University of Wisconsin Diagnostic Imaging Research

Lecture 1: Introduction (1/2) – History, basic principles, modalities

Class consists of:

1) Deterministic Studies - distortion

- impulse response

- transfer functions

All modalities are non-linear and space variant to some degree.

Approximations are made to yield a linear, space-invariant system.

2) Stochastic StudiesSNR (signal to noise ratio) of the resultant image

- mean and variance

Course Objectives

• Learn basics of 2D to n-dimensional system theory and signal processing– Emphasis on duals between space and frequency

domain– Emphasis on intuitive understanding

• Understand underlying physics of medical imaging modalities

• Study the deterministic and stochastic descriptions of medical imaging systems– Theory is applicable beyond medical imaging

Prerequisites and Postrequisites

• System Theory– ECE 330, BME/MP 573

• Statistics Helpful but Not Required– Mean and variance of stochastic processes

– ECE 331, BME/MP 574, ECE 730

• Other Courses• Microscopy of Life

• BME 568/ MP 568 MRI ( less math)

Nov. 1895 – Announces X-ray discovery

Jan. 13, 1896 – Images needle in patient’s hand

– X-ray used presurgically

1901 – Receives first Nobel Prize in Physics

– Given for discovery and use of X-rays.

Wilhelm Röntgen, Wurtzburg

Radiograph of the hand of Röntgen’s wife, 1895.

Röntgen detected: • No reflection• No refraction• Unresponsive to mirrors or lenses

His conclusions:

• X-rays are not an EM wave

• Dominated by corpuscular behavior

Röntgen’s Setup

Projection X-Ray

Disadvantage: Depth information lost Advantage: Cheap, simple

)z(f),,(μ densityelectron , zyx attenuation coefficient

Measures line integrals of attenuation )dlμ(od I I x,y,ze

Film shows intensity as a negative ( dark areas, high x-ray detection

Sagittal Coronal

Early Developments

• Intensifying agents, contrast agents all developed within several years.

• Creativity of physicians resulted in significant improvements to imaging.

- found ways to selectively opacify regions of interest

- agents administered orally, intraveneously, or via catheter

Later DevelopmentsMore recently, physicists and engineers have initiated new

developments in technology, rather than physicians.1940’s, 1950’s

Background laid for ultrasound and nuclear medicine1960’s

Revolution in imaging – ultrasound and nuclear medicine1970’s

CT (Computerized Tomography) - true 3D imaging

(instead of three dimensions projected down to two)

1980’s MRI (Magnetic Resonance Imaging)

PET ( Positron Emission Tomography)2000’s

PET/ CT

Computerized Tomography (CT)

1972Hounsfield announces findings at British Institute of Radiology1979 Hounsfield, Cormack receive Nobel Prize in Medicine(CT images computed to actually display attenuation coefficient x,y

Important Precursors:1917 Radon: Characterized an image by its projections1961 Oldendorf: Rotated patient instead of gantry

),(),(ID yxμyx Result:

First Generation CT Scanner

Acquire a projection (X-ray)Translate x-ray pencil beam and detector across body and record output

Rotate to next angleRepeat translation

Assemble all the projections.

Reconstruction from Back Projection

1.Filter each projection to account for sampling data on polar grid 2. Smear back along the “line integrals” that were calculated by the detector.

Modern CT Scanner

From Webb, Physics of Medical Imaging

Computerized Tomography (CT), continued

Early CT Image Current technology

Exhalation

Inhalation

Nuclear Medicine- Grew out of the nuclear reactor research of World War II- Discovery of medically useful radioactive isotopes1948 Ansell and Rotblat: Point by point imaging of thyroid1952 Anger: First electronic gamma camera

a) Radioactive tracer is selectively taken up by organ of interest

b) Source is thus inside body!

c) This imaging system measures function (physiology)

rather than anatomy.

Nuclear Medicine, continuedVery specific in imaging physiological function - metabolism

- thyroid function- lung ventilation: inhale agent

Advantage: Direct display of disease process.Disadvantage: Poor image quality (~ 1 cm resolution)

Why is resolution so poor?Very small concentrations of agent used for safety.

- source within bodyQuantum limited:

CT 109 photons/pixelNuclear ~100 photons/pixel

Tomographic systems: SPECT: single photon emission computerized tomography

PET: positron emission tomography

Combined CT / PET Imaging

Necessary Probe Properties

Probe can be internal or external.

Requirements:

a) Wavelength must be short enough for adequate resolution.

bone fractures, small vessels < 1 mm

large lesions < 1 cm

b) Body should be semi-transparent to the probe.

transmission > 10-1 - results in contrast problems

transmission < 10 -3 - results in SNR problems

λ > 10 cm - results in poor resolution

λ < .01Å - negligible attenuation

Standard X-rays: .01 Å < λ < .5 Å

corresponding to ~ 25 kev to 1.2 Mev per photon

Necessary Probe Properties: Transmission vs. λ

Graph: Medical Imaging Systems Macovski, 1983

Probe properties of different modalities

NMR

• Nuclear magnetic moment ( spin)

• Makes each spatial area produce its own signal

• Process and decode

Ultrasound

• Not EM energy

• Diffraction limits resolution

• resolution proportional to λ