Bioimaging Comprehensive Notes

Intro to Biomedical Imaging

Introduction to Biomedical Imaging

Biomedical imaging relies on contrast, which is the difference between dark and bright levels, reflecting the ability to distinguish image attributes. Contrast arises from image recording methods (e.g., X-ray dose) and image processing techniques. In biomedical applications, contrast is the difference in lightness between tissues intended for discrimination. The imaging equivalent of the signal-to-noise ratio (SNR) is the contrast-to-noise ratio (CNR).

Modern Medical Imaging Systems

Modern medical imaging systems involve an energy source, interaction with the body, a detector, electronics, computer control, digital conversion, image formation, digital processing, digital storage, a human interface, and electronic control. The energy sources can be visible light, X-rays, radio frequencies, gamma rays, or mechanical waves (ultrasound).

Types of Energy Sources

Visible light is primarily used outside the body or in body cavities for dermatology (imaging, Optical Coherence Tomography), gastroenterology & obstetrics (endoscopy & OCT), and pathology (microscopy). Radiography uses other regions of the electromagnetic spectrum, such as X-rays (mammography, CT), radio frequencies (MRI), and gamma rays (nuclear medicine). Mechanical waves (ultrasound) are also employed.

Light Interaction with Tissue

Light interacting with tissue results in absorption (reduced intensity) and scattering (change of angle). While interaction is necessary to visualize anything, scattering and absorption limit penetration and resolution, except for gamma rays in nuclear medicine, which pass through the body. Nuclear imaging gathers information about the location of the energy source.

Bioimaging Techniques

Several bioimaging techniques exist, including:

RX (X-Ray Imaging).
CT (Computed Tomography).
PET (Positron Emission Tomography).
MR (Magnetic Resonance Imaging).
US (Ultrasound Imaging).
EEG/MEG/fNIRS (brain imaging in Neuroscience).

Biomedical Images

Biomedical images can be 2D images with $N \times M$ pixels or 3D volumes with $K \times N \times M$ voxels. Theoretically, N, M, and K can be infinitely large, but as resolution increases, contrast and sensitivity decrease. Imaging involves a compromise between resolution and contrast, aiming to maximize a cost function that reflects the medical utility of the image.

SNR and CNR

To obtain valuable information from signals, a good SNR (Signal to Noise Ratio) is needed. SNR is a measure of the precision of a measure, defined as $SNR = S/\sigma$ , where S is the signal and $\sigma$ is the standard deviation. In imaging, signals are detected relative to different tissues. High SNR alone is insufficient if there is low or zero CNR since the signals become non-distinguishable. CNR is a measure of contrast between two signals, $S1$ and $S2$ , defined as $CNR = (S1-S2)/ \sigma$ .

CNR Optimization

Optimizing contrast involves selecting experimental parameters to maximize contrast between $S1$ and $S2$ . Trial and error is not ideal; models can predict the effects of changing parameters. For a signal $S$ that is a function of $k$ and $t$ , where $k$ is a tissue property and $t$ is an experimental parameter, the optimization involves evaluating $\frac{dS}{dk}$ , which represents how S changes due to k, and finding $t0$ where $\frac{dS}{dk}$ is maximized.

CNR Optimization Example

If the signal follows exponential behavior, then the signal is: $S(t,k) = S0 e^{-kt}$ . The derivative for $k$ is: $\frac{dS}{dk} = -t S0 e^{-kt}$ . The optimal $t$ that maximizes $\frac{dS}{dk}$ is found where the derivative equals zero.

CNR Optimization - Optimal t

The optimal $t$ is $t0 = \frac{1}{k}$ . $t0$ indicates when the measurement needs to be taken with respect to tissue characteristics. In reality, $t_0$ has a wide margin of variation for CNR values within 10-20% of the maximum value.

Bioimaging – Collaboration Across Fields

Bioimaging is highly multidisciplinary, involving life science, physics, maths, chemistry, quantum mechanics, classical mechanics, thermodynamics, neuroscience, mechanical/electrical/biomedical engineering, and medicine.

Bioimaging Techniques - Characteristics

Each imaging modality (RX, CT, PET, MR, US, EEG/MEG/fNIRS) has different characteristics in terms of portability, ease of use/interpretation, sensitivity, and price. Each has pros and cons depending on the application. The right modality depends on the application; there is no one-size-fits-all solution.

