EL CUESTIONARIO

T he im ages show n in F ig u re 2.3.13 w ere p u blished in (H ebden et al, 2001). M esh

generation and 3D im age reco n stru ctio n w ere p erfo rm ed by H am id D ehghani.

Phantom Breast phantoms

Mesh (3D) Conical 57766 nodes and 36857 quadratic elements

Basis Pixel 3 2 x 3 2 x 18

Starting parameters: 0.007mm '

Starting parameters: p's 1mm '

Iteration 6

Sources 32

Detectors per source 29 or 30

Datatypes (raw) Mean and intensity

Calibration Difference between Breast phantom - Homog breast

2d 3d correction applied? No

Simultaneous P« and p's

Acquisition time (per source) 2 X 30 secs

W avelength 800nm

Table 2 .3 .8 P roperties o f im ages shown in Figure 2.3.13

2 .3 .3 .2 .2 D iscussion (3D breast phantom)

The 3D im ages p ro d u ced u sin g d ata acq u ired o v er the su rface o f the breast p hantom h ave identified the inclusions in the correct locations. Som e cro ss-talk is visible, the p.;, only

feature appears in the \x\ im age and visa versa desp ite the use o f both m ean -tim e and intensity

d ifference data. A lso the co m b in ed increased Pa p's feature is the b rig h test o f the th ree in

both im ages. In fact it should be th e sam e as the Pa only or p's only feature.

T here is m ore artefact on th ese 3D breast p h an to m (difference) im ages than on the 2D d ifference im ages show n in F igure 2 .3 .1 1. T he im age quality also co m p ares p oorly to the 3D

H. M. C. H illm an. PhD thesis 2002 C h ap ter 2 . 3 — 1 3 9

m ulti-level im ages in F igure 2.3.8. T h is may be due to the new , and m ore co m p licated m esh g eo m etry , alo n g w ith the larger so u rce-d etecto r separations and the inclusion o f cro ss p lane m easu rem en ts. It may also be due to the use o f both m ean-tim e and intensity d ifferen ce d ata. If the intensity d ata w ere less well calib rated than the m ean-tim e data, co n v erg en ce o f the solution m ay have been im paired as suggested in section 2.2.6.2.

H ow ever, the results have show n that d ata acquired ov er the w hole volum e o f a b re a st­

shaped p hantom provide sufficient m easu rem en t density to identify lesions w ith 2 x co n trast

w ithin a phantom w hich is a realistic size.

2.3 .4 Phantom s with axial symmetry

It is often assum ed that optical to m o g rap h y d ata acquired in a single p lane on an object w ith axial sym m etry will represent 2D d ata ((H ebden et al, 1999), (B arb o u r et al, 2001), (E d a

et al, 1999), (Pogue et al, 1995), (Z int et al, 2001)). F igure 2.3.14 show s an axially sym m etric cy lin d rical p hantom co n tain in g three rods (rath er than discrete inclusions as in the phantom s ex p lo red above). T he distribution o f optical properties in this phantom can be ex p ressed as x(.v,y,z). T he w eight function that relates m easurem ents M „m to optical pro p erties is the e q u iv alen t o f the set o f P M D F s for the m easurem ents, w hich is ju s t the Jaco b ian /\,„ (.v ,v ,z ) (see section 1.3.2.1 ). A x ia lly s y m m e tr ic p h a n to m 2 D p la n a r a c q u is itio n 3 D p , a n d p ', d is tr ib u tio n \(x,\,z) 3 D w e ig h t f u n c tio n J n Jx.y rJ 2 D p., a n d p ', d is tr ib u tio n xf.v.yj 2 D w e ig h t f u n c tio n

Figure 2.3.14 Definition o f an axially .symmetric o bject with a 2 0 p la n a r m easurem ent geom etry. The weight function represents the sensitivity o f m easurem ents to changes in o ptical p ro p erties (section 1.3.2.1).

