Cardiovascular Flow Imaging

Abstract

Identifying arterial stenosis is crucial for preventing ischemic disease. Hemodynamic evaluation is helpful for detecting abnormalities before symptom onset. Additionally, hemodynamic assessment enables localization of the specific lesions responsible for ischemic events. Accordingly current clinical guidelines recommend the use of validated imaging modalities, including MRI, Doppler ultrasonography, and angiography. These techniques provide both qualitative flow visualization and quantitative analysis. Key quantitative markers include velocity, flow rate, impedance, and pressure gradients. These parameters enable objective comparison of flow patterns and facilitate sensitive monitoring of disease progression. This review outlines clinically applicable hemodynamic imaging techniques and details their methodologies and diagnostic performance.

INTRODUCTION

Fluid mechanics provides a theoretical framework for understanding flow phenomena. In medicine, hemodynamics applies these principles to blood flow, which is recognized as a unique non-Newtonian fluid. Unlike Newtonian fluids, non-Newtonian fluids exhibit variable viscosity. In blood, this variability stems primarily from the reversible aggregation of red blood cells (RBCs), known as rouleaux formation. Increased flow velocity and reduced vessel diameter inhibit this aggregation, leading to a reduction in viscosity. Electrochemical forces on RBC membranes promote aggregation; however, hemodynamic shear forces and cellular collisions counteract these forces. Consequently, RBCs disperse within the microvasculature, particularly in capillaries, where deformation occurs to maintain perfusion. Because blood viscosity fluctuates based on hemodynamic and vascular conditions, blood is clinically classified as a non-Newtonian fluid (1,2).

Blood flow imaging is a critical diagnostic tool for hemodynamic analysis. Clinical evaluation relies on medically validated modalities, including MRI, Doppler ultrasonography (US), and angiography. In research settings, experimental assessment employs additional techniques such as laser Doppler velocimetry and particle image velocimetry (3).

Blood flow imaging facilitates both qualitative and quantitative assessment. Qualitative analysis prioritizes real-time imaging with high temporal resolution to visualize flow patterns. In contrast, quantitative analysis requires high-fidelity measurement of non-Newtonian flow to reflect physiological reality. Integrating comprehensive boundary conditions, such as viscosity variations, improves patient-specific accuracy; however, this approach complicates diagnostic protocols and may reduce reproducibility. Conversely, oversimplification produces results that do not accurately reflect in vivo hemodynamics. Therefore, clinically valid quantitative methods must balance accuracy and practicality (4).

The circulatory system maintains tissue viability by delivering blood to target organs via pulsatile cardiac output. Organs extract essential nutrients and eliminate metabolic waste through processes that rely on a strict balance between supply and demand to maintain homeostasis. Ischemia occurs when an organ receives insufficient oxygen to meet its metabolic requirements. According to the 2025 Global Burden of Disease report from the American Heart Association, ischemic cardio-cerebrovascular diseases caused 19 million deaths worldwide in 2023, accounting for one-third of global mortality (5). Ischemia predominantly results from luminal stenosis of the supplying arteries or cardiac dysfunction. Early detection of arterial stenosis and hemodynamic abnormalities during the asymptomatic phase is crucial for preventing adverse outcomes. Furthermore, hemodynamic analysis assists in identifying the specific culprit lesion causing ischemic symptoms. Therefore, hemodynamic imaging remains a cornerstone of clinical practice.

Among radiologic techniques, Doppler US provides real-time hemodynamic information with the best clinical accessibility. MRI is not restricted by target location and provides objective qualitative and quantitative information. Invasive angiography provides limited hemodynamic information during first-pass enhancement. CT offers the highest spatial resolution among noninvasive imaging techniques, and CT-based hemodynamic simulation has achieved clinical availability. This review presents clinically applicable blood flow imaging techniques, along with hemodynamic information, evaluation of their methodologies, and diagnostic validity.

IMAGING MODALITIES

DOPPLER US

Clinical hemodynamic imaging predominantly uses Doppler US. Moving blood cells reflect incident ultrasound waves, producing a frequency shift proportional to the velocity of blood cells. The Doppler equation governs this relationship (Equation 1). Doppler ultrasound techniques detect this shift to computecalculate the velocity of target blood cells (6).

$$\Delta f=\frac{(2·f·v·\cos \theta )}{c}$$ (Equation 1)

(‌Δf, Frequency shift; f, Ultrasound frequency; v, Flow velocity; θ, Incedence angle; c, Ultrasound speed in body)

