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

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Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Blood flow measurement Indirect Method Sphygmomanometer (pressure cuff method) Increase in cuff pressure 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 Korotkoff sound Cuff pressure decreased futher Complete opening of artery, laminar flow Cessation of Korotkoff sound Systolic pressure Diastolic pressure Error 10 mmHg

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Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Blood flow measurement Direct Method Catheterization – Transducer sensitivity: – Filling fluid: heparinized saline (prevents blood clots) – Continuous monitoring of blood pressure catheter fluid-filled transducer diaphragm (resistance R ) e 0 : output voltage E : excitation voltage

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

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

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

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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 Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Pressure measurement Flow probe with 2 emitting crystals

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

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

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

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

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

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

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Impedance Measurement Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Blood flow measurement Pressure measurement 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) characteristic impedance Z 0

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Impedance Measurement Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Blood flow measurement Pressure measurement Input impedance in aorta of a dog (left) and human (right) Fluctuation characterization: characteristic impedance Z 0

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Impedance measurement 4. Flow Visualization Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Ultrasound Doppler velocimetry Blood flow measurement Pressure measurement

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

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

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

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

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

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Impedance measurement Pathlines, Streaklines, Streamlines Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Ultrasound Doppler velocimetry Blood flow measurement Pressure measurement Streamline: A line drawn tangent to the local velocity vector field at an instant of time

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Impedance measurement Other flow visualization techniques Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Ultrasound Doppler velocimetry Blood flow measurement Pressure measurement Hydrogen bubble technique – Electrolysis (breakdown of H 2 O molecules into H 2 at a cathode and O 2 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

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

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Flow visualization Impedance measurement 5. Ultrasound Doppler Velocimetry Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Blood flow measurement Pressure measurement

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

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Flow visualization Impedance measurement 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 Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Blood flow measurement Pressure measurement Practical implementation of ultrasound Doppler

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

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Flow visualization Impedance measurement 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) Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Blood flow measurement Pressure measurement Schematic of a continuous-wave ultrasound Doppler device overlap region

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Flow visualization Impedance measurement 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 Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Blood flow measurement Pressure measurement Continuous-wave spectrum of patient with mitral valve stenosis MV ejection velocity

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Flow visualization Impedance measurement 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) Computational fluid dynamics Magnetic resonance imaging Laser Doppler velocimetry Blood flow measurement Pressure measurement Pulse-Doppler principle

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

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

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

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

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Ultrasound Doppler velocimetry Flow visualization Impedance measurement 6. Laser-Doppler Velocimetry Computational fluid dynamics Magnetic resonance imaging Blood flow measurement Pressure measurement

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

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

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

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

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

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

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

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

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

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

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement 7. Magnetic Resonance Imaging Computational fluid dynamics Blood flow measurement Pressure measurement

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement 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 Computational fluid dynamics Blood flow measurement Pressure measurement Typical MRI scanner Cross section of a MRI scanner

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

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Magnetization Computational fluid dynamics Blood flow measurement Pressure measurement In the presence of a static magnetic field B 0, 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 B 0 – aligned along bore of scanner (z-axis)

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement 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) B 0 : local magnetic field (T) Computational fluid dynamics Blood flow measurement Pressure measurement Larmor equation

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Slice Excitation Computational fluid dynamics Blood flow measurement Pressure measurement 1 st step in MRI = select and energetically excite region to be imaged Excitation of protons by a pulsed magnetic field B 1 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

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Slice Excitation Computational fluid dynamics Blood flow measurement Pressure measurement 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 z z x x y y M0M0 M0M0 B 01 B 03 B 04 B 05 B 02 MRI axis

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Spatial Encoding Computational fluid dynamics Blood flow measurement Pressure measurement 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)

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Spatial Encoding Computational fluid dynamics Blood flow measurement Pressure measurement 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) B 01 B 03 B 04 B 05 B 02 MRI axis B 03 z x y voxels

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Spatial Encoding Computational fluid dynamics Blood flow measurement Pressure measurement 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 B 01 B 03 B 04 B 05 B 02 MRI axis B 03 z x y voxels

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Spatial Encoding Computational fluid dynamics Blood flow measurement Pressure measurement 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 B 01 B 03 B 04 B 05 B 02 MRI axis B 03 z x y voxels

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Image Reconstruction Computational fluid dynamics Blood flow measurement Pressure measurement 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)

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Velocity Mapping Computational fluid dynamics Blood flow measurement Pressure measurement 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 Z 0 : initial proton position u : proton velocity

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Laser Doppler velocimetry Ultrasound Doppler velocimetry Flow visualization Impedance measurement Velocity Mapping Computational fluid dynamics Blood flow measurement Pressure measurement : phase of signal : gyromagnetic ratio G : magnetic field gradient vector r : proton position vector Z 0 : initial proton position u : proton velocity Typical magnetic field gradient strength Phase velocity mapping (PVM)

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