Dear Biomch-L Readers,

As promised, the answers at the questions I sent a few days ago about the use of
markers in medical imaging.

Once again the principle of "the Forum List" (like Biomech-L) proved to be
particularly efficient and again (even after several years of use) I'm
still astonished when I get messages from the other part of the world
after only a few minutes after my own request was mailed!!

You'll find, below, at first the original posting, then a summary of the
answers and
at last the original answers.

Thank you to the people who shared their opinion and/or experience!! Also,
don't hesitate
to send me further comments, they are always welcome!!

Serge

-----------------------------------------------------------------------
Serge VAN SINT JAN, Ph.D. | phone: + 32 2 555 63 25 (office)
Dept. of Anatomy (CP 619) | + 32 2 555 63 76 (secretary)
University of Brussels | fax: + 32 2 555 63 78
808 Lennik Street | email: sintjans@ulb.ac.be
1070 Brussels - Belgium | WWW: http://homepages.ulb.ac.be/~sintjans
-----------------------------------------------------------------------



/***************** ORIGINAL POSTING *********************/

We are planning to start new experiments involving visualization of
external markers on CT-Scan images. We'd like to determine the centroid
of these markers from the images (with the highest accuracy of course!).

I'd like to know your opinion and/or experience about the following:

1) According to you, what is the best ratio between the size of the marker
and the thickness of the CT slice ?

A ratio 1:1 should give good resul IF each marker is included EXACTLY in one
slice. Better,
the marker should a)- be cube-shaped, b)- have the size of a voxel and c-)
be entirely
included in a particular voxel.
Unfortunatly, this is theoretical and practically (we think, maybe we're
wrong!?)
difficult to implement ...

So, what is the best marker size? We haven't found anything specific about
that particular
topic in the litterature.

2) Are tantalum markers still the best for X-rays experiment ?
If not, what is the best matter?

3) Does somebody know the name of a company selling products made of
tantalum (balls, plates)?

/*************** END OF ORIGINAL POSTING ***************************/

/*************** START OF SUMMARY **********************************/


Question 1: Optimal ratio between marker size and slice thickness ?
************************************************** *****************

It depends!

A- If a sub-voxel resolution is desired:
----------------------------------------
Then use markers bigger then the voxel size (variable magnitude in the
answers!!).
J.F. Antaki indicates that "uncertainty in locating the true centroid goes
as 1/sqrt(N), where
N is the number of pixels covered by the marker. If you use a partial volume
technique, then the accuracy is increased further. In other words, the
bigger the
marker the better -- for locational purposes".

Litterature about sub-voxel location of markers:

- Lemieux and Jagoe in Physics in Medicine and Biology (vol. 39: 1915-1928
(1994))
- Maurer in IEEE Med. Imag. (16: 447-462 (1997)).
- Randy Ellis' work in
http://www.qucis.queensu.ca/home/ellis/postscript/phantomaccuracy.ps.
- Use of a Biocompatible Fiducial Marker in Evaluating the Accuracy of
Computed Tomography Image Registration
Randy E. Ellis, Soren Toksvig-Larsen, Maurilio Marcacci, Davide
Caramella, and Marco Fadda. Investigative Radiology 31(10): 658-
October 1996
- Proceedings for MrCAS '97 (presented at, CVRMed II and MrCAS III Joint
conference, Grenoble,
France, March 19-22,1997, pg 141).
- Klaus Rupert, Tokyo ISB Congress 97 (abstract is below, make search with
"THE USE OF" as keyword).

B- If only an approximation is desired:
---------------------------------------

Then markers with size close to the voxels' is good enough because "a marker
can be displayed on two (or three) adjacent contiguous slices, although its
diameter is smaller than the nominal slice width".

Question 2: Are tantalum markers still the best for X-rays experiment ?
************************************************** *********************

Seems to be largely used, but not everybody agree to say tantalum is the
best for X-ray experiment
because it would be "VERY (too??) radiopaque" and "is expensive".

Good alternative is found with plastic balls, lead, aluminium, stainless
steel, chrome steel.

According to M. Pohl the best markers "should be those which absorb the
X-radiation best ... usually elements with high atomic weight together with
a high density".

Question 3: Name of a company selling products made of tantalum (balls, plates)?
************************************************** ******************************

- GoodFellow: http://www.goodfellow.com.
- Small Parts, Inc (USA): phone (800) 220-4242 (for aluminium balls).
- McMaster-Carr Comp (Chicago, USA): phone (708) 833-0300 (variety of metals
and size for
reasonable prices).
- Tilly Medical Products - Lung - Sweden (tantalum).