Examiners typically select a linear probe (12–18 MHz) for Doppler examination. Conversely, convex probes use a fan-shaped beam geometry, which may cause marginal image distortion. However, convex probes are required when the acoustic window is narrow or for deep-seated targets. For general vascular assessment, excluding cardiac stenotic flow, the pulse-wave Doppler technique is standard and generates intermittent incident ultrasound. This approach enables measurement of velocity at a specific depth. The examiner set the minimum imaging depth necessary to include the target vessel. Recently, multifrequency probes have become widely used, allowing adjustment of the incident frequency according to imaging conditions. Minimizing imaging depth maintains the frequency at a high level with an improved image quality. Additionally, the beam profile is designed to have the highest density at a specific focal depth. Therefore, the focal depth must be adjusted to expose the target vessel to maximum beam density. Typically, the focal depth changes when the Doppler window is repositioned.

The Doppler window superimposed the color map. Setting this window to the minimum necessary size ensures high-quality signal capture. A sample volume (or gate) is positioned within the lumen to obtain the time-velocity spectrum. This constructs the spectrum by measuring only the velocities of blood cells passing through the defined region. To determine peak velocity, the sampling volume is reduced and positioned at the center of the vessel lumen. This configuration yields a sharp time-velocity spectrum and minimizes spectral broadening. Conversely, measuring flow volume requires a sufficiently large sampling volume to encompass the entire flow diameter, including both central and marginal flow velocities. Because these velocities differ according to the flow profile, the calculation of the mean velocity becomes more reliable. Accurate measurement of mean velocity is crucial because flow volume equals the product of mean velocity and vessel lumen area (Fig. 1).

Fig. 1. Doppler ultrasonography of the carotid artery. A velocity color map is duplexed onto a B-mode image, and the time-velocity spectrum appears at the bottom.

A. The Doppler angle (arrows), representing the incidence angle of the ultrasound beam, is adjusted to 58° in this examination. To set the Doppler angle correctly, first align the angle correction cursor (thin arrow) parallel to the blood flow direction. The sampling volume (arrowhead) indicates the specific zone of signal acquisition. Because the sampling volume is set to be narrow in this examination, the Doppler spectrum shows a high-velocity central flow signal with a clear spectral window (*).

B. Inappropriately low velocity scale settings result in aliasing artifacts. In the color Doppler window, the forward flow signal (red) mixes with the opposite flow signal (blue). In the time-velocity spectrum, peak velocity information is cut off and “wrapped around” to the bottom of the baseline (arrow).

C. The Vol Flow is calculated on-site by multiplying the TAMV based on mean velocity (arrow) by the luminal area. The luminal area is derived from the Dist measured in the Doppler window (arrowhead).

Dist = diameter, EDV = end-diastolic velocity, HR = heart rate, PSV = peak systolic velocity, RI = resistive index, TAMV = time-averaged mean velocity, Vol Flow = volume flow rate

Ideally, frequency-shift measurement occurs parallel to the direction of blood flow. However, human vascular anatomy often requires an oblique lateral approach. The angle of incidence is termed the Doppler angle (Fig. 1). Measurement of the frequency shift from the side yielded lower values than measurements obtained parallel to the flow direction. To compensate for this effect, the system incorporates the Doppler angle as a cosine term, as expressed in Equation 1. The frequency shift decreases as the angle increases from 0° to 90°, and velocity measurement is ideal when the incidence angle is 0°. Theoretically, cosine correction should yield accurate measurements even as the angle increases. However, in practice, increasing the Doppler angle often leads to velocity overestimation. Simple Doppler equations do not fully account for multiple reflectors within the sample volume and do not incorporate postprocessing algorithms used for signal enhancement. Furthermore, increasing the angle decreases the signal-to-noise ratio of the color Doppler map. At 90°, the theoretical velocity equals zero; however, the equipment may still register velocity signals even at this angle. To maintain reliability of Doppler velocimetry, guidelines recommend maintaining a Doppler angle between 30° and 60° (7).

Certain vascular structures, such as the carotid artery, make it difficult to achieve the recommended Doppler angle. In these situations, electronic beam steering helps maintain an appropriate angle. Physically tilting the probe (the “heel-and-toe” maneuver) provides further inclination. Accurately indicating the flow direction is the most critical factor in setting the Doppler angle because the system calculates the angle and converts velocity based on this reference. This reference is the angle-correction cursor (or flow line), and aligning this cursor parallel to the blood flow direction is termed angle correction (Fig. 1).

