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**AME 60676 Biofluid & Bioheat Transfer**

6. Biofluid/Bioheat Transfer Measurement Techniques

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Objectives Description of different in vivo, in vitro and in silico techniques to measure the flow and thermal characteristics of blood flow

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**Outline Pressure measurement Blood flow measurement**

Impedance measurement Flow visualization Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic Resonance Imaging Computational fluid dynamics Photo-acoustics

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**1. Pressure Measurement Pressure measurement Blood flow measurement**

Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Indirect Method Sphygmomanometer (pressure cuff method)**

Increase in cuff pressure Error 10 mmHg Cuff pressure higher than blood pressure Collapse of the brachial artery, artery occlusion Decrease in cuff pressure Cuff pressure lower than systolic pressure Arterial blood release, turbulent flow Systolic pressure Korotkoff sound Cuff pressure decreased futher Complete opening of artery, laminar flow Cessation of Korotkoff sound Diastolic pressure Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Direct Method Catheterization Transducer sensitivity:**

Filling fluid: heparinized saline (prevents blood clots) Continuous monitoring of blood pressure fluid-filled transducer diaphragm (resistance R) catheter e0: output voltage E: excitation voltage Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**2. Blood Flow Measurement**

Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Blood Flow Measurement**

EMF (electromagnetic flow meter) Voltage generated between electrodes: B: flux density of magnetic field l: spacing between electrodes V: mean flow velocity Volumetric flow rate: Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Blood Flow Measurement**

EMF (electromagnetic flow meter) Pros: Very accurate for in vitro testing Cons: Invasive in vivo technique (vessel must be exposed) Loss of signal over long in vivo measurement periods (protein and thrombus coating) Probe lumen area must be precisely known EMF theory assumes flat velocity profile Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Blood Flow Measurement**

Transit Time Flow Meter Speed of sound wave in fluid depends on fluid velocity Sound wave (kHz range) transmitted through vessel along flow axis in alternate directions Flow probe with 2 emitting crystals Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Blood Flow Measurement**

Transit Time Flow Meter and where: Flow probe with 2 emitting crystals Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Blood Flow Measurement**

Transit Time Flow Meter In vitro flow meters In vivo flow meters Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**3. Impedance Measurement**

Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Impedance Measurement**

In steady flow model: resistance In unsteady flow model: longitudinal impedance input impedance Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Impedance Measurement**

Longitudinal impedance Analogous to vascular resistance defined in steady flow Depends on local vessel properties Input impedance Ratio of pressure and flow at a particular site Depends on local and distal vessel properties longitudinal impedance input impedance Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Impedance Measurement**

Depend on Womersley number and elastic tube properties Complex quantities: Real part: resistive component Imaginary part: reactive component Input impedance measurement: Simultaneous flow and pressure measurement at one point Frequency analysis: at each frequency component n: Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Impedance Measurement**

characteristic impedance Z0 Input impedance in aorta of a dog (left) and human (right) Input impedance independent of frequency (except at low frequency) Fluctuations at high frequencies (wave reflection at discontinuities in peripheral arteries, vasoconstriction) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Impedance Measurement**

characteristic impedance Z0 Input impedance in aorta of a dog (left) and human (right) Fluctuation characterization: Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**4. Flow Visualization Pressure measurement Blood flow measurement**

Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Definition and Objectives**

Method: Visible marker introduced in flow stream Photographic record of marker movement Purpose: general overview of the flow field identify fine details of flow structures (jets, separation zones, secondary motion) characterization of the flow stability (laminar vs. turbulent) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Assumptions Marker accurately follows the actual flow movement**

Requirements: balance between inertial, viscous, buoyant, gravitational forces acting on marker No effect of marker on flow small, neutrally buoyant particles Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pros / Cons Pros: Cons: Simple technique**

Full-field, real-time information Cons: Optically accessible fluid (and model) Non-quantitative technique Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pathlines, Streaklines, Streamlines**

A trajectory of a given fluid particle Method: solid particles (small, reflective, neutral density) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pathlines, Streaklines, Streamlines**

The locus of particles which have passed a specified (usually fixed) spatial location Method: colored dye (not appropriate for unsteady or well-mixed flows) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pathlines, Streaklines, Streamlines**

