Vascular applications of quantitative optical coherence tomography - Thesis

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Vascular applications of quantitative optical coherence tomography

van der Meer, F.J.

Publication date

2005

Document Version

Final published version

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Citation for published version (APA):

van der Meer, F. J. (2005). Vascular applications of quantitative optical coherence

tomography.

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Vascular Applications of Quantitative

Optical Coherence Tomography

Stellingen

behorende bij het proefschrift

"Vascular applications of quantitative optical coherence tomography"

1. Als optische biopsie methode is er een belangrijke rol weggelegd voor OCT in de studie en behandeling van vasculaire aandoeningen.

2. Kwantitatieve analyse geeft een extra dimensie aan OCT beelden.

3. De aanname van enkelvoudige verstrooiing is geoorloofd voor de analyse van verzwakkingcoëfficiënten van vaatwandcomponenten.

4. Verandering in de verzwakkingcoëfficiënt van stervende cellen maakt het weergeven van celdood met OCT mogelijk.

5. Voor de correcte vertaling van experimentele resultaten naar de klinische situatie is de temperatuur van wezenlijk belang.

6. Een gebrek aan coherentie kan heel verhelderend werken.

7. De overeenkomst tussen het Nederlands elftal en OCT is dat voor beide een goede en functionerende opstelling van cruciaal belang is.

8. De anonimiteit in het 'peer-review' proces is zeker geen garantie voor objectiviteit.

9. Managers in een ziekenhuis kunnen omschreven worden als het nieuwe snijdende specialisme.

10. Het succes van een dirigent valt of staat met zijn slagvaardigheid.

11. Het feit dat moderne muziek wel gewaardeerd wordt als zij de begeleiding is van bewegende beelden duidt op een gebrek aan voorstellingsvermogen bij de luisteraar.

Freek J. van der Meer

V A S C U L A R A P P L I C A T I O N S O F Q U A N T I T A T I V E

OPTICAL C O H E R E N C E T O M O G R A P H Y

V A S C U L A R A P P L I C A T I O N S O F Q U A N T I T A T I V E

OPTICAL C O H E R E N C E T O M O G R A P H Y

A C A D E M I S C H P R O E F S C H R I F T

ter verkrijging van de graad van doctor

aan de Universiteit van Amsterdam

op gezag van de Rector Magnificus

PROF. MR. P.F. VAN DER HEIJDEN

ten overstaan van een door het college voor promoties ingestelde

commissie, in het openbaar te verdedigen in de Aula der Universiteit

op

DINSDAG 1 NOVEMBER 2005, te 16:00 uur

door

FREEK JEROEN VAN DER MEER

P r o m o t o r : Prof. Dr. A.G.J.M, van Leeuwen

Overige leden: Prof. Dr. Ir. M.J.C, van Gemert

Prof. Dr. Ir. C. Ince

Prof. Dr. JJ. Piek

Prof. Dr. Ir. A.F.W. van der Steen

Dr. P. Baas

Faculteit der Geneeskunde, Univeriteit van Amsterdam

The research presented in this thesis was sponsored by the Netherlands Heart

Foundation (NHF-99.199). The Interuniversity Cardiology Institute of the

Netherlands ( I O N ) is acknowledged for financial support.

Financial support by the Netherlands Heart Foundation for the publication of

this thesis is gratefully acknowledged.

The printing of this thesis was also financially supported by the Jacques H. de

Jong Stichting, the Interuniversity Cardiology Institute of the Netherlands ( I O N ) ,

and the J.E. Jurriaanse Stichting.

ISBN-10: 9090196684

ISBN-13: 9789090196688

Printed by: Febodruk BV, Enschede

C O N T E N T S

General introduction 9

Quantitative measurement of attenuation coefficients of weakly

scattering media using optical coherence tomography 25

Localized measurement of optical attenuation coefficients of

athero-sclerotic plaque constituents by quantitative optical coherence tomography 45

Quantitative optical coherence tomography of arterial wall components 63

Temperature dependent optical properties of individual vascular

wall components, measured by optical coherence tomography 79

Apoptosis induces temporal increase in attenuation as measured

by optical coherence tomography 93

Discussion and Conclusion 109

Summary 123

Samenvatting 127

Nawoord 133

Curriculum vitae 135

GENERAL INTRODUCTION

C

ardiovascular disease is the leading cause of death in developed countries and is rapidly becoming the number one killer in the developing countries.' In 2002, it accounted for 34% of all mortality in the Netherlands, translating to 134 deaths per day.2 Moreover, 231 patients per day were submitted to a hospital with a cardiac event

in that year. Atherosclerosis, a disease that can lead to these chronic vascular obstruction and acute coronary and cerebrovascular syndromes, damages the lining of the coronary arteries, making them susceptible to the formation of blood clots and stenoses. Atherosclerotic plaque can build up for years before vessel narrowing becomes apparent: a debilitating or fatal heart attack is often the first indication of the underlying disease.

