Dr. M. Smith,S. M. I. L. E. Hardware / Software Co-design Laboratory,

Dept. of Electrical and Computer Engineering,Dept. of Radiology, University of Calgary

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Reason for doing the research Brief discussion of what “everybody else

was doing”. Description of the “little project we planned

to do” Our simulation study and all the problems

that arose. Why so many problems? What we are currently doing (to solve the

issue).

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Start of World War II with many men conscripted and being readied to be sent over-seas.

After basic training, the men parade through the town (in front of their kin-folk) prior to embarking on a train.

Mother (wife) and son watch the parade. Son – wanting to believe in the perfection of

his father◦ “Look, Mother! Father is the only one in step.

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Sign on my desk◦ given to me by one of my graduate students

It’s difficult being perfect Buts somebody’s got to do it!

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Stroke --the third leading cause of death and the leading cause of adult disability.

Goal of therapeutic strategies is to minimize the progression of tissue damage in the acute phase of the disease.

Methods to rapidly assess acute stroke in individual patients are highly desirable.

85% of the stroke cases are ischemic strokes due to a reduction of the blood supply by the presence of a clot in a feeding artery (adapted from www.lanacion.com).

HEMORRHAGIC ISCHEMIC

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Track a bolus of magnetic material through the brain (arterial and tissue signals)

Convert changes in “ MR signal intensity” to “concentration curves” using the “magic” log. Formula

The technology of any sufficiently advanced civilization looks like magic. – Arthur C. Clarke

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Need to deconvolve “tissue signal” ( cVOI(t) ) by “arterial signal” ( cAIF(t) ) to get “residue function” ( R(t) ).◦ Peak of residue function provides estimate of blood flow (CBF)

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Impact of delay

Impact of Dispersion

a: CBF map. b: Signal intensity time A clear delay of 2 sec in the

arrival of the bolus can be seen in the right side.

The presence of such delay (and possibly dispersion) introduced a significant underestimation in the CBF map.

The measured right to left ratio in the CBF map is 0.55 due to delay

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IMPACT OF NOISE FILTERING – LOSS OF SIGNAL

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Deconvolution causes an enhancement of high frequency noise components.

To stabilize the algorithm, you must apply a filter to reduce the noise.

However, the noise filter also reduces the high frequency signal components – so maximum of residue function is reduced – CBF appears smaller

TIME:AMPLITUDELOSS

HIGHFREQUENCYLOSS

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Step 1 - “Stand on the shoulders of giants” Repeat what everybody else is doing so we can check we “understand” the problem. ◦ Generate some artificial data (tissue and AIF)◦ Add some noise◦ Do deconvolution (standard approach) to get

residue function.◦ Noise filtering removes “high frequency

components◦ Measure CBF as a function of delay / dispersion

and tissue type

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Generate some artificial data (tissue and AIF) Add some noise Do deconvolution (standard approach) to get residue

function. Noise filtering removes “high frequency components MODEL the low frequency signal components

and extrapolate those signals into “high” frequencies

Compare “our CBF” to “their CBF”

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Use known low frequency data to generate high frequency data

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Mathematical formula for constructing arterial signal is given

“Nothing” about how to construct “tissue signal” – we suspect that “either we are missing something obvious (out-of step)” or else construction done by “numerical convolution” rather than algebraic.

“Nothing” specific about how to add noise to get “realistic data”, although some people mention adding “gaussian white noise” to the concentration

Every body discusses low and high “signal to noise ratio” – but nobody says how to measure it.

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Generating data by “convolution” is a delicate process.

If the data is not sampled “fast enough” then “Nyquist” is not satisfied.◦ MR DSC data sampled at

2.25 seconds If Nyquist not satisfied

then “data” gets distorted at high frequencies (aliasing).

All CBF results “are wrong”, but by “how much” and “when”?

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Would “everybody else” not doing things the proper “engineer way” impact on our “new” method done the “correct way”?

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Need to deconvolve “tissue signal” ( cVOI(t) ) by “arterial signal” ( cAIF(t) ) to get “residue function”.◦ Peak of arterial signal provides estimate of blood flow (CBF)

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We would expect that frequency domain deconvolution to give same results as time domain deconvolution – except for fine detail

HOWEVER literature is saying “MUCH BETTER RESULTS” are being obtained with SVD than with FT – does not make engineering sense – unless “something wonderful is happening”

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The MR signal (upper picture) has “gaussian noise” on it (unless very small in intensity and then the noise characteristics change)

This means that adding noise to the concentration curves does not model “clinical data”

Added noise

Calculated noise

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True SNR of concentration signal changes with MR signal intensity – specific “best” conditions

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Consequences – we believe that everybody is “setting the image parameters” the wrong way

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Did not cause much “controversy” Other researchers have now demonstrated

that our predictions are to be found in practice.◦ Optimize SNR through TE changes and have

different MR sequence for tissue and AIF signals

Largely ignored◦ Difficult to get the “correct” imaging parameters.◦ Takes too long to get “an DSC image sequence” ◦ “Tissue” signal have low intensity, therefore people

“push arterial signals” into an unsatisfactory “high intensity” region to compensate.

