Ultrasound Flashcards
Longitudinal vs transverse
Longitudinal: particles oscillate in direction of wave propagation - but at speed closer to 1m/s, not speed of sound in medium. Have high and low pressure regions
Transverse: shear waves, oscillate at 90 degrees to direction of propagation. Don’t create pressure changes.
Speed of sound in a medium equation
c = sqrt (K/rho)
where K is bulk modulus and rho is density
Equations for circular plane transducer
(plane waves in near field and convex in far)
L=a^2/λ
θ = arcsin(0.61λ/a)
a is diameter
Beam width at focus
w ~= Fλ/a
where F is focal length
Concave wavefronts that become plain then convex
RIL/RPL
Relative intensity level and relative pressure level
RIL = 10log_10(I2/I1) dB
RPL = 20log_10(p2/p1) dB
Decibels
Reciprocal of a number is negative - if 46dB for ratio of 200 then ratio of 1/200 would be -46.
Acoustic impedance p/u relationship
Z= +/- p/u
p is instantaneous acoustic pressure
u is instantaneous particle velocity
p=+Zu for forward travelling and p=-Zu for backwards
Acoustic impedance K, ρ, c
Z = sqrt(Kρ_0) = ρ_0c_0
I = pu = p^2/Z
What must happen at boundary
Continuity of pressure and particle velocity. If Z2<Z1 then 180 degree phase shift
Frequency won’t change, wavelength will.
Amplitude reflection coeff and amplitude transmission coeff
R_a = p_r/p_i = (Z2-Z1)/(Z2+Z1)
T_a = p_t/p_i = 2Z2/(Z2+Z1)
Intensity reflection coeff and intensity transmission coeff
R_i = R_a ^2
T_i = (Z1/Z2) T_a ^2
Specular vs diffuse reflection
Specular - smooth surface, reflects fully. Diffuse - rough on the wavelength scale, lots of angles of incidence, scattered over many angles. Allows non-perpendicular images to be seen.
Reflection and refraction equations
θi = θr for reflection
sinθt/sinθi = c2/c1
If c2>c1, bent away from normal
Eventually reach 90 degrees, can’t see that area, leads to shadows.
Focussing techniques
Concave source, focal length F = radius of curvature
Plane source with convex lens - want speed of sound lower in lens than material of body
Equation for calculating R of lens
R = F[(c2/c1)-1]
Intensity/pressure attenuation
I=I0 exp( - mu x)
p = p0 exp(alpha x)
mu = intensity attenuation coeff.
alpha = amplitude attenuation coeff
mu = 2 alpha
Attenuation parts
Absorption and scattering
alpha = alpha_s + alpha_a
Absorption
Conversion of acoustic energy to heat as wave propagates through material. Two main mechanisms: ‘classical’ one due to viscosity and one due to molecular relaxations.
Scattering
Formed by scattered echoes from small scale inhomogeneities in bulk modulus and density. If average size of scatterers is much smaller than wavelength have Rayleigh scattering, isotropic and scattered intensity proportional to f^4.
Speed of sound in water
1480ms-1
Curved array details
Lower f,15cm, abdominal or obstetric. Fan shaped. 1-6MHz 128 elements.
Relationship between attenuation coefficient and frequency
Linear: double frequency, double attenuation coeff.
Size of transducer/elements
Array length often 38mm, giving pitch of 0.2 or 0.15mm (192 or 256 elements)
1cm other direction
Why do we use multiple elements at one time
So beam is collimated - width of one element usually smaller than wavelength
Rank the components of spatial resolution from best to worst
Axial best, then lateral then slice thickness
What determines each spatial resolution
Axial determined by pulse duration
Lateral by beam width in image plane
Slice thickness by beam width in elevation direction
Limit for axial resolution of transucer
c_0T/2
T is pulse duration
Time taken to acquire a line
t=2D/c
Frame rate
Time resolution: if image is deeper, if there are more lines, if the sector is wider then it will take longer and frame rate will be lower.
Time to get image is Nt (N is number of lines and t is time to acquire a line)
FR = 1/Nt
How does B-mode work
Pulse echo technique - short pulse generated by transducer and same transducer picks up echo.
Sweep beam across view - 20-40 elements at a time, wait for echoes then move active group by one.
Time until echo
t = 2d/c_0
M-mode imaging
Motion mode - used to track features in body over time, acquire A-mode lines one after another of oen location and plot them side by side, mostly used in echocardiography.
A-mode imaging
Amplitude mode - showed trace. Echoes displayed at delays proportional to their depth. Still used in opthamology, often with high f dedicated non-imaging probe
Time gain compensation
Ultrasound attenuated through tissue - echoes from deeper become weaker. Apply gain to compensate for this - increases exponentially.
Demodulation
Gives grey scale images. First get rid of negatives with rectification and then smooth to get rid of high f components.
Compression
Dynamic range of demodulated signal is very large, 80-100dB. To overcome this we log-compress the data, comes down to 48dB. Most displays have 256 grey levels which matches this.
Effect of frequency and damping on beam
High frequency: good for resolution but bad penetration
Good damping: good for resolution but less sensitive (amplitude achievable is lower)
Bandwidth
Range of frequencies - bandwidth of a pulse is indirectly proportional to its length (short B-mode doppler pulse has wide bandwidth but PW doppler toneburst is very narrow)
If we say a 3MHz pulse, that’s the central frequency
Bandwidth of a CW sinusoidal signal
Zero
How is bandwidth of a transducer determined
Go down by -3dB and see where that is
Bandwidth of pulse needs to lie inside bandwidth of transducer
Relative bandwidth
BW/central frequency
Attenuation loss
a f^b z
(a is attenuation f, frequency, b is constant (2 for water, 1-1.2 for tissues), z is depth)
Why is the limit for MI/TI different for the eye?
Parts of the eye are more sensitive to potential damage.
Cornea, lens, vitreous body are unperfused tissues - only dissipate heat through thermal conduction
Lack of blood perfusion limits ability to repair damage from excess exposure.
What scanner settings do you use during the wire tool test
Max power output
Plane and linear scan mode
No compound mode
No special post processing
No beam steering
Should see wire reverberation pattern
Describe wavefronts from circular, focused transducer
Start out concave, become plane and then convex.
Converge and then diverge after focus
Diameter gets smaller as it converges and is minimum at focus.
Linear array details
Higher f, 8cm, vascular or MSK, breast. Rectangular. 128-256 elements (same no. scan lines) 4-12MHz (vascular)
Phased array details
Lowest f, 20cm, echocardiography. Sector. 1-5MHz (3-8 for children) 80 elements. Beam is steered - worse image quality.
Radial array details
transrectal/transvaginal - transvaginal used in antenatal, 4-10MHz.