Setting an appropriate velocity scale, defined by the pulse repetition frequency, is essential. The color scale bar indicates the maximum displayed velocity. If this velocity is set too high relative to the actual flow, the signal falls within the noise band, thereby reducing the signal-to-noise ratio. Conversely, if the velocity is set too low, aliasing occurs. Blood flow velocity exceeding the unit appears as a signal in the opposite direction, creating a mixed red and blue “color mosaic” pattern on the map. Aliasing also produces a “wrap-around” artifact in the time-velocity spectrum (Fig. 1). Therefore, the velocity range should be adjusted to adequately capture the peak flow velocity. Because the spectrum displays flow relative to a baseline of 0 cm/s, adjusting this baseline can help mitigate aliasing. This adjustment ensures clear signal information without necessarily widening the velocity scale.

Power Doppler (also termed “energy Doppler”) displays signal intensity by assessing reflector amplitude without measuring frequency shift. Although this mode displays neither velocity nor directional information, it detects blood flow with high sensitivity. This is advantageous for confirming flow in small vessels, despite its inability to analyze flow dynamics (8).

The primary hemodynamic parameters acquired using Doppler US include blood flow velocity, flow rate, and resistive index (RI). Doppler US is widely used as a first-line diagnostic technique because of its high clinical accessibility, facilitated by real-time data acquisition, and simplicity of both instrumentation and examination procedures. However, limitations regarding reproducibility persist, as certain target areas remain inaccessible to ultrasound waves, thereby restricting the scope of the examination, and results are often subject to the examiner’s interpretation. Consequently, efforts to improve reproducibility through implementation of standardized and precise examination methodologies are necessary.

MRI

MRI captures blood flow using a bipolar velocity-encoding gradient that introduces a phase shift in flowing spins within the acquisition plane. Subtracting the pre-encoded image creates a high-contrast blood-flow image with a signal intensity that reflects the flow velocity. This technique is termed phase-contrast MRI (PC-MRI) (9). PC-MRI requires setting a velocity encoding (VENC) value that encompasses the maximum velocity of the target flow. If VENC is set excessively high, velocity information is compressed into a noisy region, resulting in reduced accuracy. Conversely, aliasing occurs if the VENC is set too low. Therefore, appropriate Venc selection is critical (10).

Two-dimensional (2D) PC-MRI acquires two types of images. Phase images show velocity information perpendicular to the cross-section, and magnitude images provide blood flow morphology. In post-processing systems, placing a region of interest (ROI) within the vessel lumen generates a time-flow or time-velocity curve, and absolute values of quantitative parameters can be acquired at each time phase (Fig. 2).

Fig. 2. Axial plane cardiac phase-contrast MRI showing the great vessels.

A. Magnitude image provides anatomical reference.

B. Phase image, where signal intensity correlates with flow velocity. Ascending and descending flows appear as bright and dark signals, respectively.

C, D. Time-velocity and time-flow curves derived from the luminal area and mean velocity. The AA exhibits a higher peak velocity than the PT. However, the area under the flow rate curves is similar for both. The DA shows a peak velocity similar to the AA, but its total flow rate is lower due to blood distribution to the brachiocephalic vessels between the two measurement points. The SVC demonstrates bimodal time-velocity and time-flow curves. Right atrial dilation during systole modulates the SVC flow rate, while a second flow augmentation occurs in the SVC during the passive filling and diastasis phases of diastole.

AA = ascending aorta, DA = descending aorta, PT = pulmonary trunk, SVC = superior vena cava

3D PC-MRI acquires a volumetric image of the target vessel by obtaining six sets of velocity images along three orthogonal axes and a magnitude image. Post-processing enables 3D hemodynamic visualization with cine images during the cardiac cycle and yields “4D Flow.” 4D qualitative analysis uses color maps to express hemodynamic parameters, and quantitative acquisition of velocity in specific cross sections is also feasible (Fig. 3) (10).

Fig. 3. 4D Flow MRI of heart and aorta.

A-D. Color-mapped 4D images visualize quantitative parameters including flow velocity (A), streamline (B), and wall shear stress (C). A 3D region of interest is placed within the ascending aorta (green curve) and pulmonary trunk (red curve) for the extraction of flow rates as time-resolved curves (D).

Time-resolved contrast-enhanced magnetic resonance angiography (TR-MRA) acquires flow information over a wide field of view. It visualizes first-pass morphology in cine images, which is useful for vessel patency examinations. It is particularly advantageous for complex vascular structures, such as arteriovenous malformations. It allows distinct observation of arterial, capillary, and venous phases, facilitating differentiation of vascular lesions and measurement of arteriovenous transit time (Fig. 4) (11).

Fig. 4. Time-resolved contrast-enhanced MR angiography. This scan was performed on a patient with a clinical impression of KTS. Clinical notes indicated left lower extremity hemi-hypertrophy. Notes also described dermal vascular staining and superficial varicose veins.

