mathematics

Functional ultrasound imaging

Functional ultrasound imaging is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Functional ultrasound imaging rather than just read about it. In short: Functional ultrasound imaging (fUS or fUSI) is a medical ultrasound imaging technique for detecting or measuring changes in neural activities or metabolism, such as brain activity loci, typically through measuring hemodynamic (blood flow) changes. It is an extension of Doppler ultrasonography.

Key takeaways

Functional ultrasound imaging belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Functional ultrasound imaging to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Functional ultrasound imaging from memory before moving on to harder problems.

Reference excerpt

Functional ultrasound imaging (fUS or fUSI) is a medical ultrasound imaging technique for detecting or measuring changes in neural activities or metabolism, such as brain activity loci, typically through measuring hemodynamic (blood flow) changes. It is an extension of Doppler ultrasonography.

Background

Brain activation can be directly measured by imaging electrical activity of neurons using voltage-sensitive dyes, calcium imaging, electroencephalography, or magnetoencephalography. It can also be indirectly measured hemodynamically, that is, by detecting changes in blood flow in the neurovascular systems through functional magnetic resonance imaging (fMRI), positron emission tomography (PET), Functional near-infrared spectroscopy (fNIRS), or Doppler ultrasonography, etc. Optics-based methods generally provide the highest spatial and temporal resolutions; however, due to scattering, they are limited to measuring regions close to the surface. Thus, they are often used on animal models after partially removing or thinning the skull to allow light to penetrate into brain tissue. fMRI and PET, which measure the blood-oxygen level dependent (BOLD) signal, were the only techniques capable of imaging brain activation in depth. BOLD signal increases when neuronal activation exceeds oxygen consumption, where blood flow increases significantly, resulting in cerebral blood volume (CBV) changes. This relationship between neuronal activity and blood flow is called neurovascular coupling. In fact, in-depth imaging of cerebral hemodynamic responses by fMRI, being noninvasive, paved the way for major discoveries in neurosciences in the early stage, and is applicable on humans. However, fMRI also suffers limitations. First, the cost and size of MRI machines can be prohibitive. Second, for fMRI to achieve a high spatial resolution necessarily decreases its time resolution and/or signal-noise ratio. As a result, it is hard to image fine spatial details of transient events such as epilepsy. Finally, fMRI is not appropriate for all clinical applications. For example, fMRI is rarely performed on infants, because infants do not stay still inside MRI machines. Like fMRI, Doppler-based functional ultrasound is based on the neurovascular coupling and are thus limited by the spatiotemporal features of neurovascular coupling, specifically cerebral blood volume (CBV) changes. CBV is a pertinent parameter for functional imaging that is already used by other modalities such as intrinsic optical imaging or CBV-weighted fMRI. The spatiotemporal extent of CBV response was extensively studied. The spatial resolution of sensory-evoked CBV response can go down to cortical column (~100 μm). Temporally, the CBV impulse response function was measured to typically start at ~0.3 s and peak at ~1 s in response to ultrashort stimuli (300μs), which is much slower than the underlying electrical activity.

Conventional Doppler based approaches Hemodynamic changes in the brain are often used as a surrogate indicator of neuronal activity to map the loci of brain activity. Major part of the hemodynamic response occurs in small vessels; however, conventional Doppler ultrasound is not sensitive enough to detect the blood flow in such small vessels.

Functional transcranial Doppler (fTCD) Ultrasound Doppler imaging can be used to obtain basic functional measurements of brain activity using blood flow. In functional transcranial Doppler sonography, a low frequency (1-3 MHz) transducer is used through the temporal bone window with a conventional pulse Doppler mode to estimate blood flow at a single focal location. The temporal profile of blood velocity is usually acquired in main large arteries such as the middle cerebral artery (MCA). The peak velocity is compared between rest and task conditions or between right and left sides when studying lateralization. The temporal window is the thinnest lateral area of the skull, and it is mostly hairless. It is often used for fTCD.

Power Doppler Power Doppler is a Doppler sequence that measures the ultrasonic energy backscattered from red blood cells in each pixel of the image. It provides no information on blood velocity but is proportional to blood volume within the pixel. However, conventional power Doppler imaging lacks sensitivity to detect small arterioles/venules and thus is unable to provide local neurofunctional information through neurovascular coupling.

Ultrasensitive Doppler imaging Functional ultrasound imaging was pioneered at ESPCI by Mickael Tanter's team following work on ultrafast imaging and ultrafast Doppler.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Functional ultrasound imaging

Start with the simplest possible case. Write down what Functional ultrasound imaging claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Functional ultrasound imaging before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Functional ultrasound imaging ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Functional ultrasound imaging

In research: Functional ultrasound imaging appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Functional ultrasound imaging in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Functional ultrasound imaging is common in secondary-school and first-year university syllabi. It links to neighbouring topics Magnetic resonance imaging, Ultrasound, so understanding it makes those chapters shorter.
In everyday life: Look for Functional ultrasound imaging outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Functional ultrasound imaging in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Functional ultrasound imaging means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Functional ultrasound imaging out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Functional ultrasound imaging in simple terms?

Why does Functional ultrasound imaging matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Functional ultrasound imaging?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Functional ultrasound imaging.