/**************** END OF SUMMARY *********************************/


/**************** START OF ORIGINAL ANSWERS***********************/

From: SAM EVANS

Perhaps you would get better accuracy if you use round markers much
bigger than the voxel size and then find the centroid. Then you
average out the errors due to the size of the voxels and get better
accuracy than the resolution of the image. That's how some motion
analysis systems claim to work, anyway.

Just a thought,

Sam Evans.

Dr. Sam Evans,
Medical Systems Engineering Research Unit,
UWC School of Engineering,
PO Box 688, The Parade,
Cardiff CF2 3TE, UK.
Tel. (01222) 874533 or (01222) 874000 x5926
Fax. (01222) 874533

/************************************************** *************************/


From: antaki@pittsurg.nb.upmc.edu

I had to dust off my old thesis to find you an answer. According to my
calculations, the uncertainty in locating the true centroid goes as
1/sqrt(N), where
N is the number of pixels covered by the marker. If you use a partial volume
technique, then the accuracy is increased further. In other words, the
bigger the
marker the better -- for locational purposes. However, remember Heisenberg's
discovery: you dont get anything for free. There will inevitably be other
criteria
which will place an upper bound on size. If tracking motion, for example,
larger
markers will impede the motion.

Hope this helps

James F. Antaki, PhD
Pittsburgh, PA

/************************************************** *************************/

From: " (Louis Lemieux)"

you seem to presume that the smaller the marker the better, as long as it
is detectable. In fact, it is possible to calculate the position of the
centroid of such a marker to sub-pixel accuracy. For example, see our paper
Lemieux and Jagoe in Physics in Medicine and Biology (vol. 39: 1915-1928 (1994))
on the localisation of markers in radiographs. Thre is also a recent paper
by Maurer in IEEE Med. Imag. (16: 447-462 (1997)).

Regards,

************************************************** **************
* *
* Louis Lemieux, PhD, Lecturer in Physics *
* *
* Epilepsy Research Group *
* Department of Clinical Neurology *
* Institute of Neurology *
* Queen Square *
* London WC1N 3BG *
* UK *
* *
* MRI Unit *
* National Society for Epilepsy *
* Chalfont St Peter *
* Gerrards Cross *
* Buckinghamshire SL9 0RJ *
* UK *
* *
* Tel : ++44-1494-601361 *
* FAX : ++44-1494-875666 *
* E-mail: l.lemieux@ion.ucl.ac.uk *
* *
************************************************** **************

/************************************************** *************************/


From: "Neil Glossop"

> 1) According to you, what is the best ratio between the size of the marker
> and the thickness of the CT slice ?

Read Randy Ellis' work in
http://www.qucis.queensu.ca/home/ellis/postscript/phantomaccuracy.ps
He discusses use of a submilimetre sized markers to increase the accuracy from
CT slice thicknesses that are larger than the marker size.

> A ratio 1:1 should give good resul IF each marker is included EXACTLY in
one slice. Better,
> the marker should a)- be cube-shaped, b)- have the size of a voxel and c-)
be entirely
> included in a particular voxel.
> Unfortunatly, this is theoretical and practically (we think, maybe we're
wrong!?)
> difficult to implement ...

Not true because of the way CT beams spread. You can use smaller
than the slice size.


> So, what is the best marker size? We haven't found anything specific about
that particular
> topic in the litterature.

Also have a look at another of his papers in the proceedings for
MrCAS '97 (presented at, CVRMed II and MrCAS III Joint conference, Grenoble,
France, March 19-22,1997). pg 141

> 2) Are tantalum markers still the best for X-rays experiment ?
> If not, what is the best matter?

That's what Ellis uses. He may (or may not) be presenting further work
on this at the CAOS conference in Bern next month. For details on
that conference, see http://cranium.unibe.ch/cas/caos.html

Best wishes,
Neil


---
Neil Glossop PhD
Traxtal Technologies
neil@traxtal.com http://www.traxtal.com

/************************************************** *************************/


From: Santosh Zachariah

If you wish to achieve sub-voxel accuracy in your centroid determination,
then you are going to need markers that occupy between 5 & 10 voxels
in each direction. I offer these numbers from experience in 2-D. They
also account for the 'lighting' and segmentation routines I had in place
(yours will be differenct). To extend the rationale to three-dimensions,
suggests covering between 5 & 10 slices.