In the sim plest, linear form o f im age reco n stru ctio n , it is assu m ed that a ch an g e in

m easurem ent co rresp o n d s to a ch an g e in optical pro p erties Ax, the tw o bein g linked by

a w eight function or Jacobian f ' n . m ( x , y , z ) as show n in [ 2.3.7 ] (see section 1.3.2.1). n.m { x , y , z ) A x { x , y , z )

[ 2.3.7 ]

F or experim ental m easurem ents, p hotons travel in three d im en sio n s as d em o n strated in F igure 2.3.1. T his m eans that the w eight function relating m easurem ents to optical pro p erties

H. M. C. H illm an . PhD thesis 2002_____________________________________________________________________Chanter 2 . 3 — 1 4 0

will be th ree-d im en sio n al. T his will be true reg ard less o f the g eom etry o f the d etecto rs (e.g. co n stra in in g sources and detectors to a plane does not stop detected pho to n s h av in g m igrated out o f the plane). If a single source and d e te c to r are in the sam e p lane, the intensity field in the o b ject b ein g im aged w ill be a function o f z. A xial sym m etry m eans that:

A x (x , v , z ) = Ax(a', v)

[ 2.3.8 ] H o w ev er w e still have:

A M " '^ ,,.,,, = J" ( a , z ) A x ( a , >’)

[ 2.3.9 ] E ven if sources and detectors are all in the sam e z plane, the Jaco b ian rem ain s a function o f z and can n o t be replaced with a 2D Jaco b ian . T h is w as show n in F igure 2.3.2 w here both FE M plots and the infinite space G re e n ’s fu n ctio n s verify that m easu rem en ts m ade on a h o m o g en o u s (and hence axially sym m etric) object w ith a single source and d e te c to r w ill be d ifferen t from 2D sim ulated values.

T h e only way that ‘2D d a ta ’ can be m easu red on a 3D axially sym m etric object is if illu m in atio n is via a vertical line-source (or d etecto rs are p ositioned at m ultiple heights). T h is c reates an intensity field that is constant o v er z (sin ce any photon leaving the p lan e will be rep laced by one that has travelled from an o th er p lan e as show n in F igure 2.3.15).

S ource n illu m in a tes 'S o v e r all z

n ( a llz ) .m

---> X

Figure 2.3.15 O nly by acquiring data (sym m etrically) o ver the z direction can we effectively m easure data in 2D on an axially sym m etric phantom

In th is lim ited case, the height o f the d e te c to r and the w eight function are in d ep en d en t o f z (and then only if the object is axially sy m m etric). So w e can use a 2D m odel to solve d ata acq u ired in this w ay, i.e:

J nie.xtendecJ ).m ( A , f Z ) — J n . m ( A ,

[2.3.10] A x ( A , y’) = [ y M.m ( A , y ) ] A M ' n ( e x t e n d e ( l ) . m

[2.3.11 ] It is u nlikely that clinical optical to m o g rap h y w ill en co u n ter o b jects w ith axial sy m m etry , so it is not w orthw hile to co n stru ct a system w ith linearly ex ten d ed sources. H o w ev er since axially sym m etric phantom s have already been w idely used to acquire pseudo-

H. M. C. H illm an. PhD thesis 2002 C h ap ter 2. 3— 141

2 D d ata w ith sources and d etecto rs in a p lan e it is inform ative to ex am in e how the rods ex ten d in g b eyond the m easu rem en t plane w ill affect reconstructions.

