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

6/1/20152 / 38  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).

6/1/20153 / 38  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.

6/1/20154 / 38  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!

6/1/20155 / 38 Background  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 HEMORRHAGICISCHEMIC

6/1/20156  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

6/1/20157  Need to deconvolve “tissue signal” ( c VOI (t) ) by “arterial signal” ( c AIF (t) ) to get “residue function” ( R(t) ). ◦ Peak of residue function provides estimate of blood flow (CBF)

6/1/20158 Clinical results: Appear to make perfect sense (Calamente, MRM, 2000)  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

6/1/20159 / 38 IMPACT OF NOISE FILTERING – LOSS OF SIGNAL

6/1/  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: AMPLITUDE LOSS HIGH FREQUENCY LOSS

6/1/ / 38  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

6/1/ / 38  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”

6/1/  Use known low frequency data to generate high frequency data

6/1/ / 38  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.

6/1/  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”?

6/1/ / 38  Would “everybody else” not doing things the proper “engineer way” impact on our “new” method done the “correct way”?

6/1/  Need to deconvolve “tissue signal” ( c VOI (t) ) by “arterial signal” ( c AIF (t) ) to get “residue function”. ◦ Peak of arterial signal provides estimate of blood flow (CBF)

6/1/  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”

6/1/  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

6/1/ / 38  True SNR of concentration signal changes with MR signal intensity – specific “best” conditions

6/1/ / 38  Consequences – we believe that everybody is “setting the image parameters” the wrong way

6/1/ / 38  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.

6/1/ / 38  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

6/1/ / 38  FT shows “no time delay effects” that are so evident with SVD. We are really out of step FT deconvolution SVD deconvolution

6/1/  Noise Enhancement during deconvolution SVD deconvolution eigen-value thresholding causes “band pass” filtering

6/1/ / 38  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

6/1/ / 38  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”

6/1/ / 38 SVD well known – Why is it not working in DSC MR studies?  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.

6/1/ / 38 “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

6/1/ / 38  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 NEGATIVE SIGNAL ALLOWED “MISPLACED” NEGATIVE ENERGY SVD and FT deconvolution have different properties

6/1/ / 38  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.

6/1/ / 38  All that “dispersion effect” is also an artifact Using a “delay” insensitive deconvolution approach shows dispersion effect is much smaller than described earlier

6/1/ / 38  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

6/1/ / 38 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)

6/1/ Standard water-fall method. Tests often forgotten in time crunch. TDD approach -- Many initial tests used to describe “ideas” – later used for “regression testing” when ideas change

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6/1/ / 38  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?

6/1/ / 38  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.