therapeutic ultrasound and safety

what are the effects of ultrasound

1. thermal effect

2. bubble and cavitation effects

3. radiation effects

what is the volume rate of heat deposition? units?

$Q=\frac{aP_{A}^2(x)}{\rho_{o}C_{o}}$ $W.m^{-3}$ see notes for derivation

how does rate of heat deposition behave

it is proportional to the absorption coefficient and the square of the local pressure amplitude $P_A=P_oe^{-ax}$

after the probe is turned off:

• heating decreases due to diffusion of heat via conduction and tissue perfusion

what happens if temperature deposition is larger than it’s decrease?

$\Delta=\frac{aP_A^{2}(x)t}{\rho_oC_oC}$ where C is the specific heat capacity(J/Kg/C)

factor affecting heating

1. absorption coefficient of the tissue

2. frequency: increased absorption at higher frequencies → more heating

3. non-linear effects: harmonics moves energy to a higher frequency → more heating

how is ultrasound heating mapped?

using infrared imaging in a water tank

what does heat damage to cells depend on

1. temperature

2. exposure time

what are the heat thresholds for tissue damage?

• C < 40 → no irreversible damage

• C > 40 → protein denaturing and loss of function

• c >65 → collagen fibres shrink and tissue coagulates

what is thermal dose

measured in cumulative equivalent minutes (CEM 43C or $t_{43}$ )

→ it is the number of minutes required to achieve the same effect as heating at 43C

→ allows us to compare the thermal dose delivered at different temperatures

$$t_{43}=\int_0^{t}\!R^{43-T}\,dT$$

where:

• t: is time in minutes

• T: is temperature in celsius

• R = 0.5 when T > 43, R = 0.25 when T < 43

if temp is constant: $t_{43}=tR^{43-T}$

what is the cumulative equivalent minutes required for cell death

$$t_{43}=240 minutes$$

• for every degree above 43C the time to effect is halved

• heating is not uniform

• thermal dose required to achieve cell death is dependent on tissue and cell type

muscle/fat → GI stuff → liver→ brain →kidneys

what is thermo-tolerance

→ if tissue is heated bellow 43 tissue becomes more tolerant to heat

• due to upregulation of heat shock proteins → increases resistance to thermal toxicity

• this effect is retained even after heating is stopped

what is thermal index

measure of potential tissue heating: $TI=\frac{P_o}{P_{degrees}}$

where:

• P_o: time averaged acoustic power (Calibrated based on measurements)

• P_degrees: power required to raise tissue temp by 1 degree → depends on frequency and tissue type

how are exposure limits set

thermal dose is cumulative → timing is kept as low as reasonably achievable (ALARA)

TI of different imaging modes?

1. B-mode: short pulses with low duty cycles and moderate power

2. Harmonic imaging: uses non-linear harmonic -> higher frequencies, also requires higher transmit power

3. M-mode imaging: the same line is fired repeatedly causing energy to concentrate in one region -> tissue doesn't get time to cool

4. Colour doppler: sends multiple pulses per line with longer pulse times and higher average power

5. Spectral doppler: continuous or near continuous transmission with high duty cycles

duty → how long a pulse is on

what is acoustic cavitation

formation and activity of gas bubble or vapour due to a medium being exposed to an acoustic wave

what are the types of cavitation

1. stable cavitation

2. inertial/transient cavitation

explain stable cavitation

1. acoustic pressure variation causes the bubble to oscillate indefinitely

   1. at low pressure → bubble expands

   2. at high pressure → bubble shrinks

2. stiffness of the bubble gas and inertia of the surrounding medium and bubble shell surface tension are balance

   1. stiffness of gas → prevents bubble from shrinking too much

   2. inertia of medium and surface tension from shell → prevents bubble from expanding too much and bursting

what frequency and bubble radius does stable cavitation occur

→ radius ($R_0$ ) > 10 micrometre

→ minnaert resonance frequency: $f_o=\frac{3}{R_o}$ in water and atmospheric pressure

what is inertial/transient cavitation

bubble grows and collapses violently

when and how does collapse occur in inertial/transient cavitation

caused by rectified diffusion:

• at high pressure phase: bubble is pushed together → SA decreases → high pressure inside the bubble → less diffusion of of gas out of the bubble