Spherical markers would be unaffected by the alignment of the digitization axes,
but if your resolution is less in the axial direction, then rods/tubes may
be more
appropriate.

You could put together a quick-and-dirty experiment in 2-D with a series of
metallic discs in a planar X-ray.

Yours

-- Santosh Zachariah --

Research Associate, Dept. of Bioengineering
Univ. of Washington, Box 352255, Seattle, WA 98195, USA
ph: (206) 685-3488, fax: (206) 543-6124
zach@limbs.bioeng.washington.edu

/************************************************** *************************/


From: "Rita M. Patterson, Ph.D."

We use different size markers depending on the joint we are
studying. For our wrist kniematic studies we are using 4mm diameter
plastic balls as targets, 5mm in diameter after we paint them with
reflective paint. With a CT slice thickness of 1.5mm we get very good
results.
We use plastic because it doesn't distort the CT field. Titanium,
like any metal, still causes a "bright blurr" in the image. I just buy
craft beads at Michaels for our experiments.
Good luck,
Rita

--
Rita M. Patterson, Ph.D.
University of Texas Medical Branch
Orthopaedic Surgery and Rehabilitation
Galveston, TX 77555-0892

/************************************************** ************************/

From: LISA SILVERSTEIN/CAHS FACULTY

I am aware of a study conducted in l988 (Arne Lundberg's dissertation) at
Kongl Corolinska Medico Chirurgiska Institute in Stockholm sweden.
The study was done in accordance with a method developed by Associate
Professor Goran Selvik in his laboratory at Lund University. It was
published in 90? or 89 in Journal of BOne and Joint Surgery. Last I
heard, Dr. Lundberg was doing a fellowship at Mayo Clinic (l993?). I'm
sure if you could track him down, or the professor at Lund U, they would
be able to tell you where to buy these markers. Dr. Lundberg was very
helpful to me once, I'm sure he still is very accommodating. Good Luck
__________________________________________________ ____________________
Lisa Selby-Silverstein, PhD, PT, NCS
Assistant Professor
Director, Human Performance Laboratory
Thomas Jefferson University
130 S. Ninth St.
Suite 830
Phila., PA l9l30

email: silvers1@jeflin.tju.edu
phone: 1-215-503-1644
__________________________________________________ ____________________


/************************************************** *************************/

From: Martin Pohl

regarding your first point: I have no experience with that, but I think
the smallest marker, which you can identify without problems in your
image will give you the best resolution.

point 2: best markers for x-ray experiments:
I supoose the best markers for x-ray experiments will be those, which
absorb the x-radiation best. Usually these are the elements with high
atomic weight together with a high density. You should have look at a
periodic system of elements. Perhaps try lead.

point 3: company
I have made good experience with an enterprise called "goodfellow" (see:
http://www.goodfellow.com). They are not expensive and deliver within
one or two days.

Hope these remarks will help you.

Best regards

Martin Pohl.

--
__________________________________________________ _____

Martin Pohl
Abteilung Unfallchirurgische Forschung und Biomechanik
Universitaet Ulm
Hemholtzstrasse 14
D-89081 ULM
Tel.: +49-(0)731-502-3494
FAX: +49-(0)731-502-3498
WWW: http://lyra.medizin.uni-ulm.de
e-mail: mailto://pohl@pollux.medizin.uni-ulm.de
__________________________________________________ _____

/************************************************** *************************/

From: "John A. Hipp"

The following reference may help:

Use of a Biocompatible Fiducial Marker in Evaluating the Accuracy of
Computed Tomography Image Registration
Randy E. Ellis, Soren Toksvig-Larsen, Maurilio Marcacci, Davide Caramella,
and Marco Fadda.
Investigative Radiology 31(10): 658- October 1996

In ex-vivo cadaver models, we have been getting qualitatively good results
with 2mm Aluminum balls
And 3mm thick X 3mm spaced CT slices. We have not finished the accuracy and
precision studies.
You can get metal balls from Small Parts, Inc in the USA
(800) 220-4242

Good luck

John Hipp, PhD
Director, Spine Research Laboratory
Baylor College of Medicine
Houston, TX

/************************************************** *************************/

From: cambrose@ortho1.med.uth.tmc.edu (Catherine G. Ambrose)

We have used stainless steel ball bearings for markers in xray experiments
due to the wide availability and the guaranteed sphericity. Many companies
sell stainless steel ball bearings in a variety of sizes - we have used 3/32
inch size. We haven't worked with markers in CT images so I'm not sure of
the optimal size.

/************************************************** *************************/

From: Scott Tashman

I have a couple of comments on your application.

