Hemodynamics in Doppler ultrasonography

Hemodynamic Function

Blood flow starts in a pulsatile pattern due to the periodic contractions of the left ventricle and the one-way valve action at the ventriculo-aortic junction. The aorta and arteries dampen this pulsation to minimize pressure damage in organs. Their thicker, elastic walls expand and recoil, absorbing the pulsatile energy. However, this pulsatile nature means that simple observations of a vessel's luminal patency may not reflect actual blood flow. Structures with stiffer walls, such as bypass grafts, may even exhibit reversed flow during diastole due to this pulsation [1].

Whole blood, unlike plasma, is a non-Newtonian fluid. Newtonian fluids have constant viscosity, meaning that their resistance to flow increases linearly with increasing shear rate (the difference in velocity between adjacent layers) [2]. In contrast, the viscosity of whole blood depends on several factors, including hematocrit, the aggregation of red blood cells (RBCs), and their deformability. At higher shear rates (caused by smaller vessels or higher flow velocity), RBC aggregation decreases, and the cells deform more, leading to decreased viscosity. This is referred to as shear thinning [3]. Conversely, in slow flow conditions, RBCs aggregate into rouleaux, increasing their resistance to flow and leading to greater viscosity.

Blood vessels have a branching (arteries) or converging (veins) tree-like structure, inherently leading to turbulent flow. Turbulent flow is characterized by chaotic and unpredictable velocity and pressure patterns. It occurs when the kinetic energy of the fluid overcomes the dampening effect of viscosity. Laminar flow, with smooth and predictable layers, is more likely in viscous fluids. The Reynolds number, which reflects the ratio of inertia to viscosity, is used to estimate turbulence in continuous flow. For pulsatile blood flow, the Womersley number is used to account for pulsation [4-6].

Similar to other colloidal suspensions, blood flow exhibits the Fåhræus-Lindqvist effect. As friction at the vessel wall increases due to smaller vessel size, RBCs migrate towards the center, leaving a cell-free zone near the wall. This reduces friction and potentially lowers the overall viscosity of blood in smaller vessels [7].

Among the characteristics of blood flow, the most unique feature of whole blood is its inconsistent dynamic viscosity.

Vascular Wall Function

The vascular system exhibits distinctive features in terms of both blood flow and wall function. The vascular wall is dynamic and capable of significantly influencing blood flow. Shear stress on the vascular wall is crucial for both wall structure and blood flow. Shear stress refers to the frictional force on the vascular endothelium in the direction of blood flow. It is calculated as the product of the wall shear rate and blood viscosity. The wall shear rate describes the velocity gradient between the outermost blood flow layer and the adjacent vessel wall. Increased friction at the vessel wall, caused by faster flow or a smaller vessel diameter, leads to higher wall shear stress. Elevated wall shear stress dissipates flow energy, stimulates endothelial cells, induces vasodilation, and may alter cell arrangement [8].

The vascular wall is subjected to both shear stress and normal stress, which comprises three components: circumferential stress (loop stress, tangential stress, wall stress, or wall tension), radial stress, and axial (longitudinal) stress. Normal stress arises primarily from the intraluminal pressure exerted by the contained blood mass. In contrast to shear stress, which is generated by the kinetic energy of blood flow, normal stress originates from static pressure. Radial stress acts perpendicular to the wall of a cylindrical blood vessel and influences its dilation. Longitudinal stress acts along the long axis of the vessel. In vessels such as the descending aorta, when a person is in a standing position, longitudinal stress can increase pressure distally due to gravity. This may explain the higher prevalence of aneurysms in the infrarenal abdominal aorta than in the thoracic descending aorta. Circumferential stress (wall tension) plays a critical role in vascular rupture, particularly in aneurysms. While circumferential stress primarily threatens wall integrity, all normal stress components influence each other and contribute to the overall wall tension. Wall tension can be calculated using the Young-Laplace equation, which relates it to a ratio between pressure and wall thickness [9,10].

Wall stiffness is another important aspect of wall function, and it can be expressed using parameters such as the tangential modulus (derived from the stress-strain curve), compliance, and wall tension [11]. Compliance—a classic parameter—refers to the rate of change of volume with respect to pressure changes. In vascular structures, however, the pressure-volume (or area) relationship is non-linear. As intraluminal pressure increases, the vessel lumen expands in a sigmoid curve. Compliance and the tangential modulus exhibit corresponding changes along this curve, with initial increases followed by decreases. Additionally, vascular dilation can decrease compliance by causing an upward shift in the pressure-volume curve. Conversely, vascular wall hypertrophy can delay the peak point of the compliance curve [12].

