Ultrasound Physics formulas

Intensity

concintration of energy in sound

Power/Area (=amplitued2)

watts/cm2

Wavelength

length of one cycle

W= c/f

mm, m

Propagation Speed

rate at which sound travels though a medium

Distance/ Time

Pulse Duration

time from the start of a pulse to the end of the same pulse

PD= #cycles x Period

usec

Spacial Pulse Length

Distance that occupies in space from start to end of one cycle

SPL= #cycles x wavelength

Pulse repition period

Time from start of one pulse to the next pulse

PRD = depth x 13

(usec)

Pulse repition fequency

# of PULSES that occur in one sec

PRF = 77,000 / imaging depth

Hz

Duty Factor

% of time a sound is transmitting

PD/PRP x 100

Beam uniformity Coefficient

SP/SA

rank intensities

SPTP-Imax-SPPA-SPTA-SATA

SPTP-SATP-SAPA-SATA

Attenuation

weakening of sound as it propigates thru medium

dB= 10 x log( Pf/Pi)

relection, scattering, absorption

logarithms

power to which 10 must be raised to achive the disired #

Log(y)=x

Decibel

measure of attenuation or amplification based on logarithms

dB= 10 x log( Pf/Pi)

f-final i-initial

log 2 = 0.3

log0.5= -.3

Attenuation Coefficient

1/2 the Frequency

Total Attenuation

Toatal Att. = Atten Coef. X path length

Half-Value Layer Thickness

distance sound travels to reduce the Intensity 1/2 is original

HVL= 3/ Atten. coeff.

normal Incidence

perpendicular

orthogonal

rt angle

90*

Acoustic Impedance

resistance to sound in a medium

Z = p x c

REFELCTION DEPENDS ON

Intensity Reflection Coefficiant

IRC% = [Z1 -Z2 / Z1 +Z2]2 x100

reflection depends on Acoustic Impedance

Intensity Transmmision coefficiant

ITC% = 1- IRC

ITC% = ( Trans Intensity/ Insident Intensity) x100

Rafraction

Change in direction of the sound beam

MUST have oblique incidence and different propagation speed (c)

SNELLS LAW [(Ci/Ct) / (SINi/SINt)]

Depth

Depth= (1.54 (mm/usec) x Time) / 2

Depth= .77/time

Axial Resolution Smaller is better

measures systems ability to dispay 2 strutures along path of beam

SPL / 2

improves with less ringing & increased frequency

PZT

1/2 wavelength

generates sound waves

recieves echos

matching Layer

1/4 wavelength

minimizes acoustic impedance mismach

reduces reverberation (ditructive interferance)

Backing Layer (damping)

reduces ringing (vibration)

decreases pulse duration pulse length

improved axial resolution

decreases sensitivity

increases bandwidth

low q factor

(acoustic impedance similar to PZT)

Quality Factor

Center frequency/ bandwidth

Transducer Frequency

F = C crystal / (2 x THICKNESS crystal)

Resonant freqency

RF = single frequency

single pure freqency ( allowd to ring)

Near Zone Length

NZL=DIAMETER 2 x original FREQUENCY/6

Lateral resolution

ability to separate 2 echos perpendicular to the beam

Lateral Resolution = Bream Width

LAERAL RESOLUTION synonyms

LATAS

lateral

angular

transveres

azimuthal

side by side

AXIAL RESOLUTION synonyms

LARRD

logitudinal

axial

range

radial

depth

A-Mode

strong amplitude echo strong spike

X-deph

Y-amplitude

B-Mode

Brightness of dots determined dy the amplitude of reflector

X- Depth

Y- none width of scan

Z- amplitude (brightness)

M-Mode

refectors change in location in time

X- change in time

Y- depth

Spatial pulse length

SPL

# of cycles x Wavelengh

Lateral Resolution synonym

Angular, Transverse, Amzimuthal

--LATA--

Q-factor

(Quality Factor)

QF=(Center f)/Bandwith

Bandwidth

BW = Max f - Min f

Transducer Frequency

PW

Tƒ = (C material)/(2 x thickness)

Transducer Frequency

CW

Elc. Voltage = Tƒ

Matching layer thickness

¼ wavelength

Active Element Thickness

½ wavelength

Focal Depth

(focal length)

(Near zone length

(diamter² x ƒ )/61.6

Or

diameter²/(40 x λ)

Angle Divergence

1.85/(diameter x f)

Or

(1.2 x λ)/diameter

Distance to the boundary

(go return time)

(go return time x speed)/2

or

DTB in soft tissue = T x 0.77

Hygens' Principle

A large active element my my be thought of as a million tiny , distinct sound sources ( Hygens' source)and create Hygens' wavelets w/ a V shape)

Doppler

X- Time

Y - Fequency shift

Frame Rate

Hz

define & determined dy

Sonographer can control

imaging depth & # of pulses(speed of sound)

The ability to create numerous frames each second

Frame Time

T frame = # pulses x PRP

Temporal Resolution

Hz or per sec

define & determined dy

Determined:Frame rate

Accuracy in time

Ability to precisely position moving structures from instant to instant

Mechanical index

(Peak negative pressure)/√ƒ

Doppler Shift

(Doppler frequency)

20-20khz

(Audible

DS = (2 x speed of blood x Tf x cosᶿ)/(c)

Or

DF = ƒR - ƒE

Doppler Shift

define & determined dy

Difference btw received and transmitted frequency

Greater velocity = greater shift

Velocity (measured)

V(m) = true velocity x cos (angle)

0° or 180° = 1 cosine

60° = .5 cosine

90° = 0 cosine

Pressure Gradient

PG = flow x resistance

Measured Pressure

MP = circulatory pressure + hydrostatic pressure

Venous Pressure inhale

Diaphragm - down

↓ Thoracic

↑ arm flow

↓Flow legs

↑abdomen

↑Vena cava

Venous Pressure exhale

Diaphragm - up

↑ Thoracic

↓ arm flow

↑Flow legs

↓abdomen

↓Vena cava

Resistivity Index

RI =(Vmax-Vmin)/(V max)

Pulsatility Index

PI = (V max⁡〖- V min〗)/(V mean)

senstivity

The ability of a test to predict desease

Sensitivity = true positives / TP = FN

Accuracy

% of time the test is correct

Accuracy = TP + TN /All Test

Negative predictive value (NPV)

% of time the test is correct when perdicting absents of a disease

NPV = TN / TN =FN

Specificity

Ability of a test to predict absence of disease

Specificity = true negatives / TN + FP

positive predictive value (PPV)

% of time the test is correct when it perdicts % of disease

PPV = TP / TP+FP