and a parabolic distribution is specified at the inlet plane of the common carotid artery. The Neumann boundary condition is applied at the outlet of the internal carotid artery, using flow rates over one cardiac cycle (Fig. 1). At the outlet of the external carotid artery, the flow rate is fixed at 26% of the inlet and the velocity distribution is thereby given at interior points next to the outlet plane. In all cases, grid nodes are uniformly distributed in all three directions with the grid spacing 0.1 mm . A grid of spacing 0.2 mm was shown to be sufficient to resolve the wall shear stress [7]. The size of time step varies in time with the CFL (Courant-Friedrichs-Lewy) number fixed at 0.8. For the simulations, the carotid geometry, which is discretized using triangular meshes, is obtained based on magnetic resonance angiograms performed on patients admitted to Stony Brook Medical Center who underwent scans as part of an institutional stroke imaging protocol. The angiogram images were reviewed and obtained after approval by the institutional review board. Eleven angiograms were randomly selected for review from scans performed over a three month period in 2018. These images were only of the right carotid bifurcation and were reviewed anonymously. The criteria for selection included 1) that the images had to be obtained utilizing the same imaging protocol on the same scanner, 2) the angiograms had to be free of disease or filling defects of any kind, 3) the images themselves had to be sufficiently free of motion artifact, and 4) the patients had to be adults. Of these initial scans, six met the criteria (1 female, 5 males) and were processed to create the mesh for simulation. To process each scan, 3DTOF MRA data was cropped from the region containing the bifurcation. The 3D data was reconstructed using open-source software 3D-Slicer 4.8.1 [8] (www.slicer.org) in order to create a volume rendering. This rendering was imported into a stereolithography (STL) file and then used to create the grid. The wall shear stress (WSS) results were calculated and rendered using a WSS map (Fig. 2) and the oscillatory shear index (OSI) was then derived using the following equation:
Discussion This is an important topic for clinicians in the fields of anesthesiology and cardiology. For example, some major clinical considerations in the setting of anesthesiology or heart failure relate to the patient's volume status. Cardiomyocytes, the muscle cells that make up the heart muscle, function in such a manner whereby the more they are stretched then the more they subsequently contract. This stretch occurs when there is more fluid in the vasculature i.e. when the blood volume is larger or when more blood fills the heart (increased cardiac preload) after a contraction. However, this relationship between preload and contractility only holds up to a certain point over which increases in fluid status actually worsen contractility. This is illustrated by the Frank-Starling law. At what point along the Frank-Starling curve a patient lies is an elusive concept filled with uncertainty. If a patient is in heart failure, acutely or chronically, it is not always clear if the patient 2
Medical Hypotheses 134 (2020) 109441
A.J. Iskander, et al.
Fig. 3. The visual rendering of oscillation shear index (OSI) in six carotid bifurcations without any evidence of filling defect or stenosis on magentic resonance. An OSI of 0 corresponds to no change in direction between WSS and the primary flow. An OSI of 0.5 corresponds to zero net forward flow with only oscillation present in that region.
Declaration of Competing Interest
will benefit more from additional crystalloid, colloid, or an inotropic drug. If the carotid sinus, as we hypothesize, actually detects shear oscillations due to vortical flow, then being able to measure these oscillations, or some proxy thereof, would aid in elucidating where along the Frank-Starling curve a patient lies. Measuring oscillation from shear wall stress at the carotid sinus would serve useful in other areas of medicine. For example, chronic renal failure patients can often get volume overloaded easily since their kidneys are unable to regulate excess fluid through removal via urine. Dialysis can remove fluid in a controlled manner but it is hard to infer what the patient’s volume status is, how much fluid to remove in dialysis, or the optimum fluid intake. Similarly, during anesthesia the vasculature often dilates due to smooth muscle relaxation from anesthetic drugs. As a result, it is known that patients can become relatively volume depleted, but it is not really known how their fluid deficit can be quantified. By considering shear oscillation of blood flow to the sinus region, clinical endpoints that alter this parameter (or its proxy) become more pertinent. These include viscosity, density, and velocity of blood flow.