Since vascular wall compliance can be influenced by intraluminal pressure, vessel size, and wall properties, more consistent parameters have been introduced to represent wall stiffness. These include the elastic modulus, stiffness index, arterial distensibility index, and arterial wall stiffness index [13-16].

Blood Flow Velocity

DUS is used to evaluate blood flow by directly measuring velocity, the primary hemodynamic parameter. Other hemodynamic parameters derive from this velocity data. In duplex mode, velocity appears as a color-coded signal on a grayscale B-mode image. In the time-velocity spectrum, velocity is shown by the spectrum's height at each time point. Spectral waveform analysis provides values such as peak systolic velocity, end-diastolic velocity, and time-averaged mean velocity.

Blood vessels exhibit variations in flow velocity and pulsatile patterns due to physiological differences (Fig. 1C, D). According to Bernoulli's principle, flow velocity increases as a vessel's cross-sectional area decreases. This principle enables the use of DUS to assess vascular stenosis by analyzing velocity changes. For example, carotid artery stenosis can be graded based on peak systolic and end-diastolic velocity measurements in the internal and common carotid arteries (Table 1, Fig. 2C) [22]. Doppler stenosis grading correlates well with computed tomography angiography measurements [23]. Duplex mode can also estimate stenosis severity based on the geometry of the blood flow, although it may underestimate severity due to limitations in capturing marginal flow signals. Despite these limitations, DUS remains the standard for velocity-based stenosis evaluation of the carotid artery [24]. Carotid DUS screening has also been validated for follow-up in high-risk patients with atherosclerosis to predict cerebrovascular events [25].

Table 1.

Carotid arterial stenosis evaluation based on Doppler ultrasonographic velocimetry [22]

The clinical applications of DUS extend beyond carotid artery assessment. Park et al. [26] used DUS-based central retinal artery velocimetry to identify ocular ischemic disease in patients with sudden vision loss. A mean velocity threshold of 4.3 cm/s offered high sensitivity (89%) and specificity (95%) for predicting significant vision loss. Espahbodi et al. [27] evaluated lumbar arterial blood flow in patients with lower back pain, finding higher peak systolic flow velocity in patients than in controls. This suggests that DUS is useful for assessing the hemodynamic changes associated with lower back pain. These examples highlight the diverse applications of DUS in assessing blood flow velocity across various vascular territories.

Blood Flow Rate

The flow rate measures the volume of blood flowing through a vessel per unit time. Using DUS, the flow rate is calculated by multiplying the time-averaged mean velocity by the cross-sectional area of the blood vessel and a conversion factor (typically 60 seconds for mL/min). This technique is widely used to assess blood flow in various parts of the body (Fig. 2).

Dark and Singer [28] validated transesophageal DUS for measuring cardiac output against the pulmonary artery thermo-dilution technique. Jung et al. [29] measured flow rates in four major cerebral arteries, finding significantly reduced total cerebral blood flow volume (TCBFV) in patients with acute ischemic stroke and decreased cerebral vascular reserve compared to healthy individuals. Kalfaoglu et al. [30] compared TCBFV between chronic smokers and non-smokers, revealing significantly lower TCBFV in smokers, suggesting that smoking exerts a negative impact on cerebral blood flow. Araz Server et al. [31] linked reduced vertebral artery flow to positional vertigo, finding that patients with undiagnosed positional vertigo had lower flow rates depending on head position. Mutlu et al. [32] found significantly lower peak systolic velocity and flow rate in patients with idiopathic sudden sensorineural hearing loss (ISSNHL), implying that impaired vertebral artery flow may play a role in this condition.

DUS is also valuable for monitoring arteriovenous malformations (AVMs), which are birth defects where arteries and veins connect abnormally, bypassing capillaries. DUS is used to diagnose AVM by assessing both blood flow patterns and the flow rate, with features of increased peak systolic velocity, low-impedance pattern, and slanted linear downslope (saw-tooth appearance). Monitoring changes in the flow rate and peak systolic velocity in feeding arteries is a method for tracking AVM progression or improvement [33]. Mohammadkarim et al. [34] used DUS to monitor common carotid artery flow rate changes after external radiotherapy for cancer treatment; they found a significant decrease in flow rate, suggesting the potential of DUS for predicting late radiotherapy-related side effects.

These examples highlight the versatility of DUS in evaluating the blood flow rate across various clinical scenarios.