The size of the marker depends on the accuracy you need. If "nearest voxel" is
enough, then a marker size equal to (or even a little smaller than) the slice
thickness is fine. It will always show up in at least one slice, and usually in
two. We had success at this level using 1.6mm markers with 2mm slices. If you
want sub-pixel/voxel accuracy in the slice direction you need the marker image
to appear in multiple slices. If it appears in at least 3 slices you can (in
theory) get accuracy up to 1/10 the slice thickness (more realistically,
probably about 1/5). Since the in-plane voxel size is usually much smaller than
the slice thickness, you can try to arrange the scan to give you accuracy where
you need it most.

Spherical markers will always provide the greatest accuracy in centroid
calculations, since the centroid is in the same location regardless of viewing
angle (or slice plane orientation). Accuracy is also improved by using
gray-scale weighted (instead of binary) centroid calculations.

As for marker materials, tantalum may not be the best choice, especially if you
are using larger markers. Tantalum is VERY radiopaque - this is great for plane
films, but can cause considerable reconstruction artifacts in CT which may
interfere with visualization of other structures. It is also quite expensive.
For external markers you don't need to worry so much about long-term
biocompatibility (which is one of the main benefits of tantalum), so you could
use chrome steel (also quite radiopaque), stainless steel (medium-radiopaque) or
titanium (less radiopaque). The McMaster-Carr company (CHICAGO, IL USA,
708-833-0300) sells balls in a variety of metals and sizes at reasonable prices.

I suggest you get some balls of a variety of metals and sizes and run some tests
with them on a phantom in your CT scanner. You should be able to pick what
works best fairly easily.
__________________________________________________ ___________________
Scott Tashman, Ph.D.

Head, Motion Analysis Section Assistant Professor
Bone and Joint Center Department of Orthopaedics
Henry Ford Hospital School of Medicine
2799 W. Grand Blvd. Case Western Reserve University
Detroit, MI 48202

Voice: (313) 876-8680 or 876-7572
FAX: (313) 556-8812 or 876-8064
Internet: tashman@bjc.hfh.edu
__________________________________________________ ___________________

/************************************************** *************************/

From: Klaus Kuspert

I don't know if I can help you. I did some work on combining gait
analysis and MRT images. I visualized the gait analysis marker on the
MRT images to relate gaitdata and anatomical data. The marker have a
diameter of one inch. If you have two MRT slices of one sphere you
can exactly determine its centroid, if you have more slices you can
use a least square method to get the centroid. This solves your
problem of fitting the marker exactly in one slice. So my advice is
to make your markers bigger and visualize them on two or more CT
slices which have a constant offset.
There was a presentation ot this method on the Tokyo ISB Congrass 97,
two months ago. If you are interested I can mail the abstract to you

(NOTE FROM Van Sint Jan: THAT abstract follows just below).

Greetings

Klaus

---

Dipl.-Ing. Klaus Kuspert
University of Darmstadt
Institute of Mechanics I
Hochschulstrasse 1
D-64289 Darmstadt
Germany
tel. +49 6151 16 2386
fax +49 6151 16 6869
klaus@mech1host.mechanik.th-darmstadt.de


/************************************************** *************************/

From: Klaus Kuspert

Hello again,

this is not the last version, but it should do. If you have further
questions, please ask,

greetings

Klaus


THE USE OF MAGNETIC RESONANCE IMAGES IN GAITANALYSIS: DIRECT

DETERMINATION OF JOINT CENTERS FROM SKIN MARKER LOCATIONS.

K. Kuspert (+), D. Scale (*), T. Arndt (:), P. Brueggemann(:) and W.
Hauger(+)
(+) University of Darmstadt, Institute of Mechanics I, Germany
(*) University Hospital of Orthopedics, Frankfurt/Main, Germany
(:) German Sport University Cologne, Institute for Athletics and
Gymnastics, Germany

INTRODUCTION
An important part of every gaitanalysis is to assess the
relation of external marker data and important internal anatomical locations
like
joint centers, tibial plateau, and reference points in femur
and tibia for relating individual anatomy and anatomy of
musculoskeletal models. Especially hip joint centers are difficult to
determine.

The available methods for prediction of hip center location have
several severe inherent limitations. The procedures that do not use
radiographs or magnetic resonance images (MRI) have questionable accuracy.

For the three most common methods the accuracy is from 20 to 40 mm with a range
of 5 to 65 mm in individuals (Bell 1990). If one imagines that the leverarms of
hip muscles are in the same order of magnitude, the prediction of
adequate muscle forces is impossible.