A. In the first-pass contrast arrival phase, the left femoral artery enhances earlier than the right due to left arterial hyperplasia.

B. The arterial phase reveals hyperplastic arteries in the left thigh. A fistula drains into the great saphenous vein. Due to this arteriovenous shunting, the left saphenous vein is visualized prematurely during the arterial phase (arrowheads).

C. The venous phase shows normal, delayed enhancement of the right great saphenous vein (arrowhead), confirming an arteriovenous fistula. Consequently, the diagnosis was revised from KTS to Parkes-Weber syndrome.

KTS = Klippel-Trenaunay syndrome

The primary hemodynamic parameters obtained using MRI include blood flow velocity and flow rate, as well as indices such as wall shear stress (WSS) and oscillatory shear index (OSI). In the case of MRI, signal information obtained during a specific acquisition time is reconstructed to represent hemodynamic information over a single cardiac cycle; therefore, although it is not a real-time imaging modality, the reproducibility of blood flow parameter measurements is acceptable. Notably, 3D PC-MRI allows extraction of quantitative hemodynamic parameters from user-defined regions of interest during postprocessing. Because it facilitates the intuitive qualitative analysis of blood flow information across extensive regions, such as the aorta, it can be used for macroscopic observation or as supplementary explanatory material for non-specialists. However, owing to procedural complexity and inter-examination variability, both radiologic technologists and radiologists must maintain a high level of technical proficiency.

INVASIVE ANGIOGRAPHY

Invasive angiography uses fluoroscopy or digital subtraction angiography to visualize the movement of a contrast bolus moving along the vascular lumen. This approach provides first-pass hemodynamic information. Clinicians can infer blood flow velocity and volume and assess the blood supply to target tissues. For example, evaluation of the ‘flow velocity after thrombolytic recanalization in myocardial infarction (TIMI flow grade),’ helps predict patient prognosis (12).

CT

CT provides the highest spatial resolution among noninvasive imaging modalities. However, as a radiation-based imaging technique, it exhibits inferior soft-tissue characteristics and cannot directly detect hemodynamic parameters. Blood-flow simulation methods based on computational fluid dynamics (CFD) have been developed to enable hemodynamic analysis using CT. Fractional flow reserve (FFR) is a representative simulation parameter that quantifies the pressure gradient across a stenosis, and its clinical utility is well established (13).

CT-based FFR is used to calculate the pressure gradient across a stenotic lesion based on the laws of conservation of mass and momentum. In this process, precise segmentation of the vascular lumen is the most critical factor. Blooming artifacts, which frequently occur in coronary CT angiography, affect the lumen area and significantly affect resultant FFR values. The inlet condition utilizes blood pressure measured at the patient’s arm, which represents a limitation because it does not directly reflect the internal pressure of the target vessel. For the outlet condition, the state of maximal vasodilation, typically induced by adenosine in invasive FFR, was simulated computationally. Furthermore, the physical properties of the blood flowing through the epicardial coronary arteries are assumed to behave as a Newtonian fluid. The pressure gradient caused by stenosis is thus modeled despite numerous limitations and assumptions. Early implementations of this technology partitioned the target artery into microstructures, performing computations for each element, which required several hours of analysis time even on supercomputers. More recently, the application of artificial intelligence-driven reduced-order models has enabled analysis speeds suitable for practical use in clinical settings (14).

Blood flow velocity and volume can be assessed indirectly by measuring the velocity of the contrast bolus flowing into blood vessels or tissues through serial scanning at a fixed position. While CT offers the advantage of acquiring data on both vascular architecture and hemodynamic simulation, it presents limitations regarding patient exposure to ionizing radiation and iodinated contrast media, as well as the inherent complexity of simulation analysis techniques.

QUALITATIVE EVALUATION

In hemodynamic image analysis, qualitative visual assessment relies on observing temporal changes in blood flow signals. Real-time Doppler US is the optimal technique for this purpose. However, some regions are inaccessible to US. In such cases, PC MR can be used to reconstruct flow with high temporal resolution, although it does not provide real-time imaging.

Flow resistance generally refers to the opposition caused by stenosis in distal vessels. However, arterial blood flow is pulsatile, and flow velocity changes continuously during the cardiac cycle. Consequently, opposition to flow is dynamic. Under these non-steady conditions, flow obstruction is expressed as impedance. Impedance encompasses all factors that influence pulsatile flow as a comprehensive concept. It accounts for friction caused by stenosis and flow disturbances caused by vascular compliance, dilation, and tortuosity (15).