Blood Flow Patterns

DUS is highly useful for analyzing blood flow patterns by capturing velocity variations over time. Arterial flow is pulsatile due to the heart's intermittent pumping, and it is influenced by inflow properties and downstream resistance. In high-resistance environments, the systolic peak velocity is much higher than the diastolic velocity. In complex pulsatile flow, "impedance" (the complex-valued generalization of resistance) describes the flow resistance. In this context, flow with a larger systolic-diastolic velocity difference is described as "high-impedance flow" [35]. Venous flow is typically continuous with some pulsatile variations due to respiratory and cardiac motion, especially in larger veins closer to the chest. Capillary flow shows a steady laminar pattern.

Arteries supplying the brain have lower impedance and a more continuous flow pattern than those supplying other organs. Arteries supplying skeletal muscles show a high-impedance flow pattern with biphasic or triphasic waveforms at rest. Arteries supplying visceral organs have an intermediate-impedance flow pattern [19].

Upstream of stenosis—that is, in a pre-stenotic segment—the flow pattern is high-impedance. Blood flow through the stenotic channel creates a high-velocity jet with turbulence. Downstream, the flow pattern exhibits lower impedance and becomes more continuous (Fig. 3). In cases of severe stenosis, post-stenotic flow can exhibit a weak and delayed pulsatile pattern, known as "pulsus tardus et parvus" [36].

Fig. 3.

A 79-year-old man who underwent Doppler ultrasonography to evaluate cerebral symptoms.

A. The right common carotid artery (CCA) shows a large difference between peak systolic velocity (PSV) and end-diastolic velocity (EDV). The resistance index (RI) is increased to 0.92, suggesting downstream flow disturbance. B. The right proximal internal carotid artery (ICA) shows increased flow velocity and an effaced spectral window, suggesting a turbulent stenotic jet flow. C. The right distal extracranial ICA shows high velocity but a lower impedance pattern than stenotic flow, suggesting a post-stenotic flow pattern. D. The report shows hemodynamic stenosis and an increased RI and pulsatility index (PI) of the right ICA (red square). AWSI, arterial wall stiffness index; BMI, body mass index; BSA, bovine serum albumin; BP, blood pressure; EDV, end-diastolic velocity; HR, heart rate; LCCA, left common carotid artery; LECA, left external carotid artery; LICA, left internal carotid artery; LICAd, distal level of left internal carotid artery; LICAi, imaginary diameter of left internal carotid artery; LVA, left vertebral arte; PROX, proximal; PSV, peak systolic velocity; RCCA, right common carotid artery; RECA, right external carotid artery; RI, resistance index; RICA, right internal carotid artery; RICAd, distal level of right internal carotid artery; RICAi, imaginary diameter of right internal carotid artery; RT, right; RVA, right vertebral artery; TAMV, time-average mean velocity; VA, vertebral artery; WSS, wall shear stress.

DUS assesses relative impedance using flow velocity data. The resistance index (RI) is defined as the ratio between the systolic-diastolic velocity difference and peak systolic velocity. This parameter represents downstream impedance, but may underestimate it in large arteries with high diastolic velocity [37]. The pulsatility index (PI) normalizes velocity differences by vessel size, calculated as the ratio between the systolic-diastolic velocity difference and time-averaged mean velocity, and is also a practical parameter (Fig. 3D) [38].

Zeller et al. [39] reported that a bilateral renal artery RI difference exceeding 0.05 was highly specific for identifying significant stenosis in one renal artery. Mutlu et al. [32] found increased RI in the vertebral artery, suggesting flow disturbance in patients with ISSNHL. Mohammadkarim et al. [34] observed significant increases in the RI and PI of the common carotid artery after radiotherapy for cancer treatment.

Due to the pulsatile blood flow, DUS can evaluate both the upstream and downstream environments of blood flow by analyzing the flow patterns.

Flow Energy

The arterial system's complexity, with varying vessel diameters and branching patterns, requires efficient blood flow management to deliver oxygen and nutrients to organs. Blood flow energy combines the intraluminal pressure gradient and flow rate, which are analogous to electrical voltage and current.

Significant stenosis reduces blood flow energy due to increased friction within the narrowed segment and upstream flow diversion. The pressure gradient across the stenosis is a crucial parameter for assessing blood supply adequacy. Although DUS measures velocity rather than absolute pressure, various methods have been used to estimate pressure gradients based on velocity data.