2.3.4.1 2D absolute reconstructions of a phantom with axial sym m etry

T he first m easu rem en ts m ade using M O N S T IR w ere acquired on the ‘basic p h an to m ’ w hich has geom etry as show n in F igure 2.3.14, has background Pa = 0 .0 1 m m '' ± 0 .0 0 2 m m ' and p's = 1mm ' ± 0.2m m ' and co n tain s 3 rods, 8m m in diam eter, one w ith 5xpa, an o th er with

5 x p ' s and the third w ith 2 x p a and 2 x p 's . D ata w ere acquired using the p lan ar fibre h older ring w ith 5 d etecto rs d eactiv ated eith er side o f the active source u sin g th e V O A s (see section

1.2.3.3). T h e sam e protocol w as also used to acq u ire data on the h o m o g en o u s ph an to m

A lthough the first ev e r im age p roduced u sin g M O N S T IR w as o f the axially sym m etric ‘basic p h an to m ’, data w ere acquired by tw istin g the phantom w ithin the fibre ho ld er ring

c o n tain in g only 8 d etecto rs (H ebden et al, 1999). T his resulted in im age featu res quite

d ifferen t to those addressed subsequently, as describ ed in (H illm an, 2001a). T h erefo re we p resen t im ages reco n stru cted from d ata acq u ired once the M O N S T IR system had been u p g rad ed to 32 d etecto r ch an n els and sources and autom ated data acq u isitio n w as possible.

C alibration m easu rem en ts w ere acquired as d etailed in section 2.1.2.1. A bsolute calib rated m ean-tim e, v arian ce and L aplace (w ith s= 0.005 ps ') w ere ex tracted from the m easured T P S F s using the tech n iq u es describ ed in 2.1.4.1. A 2D :3 D co rrectio n w as applied to the absolute d ata by d e riv in g ad-hoc co rrectio n factors from h o m o g en o u s 2D and 3D m odels w ith appro x im ately the sam e average optical properties as the ph an to m as described e a rlie r in section 2.3.1.1. F igure 2.3.16 show s the resu ltin g absolute im ages, w hich are scaled b etw een their m axim um and m inim um values.

im age 0.01 m m 0.05m m ' 0 .00660m m ' 0 .0 1 722m m ' F s ’ im age 1.0m m ' 5.0m m ' 0.6156m m ' 1.3605 m m ' T a r g e t I m a g e s M O N S T I R

H. M. C . H illm an. PhD thesis 2002 Chapter 2 .3 — 1 4 2

It is d ifficu lt to com pare the 2D ab so lu te im ages above to resu lts from the n o n -ax ially sy m m etric phantom w ithout ex am in in g the potential im provem ents to the im ages likely to resu lt from u sin g difference im aging.

2.3.4.2 2D difference reconstructions of phantom with axial sym m etry

R aw m ean-tim es w ere extracted from the T P S F s acquired on both the axially sy m m etric basic phantom and the hom ogenous p h an to m s (u sin g calib ratio n m easu rem en ts only to guide the calcu latio n w indow ). N o 2D :3D co rrectio n w as applied since results in 2.3.1.3 im plied that d ifferen ce im aging co m p en sates w ell for intrinsic d ifferen ces b etw een 2D and 3D data.

T h e tw o sets o f raw data w ere read into T O A S T and reco n stru cted on a 2D m esh. T h e im ages show n in F igure 2.3.17 are the 5'^ (Pa) and 6^^ (p's) iterations.

E p o x y R e s in p h a n to m 7 0 m m d ia m e te r )i,' ~ l m m ' (ia - 0 .0 1 m m ' H o m o g e n o u s p h a n to m . 7 0 m m d ia m e te r - I m m ' Pa - O .O I m m ' 1 p., image o -o .o -o o o o o o p , image

Figure 2.3.17 Difference im ages o f the basic phantom p ro d u ce d using hom ogenous phantom (m ean-tim e) reference data.

2 . 3 . 4 . 2 . 1 D i s c u s s i o n ( 2 D i m a g e s of a x i a l l y s y m m e t r i c p h a n t o m )

T he im ages o f absorption and scatter show n in F ig u re 2.3.16 have sig n ifican tly m ore artefact than those o f the sam e p hantom show n in F igure 2.3.17. T he use o f ab so lu te d ata in the 2D :3D corrected im ages is likely to be the m ain cau se o f the artefact, in acco rd an ce w ith the results on the m ulti-plane phantom show n above.