In Doppler US, flow patterns manifest as signal intensity changes on color maps and morphological variations in the time-velocity spectrum. Standard flow patterns have been established for specific vessels, ranging from the aorta to peripheral arteries, providing a baseline for analyzing hemodynamic abnormalities. For instance, the internal carotid and vertebral arteries, which supply intracranial blood, exhibit a continuous low-impedance pattern characterized by a small difference between systolic and diastolic velocities. In contrast, resting extremity arteries demonstrate a high-impedance, triphasic flow pattern, indicating a high flow reserve. This pattern features a sharp forward systolic flow, followed by a velocity drop to zero, a subsequent retrograde flow caused by distal vascular resistance, and a final return to forward flow due to proximal elastic recoil. During exercise, this triphasic pattern transforms into a low-impedance monophasic flow to accommodate the increased blood supply to the muscles.

Significant arterial stenosis fundamentally alters flow patterns across the affected segment. Proximal to the lesion, the vessel exhibits a high-impedance pattern owing to the increased downstream resistance caused by the stenosis. At the stenosis site, flow velocity increases sharply in accordance with Bernoulli’s principle. In the post-stenotic segment, the flow transitions to a low-impedance pattern characterized by energy loss, luminal expansion, and reduced distal resistance (Fig. 5). In cases of severe stenosis, specific waveform changes emerge downstream, and post-stenotic flow often demonstrates reduced systolic velocity and delayed pulsatile upstroke, a waveform clinically known as pulsus parvus et tardus (16).

Fig. 5. High and low impedance flow patterns in carotid ultrasonography.

A. Duplex ultrasonography from the left ICA. The Doppler spectrum shows a relatively small difference between peak-systolic and end-diastolic velocities, indicating a low-impedance flow profile. The RI is calculated as 0.70. The patient exhibits an irregular Doppler spectrum due to cardiac arrhythmia. The arrhythmic beat causes flow disturbance, detected as spectral broadening or an effaced spectral window (*).

B. The Doppler spectrum from the left ECA shows a larger difference between peak-systolic and end-diastolic velocities, indicating a high-impedance flow pattern. The RI is calculated as 0.82, which is higher than that of the ICA. Since the ECA is a muscular artery with variable resistance, its resting flow impedance is higher than that of the ICA, which supplies the low-resistance cerebral vascular bed.

ECA = external carotid artery, EDV = end-diastolic velocity, HR = heart rate, ICA = internal carotid artery, PSV = peak systolic velocity, RI = resistive index, S/D = systolic to diastolic ratio (PSV/EDV), TAMV = time-averaged mean velocity

Prominent vascular dilation, often observed in dilated atria, aortic aneurysms, and pseudoaneurysms, significantly disrupts laminar flow. In these regions, blood flow is disturbed, causing directional velocity information to mix. This turbulence manifests as a “mosaic” of red and blue signals or a vortex pattern on the color Doppler map (Fig. 6). On the spectral display, irregular velocity components appear both above and below the baseline, indicating stagnation or recirculation. In addition, spectral broadening also occurs, characterized by an increase in the vertical thickness of the waveform. Specifically, the “spectral window”—the clear space typically visible beneath the systolic peak—diminishes or disappears, serving as a primary qualitative marker for turbulent blood flow (Fig. 5).

Fig. 6. Vortical flow in a 73-year-old male with an abdominal aortic aneurysm. B-mode (left) and color Doppler (right) images were acquired simultaneously in the axial plane. Within the aneurysmal lumen, the flow signal displays intermingled opposite colors, suggesting disturbed, vortical flow patterns.

Venous flow is generally continuous, low-velocity, and phasic, making it difficult to detect when flow volume is minimal. In such cases, flow augmentation maneuvers are employed. For example, compression and subsequent release of the venous lumen with the probe reveal outflow and inflow, confirming the presence of a blood-filled space in conditions such as venous malformations. In central veins, such as the vena cava, pulsations may synchronize with the respiratory and cardiac cycles. Additionally, the Valsalva maneuver is used to suppress flow, and venous insufficiency is confirmed if retrograde flow (reflux) occurs upon release. Observing respiratory phasicity further verifies the patency of the intervening veins. Gravity also aids assessment by placing the anatomical site in a dependent position to induce congestion. Unilateral lesions can be examined in the decubitus position, whereas lower extremity lesions can be assessed in the standing position to expand the vascular space.

Because MRI lacks real-time imaging capabilities, observing simultaneous hemodynamic changes is limited; however, flow alterations can be induced by repositioning the lesion or applying a tourniquet. 4D flow MR compensates for this by visualizing flow patterns via 3D mapping using parameters such as streamlines, path lines, velocity vector fields, and particle path traces. Streamlines indicate the directionality of the velocity vectors at specific instants and are advantageous for delineating flow morphology and observing temporal changes, particularly at the peak systolic velocity (PSV). In contrast, path lines display the trajectory of virtual particles over the entire cardiac cycle, allowing for the identification of the dominant intravascular streams (Fig. 3) (10).