The authors declare that they have no known competing financial interests or personal relationships that could appear to influence the work reported in this paper. References [1] Porzionato A, Macchi V, Stecco C, De Caro R. The carotid sinus nerve-structure, function, and clinical implications. Anat Rec (Hoboken) 2019;302(4):575–87. [2] Giddens DP, Ku DN. A note on the relationship between input flow waveform and wall shear rate in pulsatile, separating flows. J Biomech Eng 1987;109(2):175–6. [3] Ku DN, Giddens DP. Laser Doppler anemometer measurements of pulsatile flow in a model carotid bifurcation. J Biomech 1987;20(4):407–21. [4] Xiaolei Yang FS, Conzemius Robert J, Wachtler John N, Strong Mike B. Large-eddy simulation of turbulent flow past wind turbines/farms: the Virtual Wind Simulator (VWiS). Wind Energy 2015;18(12):2025–45. [5] Ge L, Sotiropoulos F. A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries. J Comput Phys 2007;225(2):1782–809. [6] Holdsworth DW, Norley CJ, Frayne R, Steinman DA, Rutt BK. Characterization of common carotid artery blood-flow waveforms in normal human subjects. Physiol Meas 1999;20(3):219–40. [7] Moyle KR, Mallinson GD, Occleshaw CJ, Cowan BR, Gentles TL. Wall shear stress is the primary mechanism of energy loss in the Fontan connection. Pediatr Cardiol 2006;27(3):309–15. [8] Fedorov A, Beichel R, Kalpathy-Cramer J, Finet J, Fillion-Robin JC, Pujol S, et al. 3D Slicer as an image computing platform for the Quantitative Imaging Network. Magn Reson Imaging 2012;30(9):1323–41.
Sources of support in the form of grants None.
3
Contents lists available at ScienceDirect
Medical Hypotheses journal homepage: www.elsevier.com/locate/mehy
The carotid sinus acts as a mechanotransducer of shear oscillation rather than a baroreceptor
T
⁎
Andrew John Iskandera, , Rotem Naftalovichb, Xiaolei Yangc a
Department of Anesthesiology, Westchester Medical Center, 100 Woods Road, Valhalla, NY 10595, United States Department of Anesthesiology, Rutgers-New Jersey Medical School, Newark, NJ 07101-1709, United States c Department of Civil Engineering, Stony Brook University, Stony Brook, NY 11794-2300, United States b
A B S T R A C T
The carotid sinus is a dilated area at the base of the internal carotid artery of humans and is located immediately superior to the bifurcation of the internal and external carotid arteries. It is widely accepted, in the fields of medicine and physiology, to function as a baroreceptor in its central control role. This paper presents a hypothesis challenging this paradigm - that the carotid sinus functions by detecting oscillations at the vessel wall which result from shear stress due to vortical flow. This is contrary to conventional thinking which presumes that the carotid sinus responds to blood pressure or wall pressure. Our hypothesis is based on anatomy, physiology and physical properties of fluid which make the sinus the area of highest vorticity. Utilizing magnetic resonance angiograms of undiseased carotid vessels, we computed the oscillatory shear index (OSI) via a computational fluid dynamics simulation of flow. This region of highest OSI coincides with the area where the nerve to the carotid sinus lies within the vessel wall. Accordingly, the hypothesis is that the carotid sinus acts as a mechanotransducer of wall shear stress oscillation and not as a baroreceptor.
Introduction Every medical student learns about the baroreceptor reflex whereby baroreceptors in the carotid sinus sense increased arterial pressure and in response increase parasympathetic tone and subsequent negative feedback to the heart (e.g. via the sinoatrial node). The carotid sinus is important because of its role in autonomic control and homeostasis regulation. This relevance is significant for treatments of recalcitrant hypertension, heart failure, and fluid status optimization [1]. The carotid sinus anatomical location is unique; it is the only location within the vasculature with a dilation immediately distal to a bifurcation. It acts as a physiologic aneurysm in which there is a separation of flow [2]. The site of dilatation provides room for the energy of the blood flow to create a region of vorticity or flow reversal. This, in turn, leads to secondary flows as the forward flow and reverse flow interact within the base of the internal carotid at the opening into the sinus. This results in velocity oscillation inside a region of relatively low wall shear stress [3]. Hypothesis We hypothesize that the carotid sinus detects oscillations of shear forces created by the flow reversal rather than detecting pressure as a barometer. This hypothesis implies that it is not coincidental that the nerve innervation, the link between the vascular and nervous system, of ⁎
this anatomical area is at a dilatation just distal to the carotid bifurcation; rather, it is a product of evolutionary reasoning given that this is the area where shear forces are enhanced due to more vortical flow. Blood pressure or arterial pressure is a surrogate to shear forces; higher blood pressures would typically produce greater curling of flow at this site with a concomitant increase in velocity and shear oscillation. The dilation of the carotid sinus combined with its anatomical location immediately distal to a bifurcation makes it the area of highest vorticity. Vorticity causes shear oscillation [3]. Given that this area is the region understood to be the site of innervation of the carotid sinus, we further hypothesize that the carotid sinus transduces shear oscillation. Since it is easier to measure blood pressure than oscillations, it is understandable why the carotid sinus has long been referred to as a baroreceptor. This hypothesis can be tested in silico by simulating carotid shear stress at different areas of the carotid. It can be tested using a mechanical model, as well as in animals or humans by modifying parameters that alter vorticity (i.e. blood flow speed via heart rate and contractility, blood volume, or blood viscosity) and correlating these changes with shear oscillation measurements. Empirical evidence In this study, numerical simulations of blood flow in normal human carotid bifurcations were carried out to evaluate the wall shear
Corresponding author. E-mail addresses: [email protected] (A.J. Iskander), [email protected] (R. Naftalovich), [email protected] (X. Yang).