• at low pressure phase: gas in bubble is pulled apart → SA increases → less pressure inside the bubble → more diffusion of gas in the bubble → bubble grows

total pressure of fluid surrounding the bubble =$ambient~fluid~pressure(P_O)+acoustic~pressure (P)$

• low pressure phase of wave → P is -ve → if P>P_O then P_T<0 → fluid is in tension → bubble collapses

intertial/transient cavitation factors

1. frequency: bubble more likely to collapse at low frequency → wave spends more time in low pressure phase → bubble grows more rapidly

2. bubble size: larger bubble grow more slowly as there is less of a pressure difference

3. cavitation nuclei

4. acoustic pressure

cavitation outcomes (10)

what are the tissue damaging effects of cavitation

1. bulk heating:

→ bubble motion causes viscous heating

→ non-linear scattering of ultrasound → increases absorption

→ bubble collapse → broadband and shockwave emission

2. mechanical action: bubble collapse causes jetting and microstreaming

3. chemical action: collapse generates high heat forming free radicals and sonochemicals

lead to cell lysis due to membrane rupturing + structural/functional change to cell and DNA

what is bubble rebounding

after collapse an unconstrained (not near a boundary) bubble might rebound producing oscillations at the resonant frequency of the bubble

what is sonoluminescence

collapse causes high heat → heats gas → producing a light pulse of ionised plasma

what damage does jetting cause?

vessel distension

vessel invagination

vessel hemorrhaging

what is the mechanical index?

measure of potential for inertial cavitation

$$MI = \frac{P_r}{\sqrt{f}}$$

where:

• P_R: is the peak -ve pressure in Mpa

• f: centre frequency of the US wave

it is not time dependent as it is a threshold effect

what is the radiation effect

• ultrasound hits a boundary and gives up it’s momentum to the boundary

• for the wave to be reflected by the wall it must generate twice the force (to stop then to throw it back)

F^V=-<P_T\frac{DU}{Dt}>=-\frac{1}{c_0}\frac{dI_{av}}{dx} re:

• p_t: is the total acoustic pressure

• derivative of u: is particle acceleration

• <>: averaged over time

how is the radiation effect related to the heating effect

$-\frac{1}{c_0}\frac{dI_{av}}{dx} = \frac{Q}{c_o} = \frac{aP_A^{2}(x)}{\rho_oC_o²}$ → force is proportional to heat absorption

• force required to absorb = $\frac{P_T}{C_o}$

• force required to reflect = $\frac{2P_{T}}{C_{o}}$

how is radiation force measured?

• probe places inside a water tank with deionized and degassed water on top of a sensitive scale

• weight measured before and after the transducer is turned on

• F = m * g

also used to measure time averaged acoustic power for TI index

what are the uses of radiation effect

1. particle streaming

2. particle trapping: traps a particle between two high pressure areas?

what is used for mechanical therapeutic ultrasound

Low power low frequency US + addition of microbubbles

what are the uses of mechanical therapeutic US

1. Sonothrombolysis

2. bone healing

3. drug delivery + crossing BBB

4. neurostimulation

what type of US is used for thermo-mechanical therapy

high power US waves

what are the uses of thermo-mechanical therapy

1. lithotripsy

2. HIFU

3. histotripsy

4. haemostasis

Explain HIFU

High intensity focused ultrasound → acoustic energy is absorbed causing tissue to heat up + large pressure oscillation causes inertial cavitation

what type of US trasnducer is used for HIFU and why?

uses a large area transducer → high focusing gain

• produces very high heating at the focus

• regions above and below focus are unharmed → trackless therapy

what is the area of the HIFU lesion?

how is this limitation overcome?