Image modalities differ in their energy source and how the body changes this energy.

Ultrasounds

Ultrasound is used for localization in animals and human-made systems (bats, whales, sonar, ultrasound scanners). Sounds above 20kHz are ultrasounds, above audible sounds.

Ultrasounds - Mechanical Waves

Ultrasounds are mechanical waves that travel in a body and are reflected at interfaces between different tissues. Reflected waves (echoes) reconstruct a 2D image based on the timing and intensity of the echoes.

Ultrasounds and Tissues

Ultrasound waves interact with matter in various ways:

Attenuation: The wave travels across matter but attenuates with distance following an exponential law: $I(x) = I_0 e^{-\alpha x}$ , where $\alpha$ is the attenuation coefficient in [dB/(cm MHz)]. For example, if $\alpha \approx 0.5$ dB/(cm MHz), a 6MHz signal attenuates by 3dB per cm.

Attenuation coefficients ($\alpha$) in different materials:

Water: 0.002
Blood: 0.2
Tissue: 0.7
Bone: 15
Lungs: 40

Ultrasound Waves in Tissues - Interactions

Ultrasound waves interact with matter through:

Refraction: Waves change direction when encountering tissue.
Scatter: Dispersion in all directions.
Reflection: Waves travel back to the origin; this is used to obtain images.
Other effects reduce image quality.

Ultrasounds - Echoes

Echoes depend on the mechanical impedance of a material, defined as $Z = \rho c$ (density and elastic stiffness), measured in rayls [kg/m^2s]. When an ultrasound wave encounters the interface between two tissues with different Z, the intensity of reflected energy is: $I{ref} = I0 RI$ , where RI is the reflection coefficient, $RI = (\frac{Z1 - Z2}{Z1 + Z2})^2$ .

Ultrasounds - Basic Principles

The emitter produces an ultrasound with a time duration of 1-5 µs, a multiple of the cycle 1/f, where f is the frequency of the ultrasound. A sensor measures timing and intensity of the echoes. Knowing the speed of propagation, an image is reconstructed. Diagnostic imaging uses frequencies in the range 1MHz – 20MHz.

Ultrasounds - Distance Calculation

Knowing the delay and intensity of the echo, the distance (d) between the source and the threshold between Tissue 1 and Tissue 2 can be calculated: $d = v * t / 2$ , where v is the propagation speed of the ultrasound wave, calculated as $v = \lambda f$ , where $\lambda$ is the wavelength. The values of $v$ are:

v = 330 m/s = 0.33 mm/µs in air.
v = 1.45 – 1.6 mm/µs in most tissues (it increases with density; e.g., in bones, it is 4 mm/µs).

Ultrasounds - Resolution

In tissues, multiple interfaces exist at different levels. Ultrasound resolution indicates the minimal spatial distance between two tissues that can be discriminated. Wavelength $\lambda$ determines the resolution. Since f is fixed, the length of the impulse $\Delta t$ is a multiple of $\frac{1}{f}$ , thus a multiple of $\lambda$ . $\Delta t \propto \lambda$ .

Ultrasounds - Object Separation

For two objects, O1 and O2, subject to ultrasound waves, if the objects are distant enough, two distinct echoes are observed, allowing reconstruction of their positions. The temporal distance $\Delta T$ between the echoes depends on $\Delta x$ and $v$ . $\Delta T = T2 - T1 = \frac{2\Delta x}{v}$ .

Ultrasounds - Temporal Separation

The temporal separation $\Delta T$ between echoes needs to originate from objects at a distance of at least $\frac{\lambda}{2}$ , otherwise the echoes will overlap. Thus, $\Delta T \propto \lambda$ is linked to the minimal discernible distance.

Ultrasounds - Compromises

Resolution depends on $\lambda$ , so resolution increases with frequency f since $\lambda = \frac{v}{f}$ . Higher frequency impulses are favorable, but penetration decreases as f increases. High frequencies (> 12 MHz) allow for excellent spatial resolution but do not have great penetration. Low frequencies (around 2-3 MHz) have good penetration but suboptimal spatial resolution. $I(x) = I_0 e^{-kxf}$ .

Doppler Ultrasound

The Doppler effect measures the motion (speed + direction) of blood. Color is superimposed on a regular ultrasound image, with one direction indicated in red and the other in blue.