S. Delp predicts a change of moment arm up to 40% and a change of
moment generating capacity of hip muscles up to 50% when moving the hip
joint center 20 mm (Delp 1993).

On principle, the same problems apply for knee and ankle. Existing
roentgenogram and
MRI methods are more accurate but give only internal locations in respect to
external
landmarks. The problem is to guess the distance between skin markers and
landmarks.

METHODS
For that purpose we developed a new method to determine important
internal locations,
like hip joint centers, directly from marker locations. The idea was to
leave the
markers at their specific position and to make them visible on MRI scans. We
used
Motion Analysis one inch reflective spheres mounted on plates. The markers
were altered so
that they were removable from the plates which were taped on the skin of the
subject.
We drilled threads into the plastic spheres and used plastic screws to fix
the markers
on the plates. Plastic is necessary because most other materials disturb the
MRI scans.
For transport of the subject the markers were removed. After placing the
subject in
the MRI unit, a second set of markers covered by a thick film of fat
(covered again
by a foil) was mounted. The field of view of our MRI system was not big
enough to get
the complete lower extremity on one scan. For that reason we added three
overlapping scans
together. Two scans had one joint marker so that the displacement between
the scans was known.
To hold the subject's leg absolute motionless it was supported by wedges and
an orthopaedic
L-guide for the feet. The subject rests on a plastic foam plate which has
room for the sacrum
marker. The MRI system gives now (transversal) slices of the subject's
anatomy on which
the fat around the spheres and the hip joints appear as different sized
circles. A 3-D
reconstruction of the slices gives the midpoint of the spheres and the hip
joints. Other
internal locations of interest are easily obtained from the pictures.

RESULTS
Our method gives a direct measure of hip joints and other interesting
internal structures
in relation to external markers. The accuracy of determining a midpoint of a
sphere on the
MRI scans is about 1 mm. If the movement of one segment is known (three
markers per
segment) one can easily asses the movement of an interesting location on
that segment by
using the relative vectors from the MRI scans. The problem of skin movement
between
standing and lying in the MRI unit does not seem to be very significant, if
markers are
mounted on bony external landmarks. Our results indicate only a small
dislocation compared
to position data from the Motion Analysis Video system.

DISCUSSION
A main source of error of gaitanalysis is to asses the relation of
internal locations
and external markers. The procedure described above is an easy to use and
very accurate method
of determining internal locations like joint centers directly from external
skin markers.
For high quality gaitanalysis it is absolutely necessary to use all
available informations
to reduce the amount of errors. As MRI systems do not omit radiation and
give good accuracy
the new method seems to be promising if a MRI system is available.

REFERENCES
(1) Delp, S. L. and Malony, W. (1993) Effects of hip center location
on the moment-generating capacity of the muscles. J. Biomechanics 26/4, 485-499.

(2) Bell, A. L, Pedersen; D. R. and Brand, R. A. (1990) A comparison
of the accuracy of several hip center location prediction methods. J
Biomechanics 23/6, 617-621.

(3) Brown, R. H., Burstein, A. H., Nash, C. L. and Schlock, C. (1976) Spinal
analysis using
a three dimensional radiographic technique. J. Biomechanics ), 355-365.

/************************************************** *************************/

From: Raffaella Soavi

1) Our experience on CT acquisitions demonstrated that marker centering
on a slice is not critical if thickness is of the same magnitude order
as marker size.
A marker can be displayed on two (or three) adjacent contiguous slices,
although its diameter is smaller than the nominal slice width. The
reason of this fact is the fan-shaped X-ray beam of CT systems. In this
case, the marker center can be determined with subslice accuracy by
using an interpolation algorithm. (Ellis R., Toksvig-Larsen S., Marcacci
M., Caramella D., Fadda M. - Use of a biocompatible fiducial marker in
evaluating the accuracy of CT image registration. - Invest. Radiol.,
Oct. 1996, Vol. 31, No. 10, p. 658-667).

Regarding the marker shape, we think that probably it should be cubic.
In any case, it is not possible to center an object perfectly on the
display matrix. This makes the object appear one pixel larger than it
really is.

2) We made axial scans of a femur phantom containing tantalum markers
and we obtained good results regarding the determination of the center
coordinates of such markers on the acquired images (accuracy of one
pixel).

3) We send you the name of one company that sells products made of
tantalum:

Tilly Medical Products - Lung - Sweden

/**************** END OF ORIGINAL ANSWERS***********************/