A line drawn tangent to the local velocity vector field at an instant of time Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Other flow visualization techniques**

Hydrogen bubble technique Electrolysis (breakdown of H2O molecules into H2 at a cathode and O2 at an anode) Pros: No external markers Appropriate for high-velocity flows Cons: Invasive technique (electrodes must be inserted in the flow) Fluid must be electrical conductor Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Other flow visualization techniques**

Photochromic dye Use of TNSB mixed into the fluid medium and converted selectively to a colored state upon laser activation TNSB becomes opaque when exposed to ultraviolet light emitted by nitrogen laser Pros: Laser can be positioned at any site of the flow field Chemical reaction is reversible (no accumulation of dye) Cons: TNSB soluble in hydrocarbon-based fluid (e.g., kerosene) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**5. Ultrasound Doppler Velocimetry**

Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Ultrasound Doppler velocimetry**

Principle Doppler shift: change in frequency is proportional to relative motion between source and observer Nb of peaks received Nb of peaks intercepted Nb of peaks emitted Wave motion between a source and a moving receiver Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Practical Implementation**

Use of sound wave Transmission + reflection (twice the number of peaks intercepted) Doppler transducer located outside the body, at an angle with respect to the flow axis Equation carries information on both velocity magnitude and direction Practical implementation of ultrasound Doppler Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Continuous-Wave Devices**

Description: Transmission of high-frequency sound wave (>1 MHz) Use of 2 crystals (one emitting continuously and one receiving continuously) Schematic of a continuous-wave ultrasound Doppler device Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Continuous-Wave Devices**

Description: Large sampling volume due to overlap between emitted and received beams Lack of spatial resolution Wide spectrum of shifted frequencies due to large number of particles in sampling volume ( averaging or max velocity) overlap region Schematic of a continuous-wave ultrasound Doppler device Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Continuous-Wave Devices**

Clinical applications: Provides maximum velocity along the ultrasound beam (peak signal displayed at a given temporal location on the spectrum) Maximum pressure drop across heart valves to detect potential stenosis (eliminates limitations of catheterization) Other advantage: no maximum velocity limit due to continuous processing MV ejection velocity Continuous-wave spectrum of patient with mitral valve stenosis Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pulse-Doppler Devices**

Description: Intermittent emission/reception of signal by a single crystal Provides frequency shit information Provides exact location of reflective particle (travel time for sound wave) Pulse-Doppler principle Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pulse-Doppler Devices**

Spatial resolution: depends on length of signal burst sent out Number of cycles transmitted: n Length of sample volume: n = n ( c / f ) Increased frequency produces higher resolution Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pulse-Doppler Devices**

Limitations: Maximum range depends on time period between pulses PRF: pulse repetition frequency (cycle/s) Returning echo received once every (1/PRF) sec This imposes condition on maximum detectable Doppler shift (Nyquist sampling limit) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pulse-Doppler Devices**

Limitations: PRF imposes condition on maximum detectable Doppler shift (Nyquist sampling limit) Nyquist criterion: (sampling rate > 2 x signal frequency) Since For a given flow or depth, a limited range of velocities can be accurately detected Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Pulse-Doppler Devices**

Clinical applications: Pressure drop across a stenosis Local velocity profile across a vessel Local shear stress, wall-shear stress Residence time 2D implementation with large array of crystals Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**6. Laser-Doppler Velocimetry**

Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Principle Laser light scattered by particles suspended in fluid Frequency of light reflected from a moving object is shifted by an amount proportional to the speed of the flowing material Frequency shit provides an estimate for flow velocity Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Principle Particles are illuminated by a known frequency of laser light Scattered light is detected by a photomultiplier tube generates a current in proportion to absorbed photon energy Doppler shift = incident light frequency – scattered light frequency Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Characteristics Velocity range: 0 to supersonic Up to three velocity components Non-intrusive measurements Absolute measurement technique (no calibration required) Very high accuracy Very high spatial resolution (small probe volume) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Overview fiber drive laser couplers transceivers Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Laser Beam Generation Bragg cell divides laser beam into 2 beams (direct + frequency shifted) Each beam separated into 3 wavelengths Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Laser Beam Generation 2D transceiver: blue and green, 2 probe volumes 1D transceiver: purple, 1 probe volume Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Probe Volume Each color is used for measuring one velocity component The two probes are aligned so their intersection volumes coincide The velocity components measured by the beams from the probes are orthogonal Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Probe Volume f: beam focal length d: prefocal beam spacing : half angle of beam intersection : beam wavelength De: initial beam diameter E: beam expansion ratio Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Fringe Pattern Intersection of coherent fringes Probe volume is a stable interference pattern characterized by alternating light and dark fringes (from optics theory) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Laser Doppler velocimetry**

