Medical diagnostic systems (Orvosbiológiai képalkotó rendszerek) Ultrasound velocimetry (Ultrahang sebességmérés) Miklós Gyöngy Diagnosis based on human body dynamics Motion type Typical speed (mm/s) Measurement method of choice Muscoskeletal movement external visible motion 50-5000 optical muscle contraction [Deffieux et al. 2006; Jarvis et al. 1997] 5 (transverse),500 (axial) servomotor (invasive), ultrasound Organ wall motion (e.g. heart, vessels) ultrasound Fluidic lymphatic [Fischer et al. 1996; Havas et al. 1997] 0.1 scintigraphy respiratory system peak flow meter urinary, digestive, reproductive, mammary production rate (of interest): ? excretion: optical amniotic fluid [Kinga Gyöngy] ultrasound cerebrospinal fluid [Lee et al. 2004] 40 MRI, ultrasound blood circulation [Cobbold 2007, p. 620] peak 1 m/s ultrasound Overview of this lecture • Cardiovascular system • Doppler effect and its relevance to blood • Doppler velocimetry of blood flow (and solid structures) • Other US-based motion analysis methods The cardiovascular system • Carrying oxygen from the lungs to the body (cells) for metabolism • Major determinant of health – How much flow is there? How well is organ supplied with nutrients? (stenosis/thrombosis) – Is there regurgitation of blood? Backflow can be indicator of ill-health – What is the flow pattern with time? Medical diagnostic systems – Ultrasound velocimetry The heart – a double pump oxygen pulmonary arteries pulmonary systemic veins veins systemic arteries the human heart oxygen http://commons.wikimedia.org/wiki/File:Diagram_of _the_human_heart_%28cropped%29.svg Creative Commons licence Medical diagnostic systems – Ultrasound velocimetry (AV) valves the human heart the cardiac cycle http://commons.wikimedia.org/wiki/File:Diagram_of http://en.wikipedia.org/wiki/File:Cardiac_Cycle_Left_Ventricle.PNG _the_human_heart_%28cropped%29.svg Creative Commons licence Creative Commons licence Blood velocity profiles [Gijsen et al. 1999] • Newtonian liquid: shear stress proportional to velocity gradient • In contrast, blood is non-Newtonian and exhibits shear thinning (viscosity decreases at higher shear stresses – imagine ketchup) • Newtonian liquid: fully developed flow profile in circular tube (vessel) is parabolic • In contrast, shear thinning fluid causes flattening of velocity Adapted from [Cobbold 2007, p. 629] profile • Note also: vessel wall is elastic! Blood velocity profiles [Shehada et al. 1993] • Period=0.85 s; 0o: systole • Assuming fully developed flow, [Shehada et al. 1993] modelled flow profiles of common carotid artery and femoral artery • Even assuming Newtonian fluid, pulsatile nature of flow creates non-parabolic profile and even backflow • Despite same order of magnitude parameters for common carotid and femoral arteries (diameter, viscosity, mean flow, peak flow, Womersley number), substantial difference in Adapted from [Cobbold 2007, p. 629] velocity profiles is observed Vascular blood perfusion [Uzwiak 2010] • flow due to pressure gradient • mass conservation -total flow rate constant Public domain: http://commons.wikimedia.org/wiki/File:Illu_capillary.jpg -90 % of blood returns via veins -surface area ^ velocity ¡ 120 pressure (mm Hg) 100 80 60 40 20 surface area greatest at capillaries - -40-50 cm/s at arteries -0.03 cm/s at capillaries speed again rises towards veins but - does not reach arterial blood velociy due to blood loss at capillary bed (collected by lymphatic vessels) 0 The Doppler effect • Source approaching stationary observer: observed frequency increases • Same effect if observer approaching f0 stationary source (relative velocity) f0 Examples: • Ambulance siren • Galaxies (blue-shift/red-shift) • Running towards water surface waves (perhaps best illustration of effect, since one clearly observes meeting crests of waves more often) • What scatters in blood? adapted from [Szabo2004, p. 339] • Are blood scatterers the running observers or running sources? Both...! Doppler effect quantified • Source frequency