It should be noted that different iteratio n s are show n fo r the ab so lu te and d ifferen ce im ages and different datatypes w ere used fo r each reco n stru ctio n . T h e low er iteratio n s w ere chosen for the difference im ages sin ce only m ean -tim e d ata w ere used and cro ss-talk w orsened in later iterations. M ean-tim e varian ce and L aplace w ere used in the ab so lu te reco n stru ctio n s in an attem pt to im prove q u an titatio n and Pa and p's separation although variance calibration w as suspected to have been fairly poor. A s suggested in section 1.3.3 the use o f three poorly calibrated ab so lu te d ataty p es m ay cau se m ore errors due to p o o r

E. M . C . H illm a n . P h D th e sis 2 0 0 2 C h a p te r 2 .3 — 143

convergence than using fewer datatypes. Note that Laplace difference reconstruction is not

implemented in TOAST, Variance difference data for this phantom were also quite noisy and

so were not used.

The main artefact in the absolute images is the blurring between the |ia features. Despite

the differences in the implementation of the two reconstructions, this blurring is unlikely to be

due to the presence of rods in the phantom extending beyond the measurement plane since a

similar effect is not seen in the difference images of the same phantom.

The distortion of the p-a rod in the difference image (causing it to be further out from

the centre than the p,'s rod in the p.'s image) is very similar to the distortion seen in the 2D

difference breast phantom images (Figure 2.3.11), meaning that it is unlikely to be due to the

presence of the rods above and below the plane.

In fact there are no discernible features in the absolute and difference images of the basic

phantom that seem to relate to the rods extending beyond the plane. However we can

ascertain whether there is information within the measurements that corresponds to the out-of-

plane presence of the rods by examining a 3D reconstruction of the data as shown below.

2 .3 .4 .2 .2 Im a g e sum m ary (ab solu te 2D b a sic phantom Im ages)

These results were published in (Schmidt et al, 2000a) (submitted July 1999).

Phantom Basic

Mesh C ircular 3781 nodes, 7392 linear elem ents (2D)

Basis Pixel 16x16

Starting parameters: p . 0.01 m m '

Starting param eters: p's 1 m m '

Iteration 17

Sources 32

Detectors per source 22

D atatypes M ean, Cvar, lap (s = 0.005 ps ')

Calibration De-conv equivalent

2d 3d correction applied? Yes

Sim ultaneous Pa and p's

Acquisition tim e (per source) 30 secs

W avelength 800 nm

Table 2.3.9 P ro p e rties o f im ages shown in Figure 2 .3 .1 6

2 .3 .4 .2 .3 Im age sum m ary (difference 2D b a sic phantom im a g es)

Phantom Basic - H om ogenous

Mesh C ircular 3781 nodes, 7392 linear elem ents (2D)

Basis Forw ard mesh - m edian filtered (2)

Starting parameters: Pa 0.01 m m '

Starting param eters: p's 1 m m '

Iteration Pa = 5 P s = 6

Sources 32

Detectors per source 22

Datatypes (raw) Mean

Calibration D ifference to hom ogenous

2d 3d correction applied? No

Sim ultaneous Pa and p's

A cquisition tim e (per source) 30 secs

W avelength 8(X) nm

H. M. C . H illm an . PhD thesis 2(K)2 C h ap ter 2 . 3 — 1 4 4

2.3.4.3 3D difference reconstructions of phantom with axial symmetry

T o ex am in e the effects o f hav in g rods in the basic phantom , rath er than d iscrete in clu sio n s, the sam e d ata as used for the 2D (m ean -tim e d ifferen ce) reco n stru ctio n s above w ere reco n stru cted on a 3D cylindrical m esh.

T h e d ata w ere presented to T O A S T as if they w ere co llected in tw o p ositions, 20 mm