Fringe Pattern Moving particle fluctuations in scattered light intensity Particle crossing a destructive (dark) fringe: zero light intensity particle crossing a constructive (bright) fringe: peak in the light signal Typical Doppler burst Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**7. Magnetic Resonance Imaging**

Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Capabilities and Characteristics**

High quality images that provide: detailed anatomical information qualitative (signal intensity)/quantitative (signal phase) flow information Main characteristics: Large static magnetic field Super conducting magnet cooled with liquid helium and nitrogen 60 cm diameter, 2 meter long Typical MRI scanner Cross section of a MRI scanner Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Magnetization Moving electric charge produces a magnetic field Nucleus = protons + neutrons Protons have a positive charge and spin Protons create a magnetic field Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Magnetization In the presence of a static magnetic field B0, magnetic moment vector of the proton aligns: with the field (low energy state) at an angle with respect to the field (high energy state) Net magnetization vector = sum of vectors of magnetic moments of all protons aligned with B0 aligned along bore of scanner (z-axis) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic Resonance Effect**

Protons placed in a magnetic field resonate or spin at a particular frequency Resonance frequency depends on the applied magnetic field: : Larmor frequency : gyromagnetic ratio (material specific) B0: local magnetic field (T) Larmor equation Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Slice Excitation 1st step in MRI = select and energetically excite region to be imaged Excitation of protons by a pulsed magnetic field B1 at frequency switches proton energy state between parallel and anti-parallel states first pulse forces switch from lower to higher energy state (excitation) Excitation energy is proportional to the frequency and Plank’s constant h Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Slice Excitation z M0 magnetization vector is tipped from z-axis to x-y plane (: flip angle) Only protons spinning at Larmor frequency are excited Slice selectivity is achieved by generating a spatial gradient in magnetic field y x MRI axis B01 B02 B03 B04 B05 Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Spatial Encoding At the end of RF excitation, all protons in a specific slice have a high energy level After excitation, energy released by protons can be detected Magnetic field in xy-plane creates a current in receiving coil of the MRI scanner (free induction decay) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Spatial Encoding Practically, need to differentiate different locations within one slice (for spatial registration) Slice divided into voxels (small volumes containing several protons) Each voxel corresponds to a specific Larmor frequency magnetic field gradients along x and y (phase and frequency encoding) MRI axis B01 B02 B03 B04 B05 voxels x z B03 y Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Spatial Encoding Phase encoding step Differentiate Larmor frequency in each row of voxels for short period of time At end of step: all rows return to original frequency Each row of voxels now includes small phase difference with respect to the next and previous rows MRI axis B01 B02 B03 B04 B05 voxels x z B03 y Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Spatial Encoding Frequency encoding step Differentiate Larmor frequency in each column of voxels At the end of encoding step, each voxel characterized by a unique (Larmor frequency, phase) pair MRI axis B01 B02 B03 B04 B05 voxels x z B03 y Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Image Reconstruction Receiving coil captures the resulting signal Phase and frequency can be retrieved using 2D FFT Final image is reconstructed (contrast based on variations of magnitude of received signal) Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Magnetic resonance imaging**

Velocity Mapping Motion of proton in magnetic field gradient results in phase shift in its spinning frequency proportional to strength and duration of magnetic field gradient : phase of signal : gyromagnetic ratio G: magnetic field gradient vector r: proton position vector Z0: initial proton position u: proton velocity Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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**Velocity Mapping : phase of signal : gyromagnetic ratio**

G: magnetic field gradient vector r: proton position vector Z0: initial proton position u: proton velocity Phase velocity mapping (PVM) Typical magnetic field gradient strength Pressure measurement Blood flow measurement Impedance measurement Ultrasound Doppler velocimetry Laser Doppler velocimetry Magnetic resonance imaging Computational fluid dynamics Flow visualization

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