→ produces a small 2×10mm focal lesion

→for large areas multiple sonications or a spiral scanning pattern is used

how does cavitation enhance the heating effect

inertial cavitation → mechanical tissue damage

1. bubble collapse releases broadband shockwaves → energy is absorbed and converted to heat

2. movement of the bubble shell → viscous heating

3. non-linear effects → energy is scattered → increased absorption

4. collapse leaves microbubble → scatters and traps US

control of cavitation vs thermal effects

thermal effects are much easier to control than cavitation as bubble collapse leads to various knock-on effects that are hard to quantify

→ sound is reflected back towards transducer → tadpole shaped lesions

→ produces larger legions in the same treatment time

energy vs average power

for the same average power:

→ low energy for longer time → produces smaller well controlled lesions

→ high energy shorter time → produces a larger lesion due to cavitation effect

how is HIFU treatment monitored?

using MR or US monitoring

MR:

• Gold standard

• allows for mapping temperature elevations and thermal dose

• treatment tries to avoid cavitation

US:

• low cost and portable

• high frame rate → image organ motion

• allows mapping of changes in backscatter and mechanical properties

• treatment tries to induce cavitation as it improves contrast

explain MR thermometry

measures the shift in proton-resonance frequency due to temp changes

resonant frequency is determined by local magnetic field:

$$\omega ~ (1-S)B_o$$

where:

• w: resonant frequency

• s: shielding constant

• B: magnetic flux

how does heating change proton-resonance frequency

heating → strength of hydrogen bonds in water weaken → protons donated from H to O is pulled back to the hydrogen → increased nucleus screening → resonant frequency decreases

how is proton-resonant frequency measured

shift is measured using gradient-recalled echo → change in frequency causes MR signal to accumulate phase difference over time proportional to temp induced PRF

$\Delta T=\frac{\Delta\phi}{\alpha\cdot\gamma\cdot T_{E}\cdot B_{o}}$

where:

• $\Delta\phi$ : phase difference

• a: thermal coefficient → depends on tissue

• y: gyromagnetic ratio → conversion of magnetic field to resonance frequency

• Te: echo time (time between excitation and signal readout)

• Bo: magnetic field strength

how is MR monitoring callibrated

1. low-power sonification is done to check focal position

2. corrections are made for misalignment and phase aberration

phase aberration → changes in phase not due to temperature ex: motion, scanner drift, field changes

what are the drawbacks of MR monitoring (5)

1. need MR compliant anaesthesia and US equipment

2. insensitive to bone and fat due to low water content

3. temp is given relative to the initial phase → assumed to be homogenous and at body temp

4. MR has low frame rate → depends on sequencing and voxel size

5. voxel size causes temperature to be averaged spatially which causes underestimation of temp change

explain ultrasound cavitation monitoring

requires cavitation effect → cannot monitor thermal only lesions

• coagulative necrosis and bubble formation changes US backscatter

• gas has low impedance → increased backscatter → hyperechoic region

• region fades a few minutes after HIFU exposure

explain US thermometry

• temperature changes sound speed → apparent shift in medium position

• thermal expansion of medium → produces actual shift in medium position

• causes shift in speckle pattern

$$\Delta T=k \frac{dD}{dx}$$

where:

• k: tissue dependent parameter → depends on thermal expansion coefficient and how sound speed changes with temp

• D:displacement

drawbacks with US monitoring

• B mode imaging: requires cavitation to see hyperechoic region → difficult to see tumour margin

• thermometry:

  • very sensitive to motion artefacts

  • requires knowledge of tissue dependent parameters

  • only works for low temp elevations as changes in sound speed is only linear over a limited range

patient comfort and procedure considerations

• lesion → painful and uncomfortable → require anaesthesia

  • general → abdominal ablation

  • regional → epidural for prostate

  • monitored anaesthesia → patient is conscious ex: brain ablation

• long treatment time

application of US therapy

1. prostate cancer → HIFU rectal or urethral probe at 4MHz → MR or US

2. uterine fibroid → HIFU 1MHz → MR or US

3. transcranial → HIFU 0.6MHz → MR

cosmetic:

4. ultrasonic liposuction → low frequency US used for cavitation of fat → lipolysis

5. ultratherapy → ablation of superficial musculoaponeurotic system → wound healing

brain and drug delivery

5. neuromodulation → 250 - 500KHz low frequency and intensity US → alters ion channel gating

6. sonoporation + BBB→ cavitation, jetting and microstreaming alter cell membranes → allows drug filled microbubble to enter cell

7. sonotrhombolysis → clot busting

8. extracorporeal shock wave lithotrupsy → short high pressure pulses break up kidney stones

9. bone healing:

10. histotripsy → large shockwave generate bubbles → bubbles have lower impedance than tissue → acoustic reflection → cavitation and generation of large amount of microbubbles → breaks up tissue