https://doi.org/10.1016/j.mehy.2019.109441 Received 27 August 2019; Received in revised form 12 October 2019; Accepted 17 October 2019 0306-9877/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Medical Hypotheses 134 (2020) 109441
A.J. Iskander, et al.
Fig. 1. The flow rate of blood over one cardiac cycle utilized for the simulations, corresponding to a heart rate of 60 bpm.
characteristics in the region where the carotid sinus nerve (CSN) is noted to insert into the wall adventitia. As this example is in a larger vessel rather than a capillary, the blood is assumed to be incompressible Newtonian fluid. The Virtual Flow Simulator (VFS) code [4] is employed to simulate the blood flow in the carotid bifurcation. In VFS the blood flow is governed by the following incompressible Navier-Stokes equation and continuity equation:
Fig. 2. An example of a wall shear stress (WSS) map rendered for the carotid angiograms. This is carotid 1 in Fig. 3.
OSI =
T τw dt ⎞ ∫0 → 1⎛ 1 − T → 2⎜ ∫0 | τw | dt ⎟⎠ ⎝
→
∂v + v·∇v⎞ = −∇p + μ∇2 v + , ∇ ·v ≠ 0, ρ⎛ ⎝ ∂t ⎠
where τw represents the WSS vector and T represents the period of the cardiac cycle (Fig. 3). It is a metric that depicts how aligned the vector of greatest WSS is with the primary flow. An OSI of 0 suggests no change of direction between the WSS and the primary flow. An OSI of 0.5 corresponds to zero net forward flow with only oscillation present in that region. It quantifies the magnitude of change in WSS direction. On visual inspection, the WSS results for the six carotids chosen resulted in WSS patterns that isolated the region where the CSN is understood to insert into the adventitial layer of the carotid artery. In the area of recirculation where the base of the internal carotid dilates, the change in direction of the flow results in WSS patterns that resulted in regions of shear that are consistent with less laminar flow, an example of which is depicted in Fig. 2. As the direction of flow is directed away from the endothelium, the WSS decreases as the vectors of flow are directed away from vessel wall. Qualitatively, when OSI is tabulated for the six carotids, the areas of greatest change in WSS or flow directionality overlap with the regions understood to comprise the carotid sinus. Values for OSI in areas outside the sinus region were largely at or near zero. The region at the origin of the internal carotid where the vessel is dilated has the highest values for OSI, with values at or near 0.2 (Fig. 3). This was seen in all six carotids. The areas of highest OSI correlate with the carotid sinus which is the area of nerve insertion.
where ρ is the fluid density, v is the blood velocity, t is the time, p is the pressure, μ is the dynamic viscosity. In the present work, μ = 0.0037 Ns / m2 , and ρ = 1050 Kg / m3 . The geometry of the carotid is represented using the immersed boundary (IB) method [5]. The wall of the carotid is assumed to be rigid. The velocity boundary condition with the waveform from Holdsworth et al. [6] (Fig. 1) and a parabolic distribution is specified at the inlet plane of the common carotid artery. The Neumann boundary condition is applied at the outlet of the internal carotid artery, using flow rates over one cardiac cycle (Fig. 1). At the outlet of the external carotid artery, the flow rate is fixed at 26% of the inlet and the velocity distribution is thereby given at interior points next to the outlet plane. In all cases, grid nodes are uniformly distributed in all three directions with the grid spacing 0.1 mm . A grid of spacing 0.2 mm was shown to be sufficient to resolve the wall shear stress [7]. The size of time step varies in time with the CFL (Courant-Friedrichs-Lewy) number fixed at 0.8. For the simulations, the carotid geometry, which is discretized using triangular meshes, is obtained based on magnetic resonance angiograms performed on patients admitted to Stony Brook Medical Center who underwent scans as part of an institutional stroke imaging protocol. The angiogram images were reviewed and obtained after approval by the institutional review board. Eleven angiograms were randomly selected for review from scans performed over a three month period in 2018. These images were only of the right carotid bifurcation and were reviewed anonymously. The criteria for selection included 1) that the images had to be obtained utilizing the same imaging protocol on the same scanner, 2) the angiograms had to be free of disease or filling defects of any kind, 3) the images themselves had to be sufficiently free of motion artifact, and 4) the patients had to be adults. Of these initial scans, six met the criteria (1 female, 5 males) and were processed to create the mesh for simulation. To process each scan, 3DTOF MRA data was cropped from the region containing the bifurcation. The 3D data was reconstructed using open-source software 3D-Slicer 4.8.1 [8] (www.slicer.org) in order to create a volume rendering. This rendering was imported into a stereolithography (STL) file and then used to create the grid. The wall shear stress (WSS) results were calculated and rendered using a WSS map (Fig. 2) and the oscillatory shear index (OSI) was then derived using the following equation:
Discussion This is an important topic for clinicians in the fields of anesthesiology and cardiology. For example, some major clinical considerations in the setting of anesthesiology or heart failure relate to the patient's volume status. Cardiomyocytes, the muscle cells that make up the heart muscle, function in such a manner whereby the more they are stretched then the more they subsequently contract. This stretch occurs when there is more fluid in the vasculature i.e. when the blood volume is larger or when more blood fills the heart (increased cardiac preload) after a contraction. However, this relationship between preload and contractility only holds up to a certain point over which increases in fluid status actually worsen contractility. This is illustrated by the Frank-Starling law. At what point along the Frank-Starling curve a patient lies is an elusive concept filled with uncertainty. If a patient is in heart failure, acutely or chronically, it is not always clear if the patient 2
Medical Hypotheses 134 (2020) 109441
A.J. Iskander, et al.
Fig. 3. The visual rendering of oscillation shear index (OSI) in six carotid bifurcations without any evidence of filling defect or stenosis on magentic resonance. An OSI of 0 corresponds to no change in direction between WSS and the primary flow. An OSI of 0.5 corresponds to zero net forward flow with only oscillation present in that region.
Declaration of Competing Interest
will benefit more from additional crystalloid, colloid, or an inotropic drug. If the carotid sinus, as we hypothesize, actually detects shear oscillations due to vortical flow, then being able to measure these oscillations, or some proxy thereof, would aid in elucidating where along the Frank-Starling curve a patient lies. Measuring oscillation from shear wall stress at the carotid sinus would serve useful in other areas of medicine. For example, chronic renal failure patients can often get volume overloaded easily since their kidneys are unable to regulate excess fluid through removal via urine. Dialysis can remove fluid in a controlled manner but it is hard to infer what the patient’s volume status is, how much fluid to remove in dialysis, or the optimum fluid intake. Similarly, during anesthesia the vasculature often dilates due to smooth muscle relaxation from anesthetic drugs. As a result, it is known that patients can become relatively volume depleted, but it is not really known how their fluid deficit can be quantified. By considering shear oscillation of blood flow to the sinus region, clinical endpoints that alter this parameter (or its proxy) become more pertinent. These include viscosity, density, and velocity of blood flow.
The authors declare that they have no known competing financial interests or personal relationships that could appear to influence the work reported in this paper. References [1] Porzionato A, Macchi V, Stecco C, De Caro R. The carotid sinus nerve-structure, function, and clinical implications. Anat Rec (Hoboken) 2019;302(4):575–87. [2] Giddens DP, Ku DN. A note on the relationship between input flow waveform and wall shear rate in pulsatile, separating flows. J Biomech Eng 1987;109(2):175–6. [3] Ku DN, Giddens DP. Laser Doppler anemometer measurements of pulsatile flow in a model carotid bifurcation. J Biomech 1987;20(4):407–21. [4] Xiaolei Yang FS, Conzemius Robert J, Wachtler John N, Strong Mike B. Large-eddy simulation of turbulent flow past wind turbines/farms: the Virtual Wind Simulator (VWiS). Wind Energy 2015;18(12):2025–45. [5] Ge L, Sotiropoulos F. A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries. J Comput Phys 2007;225(2):1782–809. [6] Holdsworth DW, Norley CJ, Frayne R, Steinman DA, Rutt BK. Characterization of common carotid artery blood-flow waveforms in normal human subjects. Physiol Meas 1999;20(3):219–40. [7] Moyle KR, Mallinson GD, Occleshaw CJ, Cowan BR, Gentles TL. Wall shear stress is the primary mechanism of energy loss in the Fontan connection. Pediatr Cardiol 2006;27(3):309–15. [8] Fedorov A, Beichel R, Kalpathy-Cramer J, Finet J, Fillion-Robin JC, Pujol S, et al. 3D Slicer as an image computing platform for the Quantitative Imaging Network. Magn Reson Imaging 2012;30(9):1323–41.
Sources of support in the form of grants None.
3