QUANTITATIVE EVALUATION

Quantitative analysis facilitates an objective comparison of flow patterns during hemodynamic assessment. The acquisition of measurable surrogate markers of hemodynamic status enables the sensitive evaluation of temporal changes, which is essential for both diagnosis and monitoring of disease progression. Key quantitative parameters include velocity, flow rate, impedance, and pressure gradients.

FLOW VELOCITY

Flow velocity, typically expressed in cm/s, represents the distance travelled by blood per unit time. As the primary signal is obtained in both Doppler US and PC-MRI, it is considered a fundamental parameter of hemodynamics. Velocity exhibits pulsatile variations throughout the cardiac cycle. In the spectral display, the vertical maximum representing the peak velocity is shown as PSV) and end-diastolic velocity (EDV). Additionally, the time-averaged mean velocity (TAMV) is derived by averaging the velocity signal over a specific period (Fig. 1).

PC-MRI generates a similar time-velocity curve, representing the average velocity per pixel within an ROI across the vessel cross-section; this is termed the time-ROI mean velocity curve (Fig. 2). However, if the ROI encompasses the entire lumen, it averages the high-velocity central flow with the low-velocity marginal flow near the vessel wall, thereby underestimating the true central peak velocity. Therefore, accurate peak flow measurement requires the positioning of a small ROI, specifically at the center of the lumen. In clinical practice, where PSV and EDV are the primary metrics, this methodology creates discrepancies. Doppler US positions a small sampling volume at the center, yielding higher-velocity measurements. Conversely, routine clinical MRI often semi-automatically contours the lumen. Consequently, flow velocities measured by MRI tend to be systematically lower than those measured using Doppler US.

The velocity vector field acquired from 4D Flow MR offers a comprehensive representation. Particle path tracing provides velocity information across the entire vessel lumen throughout the cardiac cycle, enabling measurements at specific spatial coordinates (10). Although time-of-flight MR angiography (TOF-MRA) is the standard for noninvasive high-contrast anatomical imaging, velocity measurement is typically the domain of PC MRA. However, Koktzoglou et al. (17) recently extracted velocity data from TOF-MRA using advanced acquisition techniques, thereby validating its utility against PC MRA. This emerging quantitative TOF-MRA (qTOF-MRA) technique may enable simultaneous high-quality angiography and quantitative velocity assessment, with promising clinical applications.

FLOW RATE

Flow rate represents the volume of blood transported per unit time and is calculated as the product of mean velocity and vessel lumen area. In Doppler US, this calculation typically utilizes the TAMV and vessel cross-sectional area (derived from the diameter), providing a mean flow rate over the cardiac cycle (Fig. 1). In PC-MRI, although the ROI area generally remains constant throughout the cycle, the system converts the time-velocity curve into a time-flow curve. This capability allows the assessment of flow rate changes by cardiac phase and enables the separate quantification of forward and reverse flow volumes (Fig. 2).

Cardiac CT employs retrospective electrocardiogram gating to acquire data across the entire cardiac cycle, dividing it into 10–20 phases to reconstruct time-resolved cine images. These images yield time-volume curves for the ventricles and atria, where the volume difference between adjacent phases allows for the calculation of interchamber flow rates. Specifically, in the absence of aortic regurgitation, the rate of change in left ventricular volume during diastole represents the flow across the mitral valve. Flow velocity is calculated by dividing the derived flow rate by the mitral valve orifice area. This allows the estimation of a surrogate marker for the early/atrial (E/A) peak velocity ratio, a representative index of left ventricular diastolic function (18).

IMPEDANCE

Impedance encompasses various factors opposing flow within a nonsteady, complex system; it is a pulsatile analog to resistance in steady-flow systems. Blood flow is inherently pulsatile, and characterized by laminar acceleration during systole and complex, unsteady behavior during diastole. Furthermore, factors such as vessel bifurcation and diameter variations introduce flow disturbances. Consequently, impedance characterizes the hemodynamic load more accurately than simple vascular resistance. A high-impedance flow pattern indicates significant downstream resistance. This manifests as high velocity during systole but low, absent, or even reversed flow during diastole. Conversely, low-impedance flow maintains a substantial forward velocity throughout the diastolic phase (Fig. 5).