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We have the noise simulation problems understood

Lets try using frequency domain deconvolution (about which we have much knowledge) rather than SVD – time domain deconvolution

As engineers we expect Equivalent results between SVD and FT

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FT shows “no time delay effects” that are so evident with SVD. We are really out of step

FT deconvolution

SVD deconvolution

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Noise Enhancement during deconvolution

SVD deconvolution eigen-valuethresholding causes “band pass” filtering

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The delay sensitivity of SVD deconvolution is “breaking” the deconvolution rules◦ BUT the SVD is a VERY well-known algorithm and

NOBODY has reported problems like this in 50 years

The noise effect shows that the SVD filtering is a series of band pass filters.◦ Band pass characteristics controlled by

“eigenvalues” which are identical to the (ordered) Fourier transform coefficients of the arterial function

◦ This was found empirically by us, but turns out to be well-known effect from radar studies in 1991

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Consider convolving (or deconvolving) two signals

LINEARITY PROPERTY: ◦ Double the amplitude of one input – doubles output

amplitude – no change in shape

POSITION INDEPENDENT:◦ Shift position of input by amount x. Output will shift

position by amount x – no change in shape

Theory indicates that a “proper” deconvolution algorithm should be “delay independent”

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Actually neither SVD nor FT have ever really worked in one sense – but nobody says it.

Deconvolution works by deconvolving the “effect” by its “cause” – and a “cause” signal always arrive before the “effect.◦ The “tissue” is not the “effect” that is produced by

the “arterial” signal, but is the effect of the “injection into the arm.

◦ Thus it is physiologically possible for the tissue “effect” signal to arrive BEFORE the “proxy” arterial “cause” signal.

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“UNWRAPPED” HIGH TIME SIGNAL

The FT deconvolution algorithm has “cyclic” properties

In the presence of a delay, any “negative time residue function signals” are wrapped around (aliased) to become a false “high time signal”.

However, PROVIDED THERE ARE NO TRUE HIGH TIME SIGNALS, we can unwrap and get “correct answer” .

NEGATIVE POSITIVE TIME TIME

SVD and FT deconvolution have different properties

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The SVD deconvolution algorithm was not being implemented with “cyclic” properties

No negative time signals are allowed.

But that “energy” must go somewhere – and it goes into boosting the early residue function peak

For a zero delay -- This boost counterbalances the signal loss from noise filtering

SVD acts as “the better algorithm” when incorrectly implemented

However, the “improvement” is very unstable

NO NEGATIVESIGNAL ALLOWED

“MISPLACED”NEGATIVE ENERGY

SVD and FT deconvolution have different properties

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First of all reviewers would not accept that◦ There was an effect or◦ that our theory was valid

Later, when somebody “well known” published a circular SVD implementation, we were told by the reviewers that “since a better algorithm had already been published, then ours should not be published”.

Fortunately the editor stepped in and we published our improved SVD algorithm (as a short note), but we never recovered the precedence.

New papers are still showing misunderstanding of the significance of what we have explained about delay issues.

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All that “dispersion effect” is also an artifact

Using a “delay” insensitivedeconvolution approach shows dispersion effect is much smaller than described earlier

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We are continually changing our algorithms as we better understand the “engineering” theory.

How can we (easily) check that the changes we are making are not having an unexpected effect in “previously working” parts of our code.

In the business world, a new concept in software development is “Agile” – a light weight, low-document producing development process.

A key element of “Agile” is test driven development and an automated testing framework – two issues useful in different ways

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The scientific method Test-Driven Development (TDD)

We don’t need to change our thought processes very much to switch to TDD. Biggest issue is having to change our work habits and beliefs.

As a physicist I had been trained to “think about tests and testing issues” before coding, therefore formalizing those thoughts into real tests is not too hard (30% of the time)

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Standard water-fallmethod. Tests often forgotten in time crunch.

TDD approach -- Many initial testsused to describe “ideas” – later used for“regression testing” when ideas change

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How do you move the “idea behind applying the scientific method” in planning your research procedure

over into

“using test-driven development” in planning the software code (Matlab) you need for that research procedure and later use those tests when commercializing onto the biomedical instrument?

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When starting your research project – make sure you understand your goals.

Be prepared to change your goals as opportunities arise.

Try to duplicate the results in existing literature, but remember, you are “engineers” and have a different knowledge set that many of the “clinical” people

Be prepared for unexpected results. Have an automated testing approach so that

you can duplicate your (software) results easily and provide easily repeatable evidence that “everybody else has “not handled things correctly.