Radiography

A pulse of X-rays is passed through the body, with different body parts absorbing more or less. Transmission projection imaging is used. Transmission involves the object being between the source and detector, with X-rays passing through. Projection captures the cumulative effects of the body along a line between the source and detector.

Radiography - Applications and Risks

Radiography is used in diagnosing broken bones, lung cancer, and cardiovascular disorders. It involves ionizing radiation, which is energetic enough to break chemical bonds in DNA and potentially cause cancer, so the dose must be carefully limited. Fluoroscopy, mammography, and CT also use X-rays.

Radiography: Fluoroscopy

Fluoroscopy consists of video made up of frames, each of which is an X-ray. It is used for positioning catheters in arteries, visualizing contrast agents in the GI tract, and certain invasive procedures requiring real-time feedback. It provides X-ray movies of anatomic motion (e.g., heart or oesophagus).

Radiography: Mammography

Mammography involves radiography of the breast. To achieve higher contrast, it uses lower energy (frequency) X-ray pulses. Mostly uses digital detectors now. Some tomographic techniques are used to help image a single slice and reject out-of-focus light. It is used for screening and diagnosis of breast cancer.

Radiography: Computed Tomography (CT)

Clinically available since the 1970s, CT takes X-rays from a large number of angles and uses a computer to estimate a 3D distribution. Slices of the 3D image can be rendered. It is used to find the extent of trauma, location and type of tumors, ruptured disks, hematomas, aneurysms, etc.

CT - Impact and Usage

The development of CT changed the practice of medicine and reduced the need for exploratory surgery. Modern CTs capture 800 images in less than 5 seconds, typically with 0.5 – 0.62 mm thick slices. Injecting iodinated contrast agents allows functional assessment of various organs. It is a very common modality, with about 60 million CT scans per year in the USA.

Magnetic Resonance Imaging (MRI)

MRI utilizes radio frequency (non-ionizing). Drawbacks include slow acquisition (motion blur), strong magnets (complicated siting), and noisy confined spaces (claustrophobia). It is based upon nuclear magnetic resonance. Protons in hydrogen (water) can absorb & emit RF energy in an external magnetic field. Different tissues, water, and fat all have different properties, providing contrast. Magnetic field gradients localize the signal in space.

MRI - Steps

The energy emitted (in the form of a radio-frequency wave) during relaxation is used to derive the image via Fourier Transform.

MRI - Tomographic Technique

MRI is a tomographic technique, just like CT. It is a competing technique for many applications. Some specialized high-speed applications include MR angiography (blood flow in arteries) and functional MR (blood flow in the brain). MR Spectroscopy evaluates the chemical composition of a specific location in the body by suppressing the water contribution.

Nuclear Imaging - Mechanism

The patient swallows, is injected with, or inhales a substance containing a radioactive isotope. After waiting for the material to distribute naturally, a radiation detector examines the distribution of the isotope. The isotope emits X-rays / gamma rays. This is functional imaging, telling us about how the body is working rather than the distribution of tissues, etc. Pathologies appear as unusual hot/cold spots. It is used to find tumors, blood cell disorders, organ function, and aneurysms.

Nuclear Imaging: Planar Imaging

Planar imaging produces projection images, like X-rays. Each point on the image represents all activity along a line through the patient. A whole-body bone scan can show a number of features, e.g., increased uptake at the right knee patella, probably showing degenerative changes.

Nuclear Imaging: Single Photon Emission Computed Tomography (SPECT)

SPECT is to nuclear imaging as CT is to radiography. A nuclear camera records X-ray or gamma ray emissions from multiple angles, and a 3D image is reconstructed. It has similar diagnostic functions to nuclear medicine planar imaging, but 3D can be useful in some situations.

Nuclear Imaging: Positron Emission Tomography (PET)

A positron is an anti-electron. They are emitted by, e.g., fluorine-18 and oxygen-15. Those radioisotopes are incorporated into metabolically relevant compounds. Positrons and electrons annihilate, releasing energy (pairs of gamma ray photons), which are detected by rings of scanners.

Image Fusion: Combined Modalities

Image fusion combines modalities like CT and PET to better define tumor margins and identify metabolically active tumor regions. PET-MRI can also be used, combining the anatomical detail of MRI with the functional information of PET.