f0, velocity vs away t =0 from receiver • Peak transmitted at t=0, z=0 • A period later (t=1/ f0), another peak t=1/ f0 transmitted • By this time • (left portion of) t=0 emission moved to z=-1/f0c • source moved to z=1/f0vs • wavelength between pulses . = 1/f0(1/v+ 1/c)=(v+ c)/vcf0 s ss source Doppler effect quantified wave velocity frequency received frequency source velocity (away from observer) Doppler frequency The Doppler effect – a moving scatterer [Szabo 2004, p. 342; Cobbold 2007, pp. 617-618] Doppler effect varies with angle Doppler effect „doubles” – frequency shift experienced by scatterer receiver – frequency shift experienced by receiver Continuous Wave (CW) insonation: – Array split into two subapertures Scattering by blood [Burns 2005; http://en.wikipedia.org/wiki/Hematocrit] • Red blood cells (RBC) form ~38%(+),48%(>) of blood volume • Proportion known as the hematocrit (Hct) • Scattering dominated by RBC and dependent on Hct and RBC state (eg health, aggregation) • 7 µm mean diameter ‚ps~a3f 2 (characteristic of sub-. (Rayleigh) scatterers) • increasing frequency increases scattering, but • scattering still relatively weak plasma white blood cells red blood cells Test tube of blood after being placed in a centrifuge. Due to different densities, blood has fractionated into plasma (yellow), white and red blood cells. Red blood cells are the strongest sources of ultrasound scattering in blood. Doppler velocimetry of blood flow • continuous wave (CW) • (single-gate) pulsed wave (PW) – Doppler effect? Depends on your definition. • color flow imaging (CFI) – pulsed wave – power Doppler Continuous Wave (CW) Doppler • Small frequency shifts better detectable over long integration times • Thus, CW detects Doppler shift sensitively transmit receive • However, transducer cannot transmit and receive simultaneously (isolation of high power transmission and high sensitivity receive circuitry) • Thus separate transducers needed (or else splitting of transducer into subapertures) • Limited spatial resolution (overlap region of two beams) • Thus, region of observation often encompasses several vessels Continuous Wave (CW) Doppler • Frequency shift observed clinically (e.g. vs=0.1 m/s; f0 = 1 MHz; .,.=45o,5o) fD =-2×0.1/1540×cos45o×cos(5o/2) = -92 Hz • Demodulated Doppler signal in audio domain! • Thus, in addition to observing frequency spectrum of return signal, the Doppler shift may be connected to a headphone and a trained doctor can diagnose based on the Doppler shift signal (cf. stethoscope) adapted from [Burns 2005] Continuous Wave (CW) Doppler What does the doctor hear? • Mixture of velocities along cross-section of vessel at any one time: distribution of freqeuencies in Doppler shift signal • Velocity distribution changes over heartbeat cycle: ditto Doppler shift signal • Backflow causes negative frequency: process demodulated signal so that backflow signal (often a sign of disease, e.g. vessel narrowing [Cobbold 2007, p. 634]) directed to on one ear while forward flow signal directed to other ear • How to process? Think of Fourier transforms of sine, cosine... Blood velocity profile in common carotid artery over one heartbeat cycle. Adapted from [Cobbold 2007, p. 629] Beyond CW Doppler • CW Doppler offers high sensitivity • CW Doppler provides detailed information: • velocity distribution across vessel (e.g. vessel narrowing will cause combination of forward and backward flow [Cobbold 2007, p. 634]) • evolution of velocity distribution with time (e.g. heartbeat regularity) • As a consequence, CW still widely used • However, in some situations, high spatial resolution is crucial • One possible solution [Burns 2005, p. 18]: use high transmit frequency. – High attenuation • only first vessel is traversed – High frequency • higher backscatter from RBC • Another solution: pulsed transmission • But how can frequency shift be detected for a pulse (cf time-frequency uncertainty)??? Pulsed Wave (PW) “Doppler” • Transmit pulses so as to have axial (range) resolution • Reconstruct Doppler signal from succession of pulses sent at high pulse repetition frequency (PRF) (e.g. 5 kHz) • Sample A-lines at depth of interest to recover pulse in ‘slow-time’ • Central frequency of ‘slowtime’ pulse returns scatterer speed depth of interest ‘Fast time’ (over µs) sampled amplitude single scatterer moving away from transducer causes increasing delay of echo for each successive A-line Adapted from [Cobbold 2007, p. 659] Pulsed Wave (PW) “Doppler” • PRF determines maximum velocity that can be detected without aliasing (Nyquist sampling) (exercise) • Note similarity of expressions for conventional Doppler shift and PW Doppler shift (exercise): depth of interest ‘Fast time’ (over µs) sampled amplitude single scatterer moving away from transducer causes increasing delay of echo for each successive A-line Adapted from [Cobbold 2007, p. 659] Gated PW • take envelope of echoes • integrate over gated time corresponding to some range of depths • multiply by slow-time cosine wave • resulting reconstructed „Doppler signal” waveform has – improved SNR – decreased axial resolution gate modification of single-location PW in order to increase SNR the envelope of A-line echoes are summed over a gate around the location of interest Adapted from [Cobbold 2007, pp. 659,673] Duplex scanning • B-mode/single-gated PW • Use B-mode to find location of interest • Place PW gate at that location • Various methods to estimate frequency spectrum • User can often specify angle of flow to compensate for angular term in Doppler equation Color flow imaging Aim: display mean velocity as 2-D map Mean Doppler shift‚mean v Solutions – generate Doppler signal for many gates, calculate mean f shift for each (obsolete) – generate continuous estimate of mean f shift (preferred) Pulmonic regurgitation Courtesy of Zonare Medical Systems http://www.zonare.com/products/clinical-images/id_15/ Color flow imaging – autocorrelation processor [Burns 2005, p. 23; *Cobbold 2007, pp. 701–706; Wells 1999, p. 29] Instantaneous frequency given by the derivative of instantaneous phase Compute changes in phase from one A-line to the next for each location to estimate local frequency shift Example of phase estimation*: quadrature signal in-phase signal Vector flow: Combine color flow images from several angles to yield vector flow of blood See [Maniatis 1994] for illustration Color flow imaging – Power Doppler [Rubin 1994] • Display integrated power of Doppler signal rather than mean frequency shift (i.e. variance of image pixel across subsequent transmissions) • Not really based on Doppler effect! • Much greater sensitivity • Can be used normal to direction of blood flow • No directional information (or dependence) • Difficult to obtain quantitative information about velocity Tissue Doppler [Cobbold 2007, pp. 722-723] Blood is also tissue! It is a special form of connective tissue. Solid tissue moves slower (<10 cm/s) than blood Solid tissue creates stronger echoes Appropriate filtering can filter out Doppler signal from solid structures Adapted from [Cobbold 2007, p. 723] Other ultrasound-based motion analysis methods • M-mode • Transit time velocimetry • B-flow • Scatterer tracking M-mode (motion-mode) [Cobbold 2007, pp. 423– 425; Szabo 2004, pp. 303–304] • Observe single A-line with time • Motion of organ boundaries clearly visible (e.g. heart wall motion) • Very simple and effective z transducer Transit time velocimetry sound The concept propagation • Arises from the propagating medium • Effective speed of propagation changed material flow tr • Spectral characteristics of signal not affected! • Measure bulk flow – wind speed (anemometry) – production control Transit time velocimetry The application [Cobbold 2007, p. 614] • Width of vessel not known a priori • Calculate difference in arrival times .t • Changing flow profile • v needs to be integrated over the propagation path in the vessel upstream transceiver downstream transceiver upstream downstream transceiver reflector B-flow – motivation