Doppler US utilizes velocity measurements to derive secondary hemodynamic indices, because calculating absolute impedance or resistance based solely on velocity is impossible without pressure data. The RI is a widely used indirect marker. It is defined as the ratio of the difference between PSV and EDV to the PSV (RI = [PSV - EDV]/PSV). An increase in RI indicates a transition toward high-impedance flow (Fig. 5). Normal ranges are vessel-specific; for instance, the renal artery typically exhibits an RI of 0.7 (19). In contrast, resting extremity arteries often exhibit an RI of 1.0, because diastolic velocity drops to zero. However, because RI relies exclusively on peak velocity points, it fails to reflect the full pulsatile shape of the waveform (spectral width). To address this limitation, the pulsatility index is used, which normalizes the systolic-diastolic difference against TAMV (20). Although RI can also be derived using PC-MRI, MRI typically calculates the mean velocity within an ROI. This spatial averaging may underestimate the peak velocities at the center of the stream. Therefore, the clinical criteria established for Doppler US are not directly interchangeable with MRI measurements.

PRESSURE GRADIENT

Blood flow supplies oxygen and nutrients to target organs, and ischemia occurs when this supply fails to meet the metabolic demands. Arterial stenosis reduces hemodynamic energy transmission and is the most common cause of arterial insufficiency. Although the gold standard for assessing this energy reduction is direct pressure measurement via catheterization, a noninvasive assessment is highly desirable. Consequently, the measurement of pressure gradients serves as a representative surrogate method.

Measuring absolute energy or static pressure based solely on velocity is impossible; however, the Bernoulli equation allows for the inference of pressure gradients. Hemodynamic energy comprises intrinsic (static pressure), kinetic, and potential energy. According to the principle of energy conservation, the sum of these components remains constant along a streamline (Equation 2).

Ei + Ek + Ep = P + 1/2 · ρ · v ² + ρ · g · h = Constant (Equation 2)

(Ei, Intrinsic energy; Ek, Kinetic energy; Ep, Potential energy; P, Pressure; ρ, Density; v, Velocity; g, Gravitational acceleration; h, Height)

Because quantifying energy loss due to viscosity and flow disturbance is complex, clinical Bernoulli models neglect these factors. By assuming total energy conservation and negligible pre-stenotic velocity and viscosity, the pressure gradient is estimated using the maximum velocity of the stenotic jet. This indicates that the simplified Bernoulli equation (pressure gradient = 4 × v _max ²) is widely used (Fig. 7). However, this equation relies on the significant assumption that kinetic energy dissipates entirely without pressure recovery. Consequently, velocity-based pressure gradients tend to overestimate the severity of stenosis compared with catheter-based measurements (21).

Fig. 7. Pressure gradient calculation via echocardiography.

A 13-year-old male underwent echocardiography to monitor surgically corrected Tetralogy of Fallot. Continuous-wave Doppler was acquired at the pulmonary trunk, revealing pulmonary valvular stenosis and regurgitation. The peak velocity (V_max) was measured. Using this, the pulmonary valvular maximum pressure gradient (maxPG) was calculated via the simplified Bernoulli equation: PG_max = 4 × (V_max)²= 4 × (1.88)² ≈ 14.10 mmHg.

Doppler US accurately measures PSV, allowing for automatic calculation of the pressure gradient. In this calculation, velocity is input in m/s to derive a pressure gradient in mmHg (Fig. 7). PC-MRI also measures PSV, making the simplified Bernoulli equation applicable. However, because PC-MRI typically uses ROI-averaged mean velocity, it often underestimates the true PSV. This leads to a systematic underestimation of the pressure gradients. Adriaans et al. (22) compared aortic valve pressure differences using echocardiography and PC-MRI and confirmed that MRI underestimated the pressure difference relative to echocardiography.

Invasive angiography remains the most accurate technique for this purpose. For the coronary arteries, pharmacological agents are administered to induce maximal myocardial hyperemia, thereby minimizing downstream resistance. A pressure wire then measures the pressure at the pre- and post-stenotic segments, and their ratio constitutes the FFR. FFR assesses hemodynamic energy reduction under maximal flow conditions and is crucial for guiding treatment strategies for intermediate coronary stenosis, as endorsed by current revascularization guidelines (15).

Coronary CT has high sensitivity but relatively low specificity for detecting significant stenosis, which limits its ability to identify hemodynamically significant borderline lesions. CT-derived FFR (CT-FFR) addresses this limitation by noninvasively estimating the pressure gradient ratio, thereby improving the positive predictive value of coronary CT (Fig. 8). CT-FFR utilizes CFD and artificial intelligence to model flow. Its effectiveness has been verified in clinical settings, and recently, the South Korean Ministry of Health and Welfare designated it as an innovative medical technology. Hwang et al. (23) reported a 20% increase in diagnostic accuracy using a CT-FFR program (HeartMedi + 1.0, AiMedic, Seoul, Korea). Although the analysis requires specific post-processing software, its clinical feasibility is well recognized.