Bernoulli's principle states that the total energy (kinetic, potential, and intrinsic) of a moving fluid remains constant. Intrinsic energy refers to the static pressure exerted by blood within the vessel, kinetic energy represents blood flow movement, and potential energy relates to the position of blood relative to gravity. Dynamic pressure is defined as the kinetic energy per unit volume of blood [2,40]. Some DUS protocols estimate pressure gradients using a simplified version of the Bernoulli equation. This method assumes negligible stenotic flow acceleration, viscous friction, and zero inlet flow velocity [41]. While suitable for high-velocity jets from near-complete flow stoppage (e.g., in heart valve regurgitation), its accuracy for moderate arterial stenosis with continuous inflow is debated [42,43]. In vitro studies have shown that this method overestimates pressure gradients compared to direct pressure measurements, possibly due to neglecting post-stenotic pressure recovery [43]. DeGroff et al. [44] also found significant discrepancies between Doppler-derived and catheter-measured pressure gradients across modified Blalock-Taussig shunts.

More complex fluid dynamic models such as the Hagen-Poiseuille and Navier-Stokes equations have been explored for estimating pressure gradients. However, their requirements (e.g. a, Newtonian fluid and straight laminar flow) are not always met in vivo, and successful results have not been consistently achieved [45,46].

DUS provides valuable information on blood flow velocity, but has limitations in directly measuring pressure gradients. Simplified methods exist, but their accuracy can be limited. Further research is needed to develop reliable Doppler-based techniques for pressure gradient estimation in blood vessels.

Wall Shear Stress

Wall shear stress triggers endothelial cells to initiate vasodilation and tighten intercellular junctions. Oscillating wall shear stress widens intercellular gaps, potentially promoting atherosclerotic plaque development, particularly in regions like arterial bifurcation shoulders [47].

Measuring wall shear stress in vivo requires acquiring the dynamic viscosity and shear rate of blood flow. Dynamic viscosity is often assumed based on hematocrit, which correlates with blood shear yield in vitro [48]. Using duplex DUS images, Wang et al. [49] calculated the shear rate by measuring velocity differences between pixels near the vascular wall. Assuming constant viscosity, they derived wall shear stress, which was validated against computational fluid dynamics (CFD) simulations for spatial wall shear stress distribution along the arterial wall.

DUS is a convenient method for calculating wall shear stress using the formula "4×viscosity×maximum velocity/vessel diameter," assuming a parabolic (Poiseuille) velocity profile (Fig. 3D) [50]. However, this method's reliability is limited in curved, branching arteries due to non-axisymmetric and turbulent flow profiles [51]. Gates et al. [52] highlighted inaccuracies in DUS-based wall shear stress measurements. Mynard et al. [51] recommended adjustments using CFD techniques.

Despite challenges in accurately measuring the shear rate, simplified techniques for translating wall shear stress to clinical settings are under development but remain a matter of debate. Clinical utility and the significance of wall shear stress values and their circumferential distribution remain unclear. However, DUS-based wall shear stress techniques continue to intrigue clinicians due to their theoretical representation of wall stress via blood flow kinetic energy.

Wall Stiffness

Arterial wall stiffness results from the balance between collagen and elastin proportions and the smooth muscle tone in the tunica media. Smooth muscle tone can be influenced by nervous activity, hormones, vasoactive substances such as nitric oxide from endothelial cells, and drugs. Normally, arterial wall stiffness varies based on the physical properties of arteries at different sites. Under abnormal circumstances, arterial wall stiffness increases with aging, hypertension, and certain medications. These influences also vary depending on the location of the arteries. Increased arterial stiffness reduces the damping effect of pulsatile arterial flow produced by cardiac motion, causing arteriolar and capillary flow to become rougher in the downstream end-organ parenchyma and contributing to the development of arterial hypertension [8].

In the clinical field, various indices have been proposed to evaluate arterial wall stiffness, aiming to overcome the limitations of the primary parameter known as compliance, which varies with intraluminal pressure changes. Since blood pressure and arterial luminal diameter are input variables, DUS is a convenient modality for measuring arterial wall stiffness (Table 2). Although no single index has proven superior to others, a commonly used index in clinical practice and research is arterial distensibility. This parameter is defined as the ratio between arterial luminal diameter change and the product of pulse pressure and diastolic luminal diameter [14].

Table 2.

Various indices of arterial wall stiffness [14]

Ultrasonography is a convenient modality for measuring arterial wall stiffness by assessing the luminal diameter alongside blood pressure information acquired from brachial cuff manometry. Additionally, various indices have been developed to normalize different arterial sizes and blood pressures. However, these indices still have limitations, such as indirectly measured pulse pressure, low spatial resolution to detect subtle diameter changes, and variations in the physical properties of arteries based on their location (Fig. 1E).