Problem [Cobbold 2007, p. 657]: • RBC scattering weak • 20–60 dB less than surrounding tissue • 0–20 dB SNR • As a consequence, B-mode images do not show RBC well Aim: • Modify B-mode to highlight scattering from RBCs • This would allow visualisation of blood flow B-flow – application [Chiao et al. 2000] • Transmit coded pulse sequence • Compress pulse sequence using matched (cross-correlation) or mismatched filtering (latter suppresses range lobes) • Range lobes produced by coded excitation (partially) cancelled using two transmissions • Suppress stationary signals (“tissue equalization”) • Combination of pulse compression and tissue equalization allows blood to have significant enough signal • See http://www.gehealthcare.com / usen / ultrasound / genimg / images / bfc_spleen_500.jpg for illustration Scatterer tracking – 1-D tracking [Hein and O’Brien 1993] • Comparison of A-lines over several frames • Pseudo-algorithm: For each segment of each A-line: • divide into short (~µs) segments; • perform 1-D cross-correlation on corresponding segment of previous A-line • peak of cross-correlation corresponds to maximum-likelihood estimate of scatterer displacement • In practice, source of tracked signal is often speckle • Although speckle is an interference effect from several scatterers • short durations: scatterers move together, speckle unchanged, tracking successful • longer durations: speckle decorrelation occurs Scatterer tracking – optical flow • Extend tracking to 2-D cross-correlation to yield maps of optical flow • Similarly to segmentation-registration of multiple modalities, combination of scatterer tracking and boundary segmentation mutually beneficial for both tasks [Hillier 2010] Optical flow image of a heart arrows indicate direction of motion [Hamou and Sakka 2009] [Burns 2005] Introduction to the physical principles of ultrasound imaging and Doppler. http://medbio.utoronto.ca/students/courses/mbp1007/Fall2009/MBP1007_Burns_Utrasound.pdf [Chiao et al. 2000] B-mode blood flow (B-flow) imaging [Cobbold 2007] Foundations of biomedical ultrasound [Deffieux et al. 2006] Ultrafast imaging of in vivo muscle contraction using ultrasound [Fischer et al. 1996] Flow velocity of single lymphatic capillaries in human skin. http://ajpheart.physiology.org/cgi/content/abstract/270/1/H358 [Gijsen et al. 1999] The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model. http://www.mate.tue.nl/mate/pdfs/215.pdf [Hamou and Sakka 2009] Optical Flow Active Contours with Primitive Shape Priors for Echocardiography. http://www.hindawi.com/journals/asp/2010/836753.html ... ... [Havas et al. 1997] Lymph flow dynamics in exercising human skeletal muscle as detected by scintography. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1159951/pdf/jphysiol00377-0229.pdf [Hein and O’Brien 1993] Current time-domain methods for assessing tissue motion by analysis from reflected ultrasound echoes. http://www.brl.uiuc.edu/Publications/1993/Hein-UFFC-84-1993.pdf [Hillier et al. 2010] Online 3-D reconstruction of the right atrium from echocardiography data via a topographic cellular contour extraction algorithm [Jarvis et al. 1997] Relationship between muscle contraction speed and hydraulic performance in skeletal muscle ventricles [Lee et al. 2004] CSF flow quantification of the cerebral aqueduct in normal volunteers using phase contrast cine MR imaging. http://synapse.koreamed.org/Synapse/Data/PDFData/0068KJR/kjr-5-81.pdf ... ... [Maniatis et al. 1994] Flow imaging in an end-to-side anastomosis model using two-dimensional velocity vectors [Rubin et al. 1994] Power Doppler US: A potentionally useful alternative to mean frequency-based color Doppler US [Shehada et al. 1993] Three-dimensional display of calculated velocity profiles for physiological flow wave-forms [Szabo 2004] Diagnostic ultrasound imaging: Inside out [Uzwiak 2010] Anatomy and Physiology online lecture notes http://www.rci.rutgers.edu/~uzwiak/AnatPhys/APSpringnotes.html [Wells 1999] Ultrasonic imaging of the human body