Fig. 8. CT-based FFR measurement.

Coronary arteries are segmented from CT coronary angiography. Fluid analysis is performed using the segregated finite element method with 2.2 million elements (left). FFR values are simulated and displayed with a color map overlay (right).

Courtesy of Shim EB (Gangwon University) and Shin ES (University of Ulsan).

FFR = fractional flow reserve

OTHER PARAMETERS

The WSS represents the tangential force exerted by blood flowing on the vessel wall. Post-processing of Doppler US and MRI data extracts the longitudinal velocity profile, and the slope of this profile near the wall is defined as the wall shear rate (WSR). Multiplying WSR by blood viscosity yields the WSS. In pulsatile flow, WSS fluctuates dynamically, reaching its maximum during systole and minimum during diastole. Retrograde WSS may occur during certain phases. The OSI quantifies this directional variation and represents the ratio of retrograde shear to total shear over the cardiac cycle (24). Both WSS and OSI influence endothelial cell morphology and permeability. Because a high OSI is associated with atherogenesis, these metrics are used to assess the risk of atherosclerosis.

Some 4D flow MR programs display WSS as a color map (Fig. 3); however, accurate measurement of the near-wall velocity profile remains challenging because the accuracy of vessel lumen segmentation is critical. Accurate segmentation of the flow region in each phase is technically difficult because the arterial cross-sectional area changes during the cardiac cycle. Applying a fixed systolic ROI to all phases underestimates diastolic WSS, whereas using a diastolic ROI renders systolic WSS measurements unreliable. Furthermore, the direct clinical implications of specifically increased WSS or OSI values remain unclear, and their diagnostic utility has not yet been fully established.

Fluid kinetic energy is proportional to the square of fluid velocity (Equation 2). A 4D flow MR system acquires both velocity information and signal magnitude. Within a single voxel, turbulence causes proton velocity vectors to misalign. These vectors cancel each other out, leading to a reduction in signal intensity, known as “intravoxel dephasing.” Quantifying this signal loss yields turbulent kinetic energy, a robust index of disturbed flow derived directly from voxel signal intensity. Conversely, the simplified Bernoulli equation has limitations in hemodynamics because it disregards viscosity. Blood is a viscous, non-Newtonian fluid, and frictional loss, termed viscous energy loss, is significant (25). Theoretically, Doppler US can measure kinetic energy loss via short-axis velocity profiles; however, commercial applications are not yet available.

Disturbed flow encompasses both stochastic turbulence and organized helical flows. Vorticity quantifies the degree of local rotation (defined as the curl of the velocity field). Park et al. (26) analyzed left atrial blood stasis in patients with atrial fibrillation by measuring vorticity in the left atrial appendage. They assessed vortex parameters, including depth, length, width, sphericity, and relative intensity. Although statistical significance was not achieved, the study confirmed observable differences in flow characteristics between the atrial fibrillation group and normal control groups.

CONCLUSION

Radiological methods have evolved primarily to enhance spatial resolution, with the traditional goal of visualizing static anatomical structures. However, contemporary techniques, such as Doppler US and PC-MRI, have expanded this scope to provide critical hemodynamic information.

The analysis of hemodynamic imaging requires a fundamental understanding of blood flow characteristics. Specifically, blood must be recognized as a non-Newtonian fluid characterized by a variable viscosity. Furthermore, blood flow is inherently unsteady, exhibiting pulsatile and often disturbed behaviors. A solid understanding of these physical principles enables both qualitative and quantitative hemodynamic analyses.

Furthermore, a thorough understanding of the technical capabilities and limitations of available equipment is essential. Doppler US offers real-time imaging with high temporal resolution but is restricted by the acoustic window and a potential inter-observer variability. In contrast, PC-MRI offers high objectivity and 3D volumetric coverage; however, it relies on retrospective (reconstructed) temporal resolution rather than real-time data. Additionally, optimizing MRI image quality requires significant technical effort. Balancing these advantages and disadvantages is crucial for selecting the most appropriate imaging technique for specific clinical scenarios.

Although physiological cardiac function and hemodynamics may be less familiar in general radiology practice, they remain critical elements in cardiovascular imaging. Therefore, sustained interest and education in these domains are necessary to improve clinical interpretation and patient care.

Supplementary Materials

Korean translation of this article is available with the Online-only Data Supplement at http://doi.org/10.3348/jksr2025.0124.