ATHEROSCLEROSIS

Previously, atherosclerosis was regarded as a straightforward plumbing problem: fat deposits on the surface of static arterial walls, eventually blocking the pipe.' Nowadays it is recognized that the lesions result from an excessive, inflammatory-fibroproliferative response to various forms of insult to the endothelium and smooth muscle of the arterial wall.4'5 Atherosclerotic lesions do not occur in a random fashion; the coronary arteries, the

major branches of the aortic arch, the abdominal aorta and its visceral and major lower extremity branches are particularly susceptible sites. Hemodynamic forces interacting with an active vascular endothelium are responsible for localizing lesions in this nonrandom pattern of distribution. Shear stress and cyclic circumferential strain are the predominant forces that for example modify the endothelial cell structure and function/'

The normal arterial wall (figure 1-1 A) is composed of three layers, which are separated by elastic laminas. The innermost layer, the intima, is separated from the blood stream by endothelial cells and is in normal condition a thin layer of extracellular matrix and an

adventitia media intima lipid pool calcification • • thrombus •*• macrophages

F i g u r e 1-1. S c h e m a t i c d r a w i n g of t h e n o r m a l arterial wall A and of

atherosclerotic lesions, showing lipid accumulation (B), ruptured lipid rich plaque with n o n - o c c l u s i v e t h r o m b u s (C), t h r o m b o s i s due to e r o s i o n , endothelial denudation (D), calcification (E) and chronic occlusion I .

i n c i d e n t a l s m o o t h m u s c l e cell (SMC). The i n t i m a is s e p a r a t e d from the m e d i a by t h e i n t e r n a l elastic lamina. T h e m e d i a c o n s i s t of S M C s , b u n d l e s of collagen fibers and elastic fibrils, e m b e d d e d in an extracellular matrix, li is separated from the o u t e r m o s t a d v e n t i t i a b\ t h e e x t e r n a l elastic l a m i n a . T h e adventitia is a layer of c o n n e c t i v e tissue, collagen a n d elastic l i b e r s e m b e d d i n g the e n u r e vessel within its s u r r o u n d i n g s .

In g e n e r a l , a t h e r o s c l e r o s i s starts w i t h lipid d e p o s i t i o n in the intima, the so-called 'fatty s t r e a k ' . T h e lipid d e p o s i t i o n gradually increases and the i n t i m a t h i c k e n s d u e to m i g r a t i n g S M C s t r o m the m e d i a a n d m o n o c y t e s t h a t e n t e r from t h e b l o o d . T h e m o n o c y t e s differentiate into m a c r o p h a g e s that internalize the lipid d e p o s i t i o n , b e c o m i n g lipid loaden f o a m cells, w h e r e a s S M C c h a n g e from migrating i n t o a s e c r e t i n g p h e n o t y p e , p r o d u c i n g c o l l a g e n to f o r m a p r o t e c t i v e cap figure 1 - I B ) . D u e t o c o m p e n s a t o r } e n l a r g e m e n t of t h e

GENERAL INTRODUCTION

vessel, early lesions can c o n t i n u e to develop without c o m p r o m i s i n g the lumen ('remodeling').7 However, some plaques with a large lipid core, which by now contain both

apoptotic and necrotic cells and cellular debris and have a thin fibrous cap, are prone to rupture. Further lipid deposition and necrosis of foam cells result in a lipid pool, which thrombogenic contents cause thrombus formation when cap rupture occurs (figure 1-1C). Thrombus formation may also occur when the endothelial lining is damaged (erosion) (figure 1-1D). The thrombus can embolize in other vessels causing symptoms of acute syndromes, such as the abrupt reduction in flow to a region of the myocardium (myocardial infarction), or strokes. Further advanced plaques show calcifications (figure 1-1E) which can result in thrombus formation by protruding into the lumen through a disrupted thin fibrous cap. Healing of cap rupture and further accumulation of lipid, calcifications, SMCs and fibrous tissue can eventually compromise the vascular lumen (figure 1-1F).

V U L N E R A B L E PLAQUE

Vulnerable plaques have been defined as precursors to lesions that rupture. A large number of vulnerable plaques are relatively uncalcified, relatively nonstenotic, and similar to type IV atherosclerotic lesions described in the American Heart Association classification.'' They are morphologically characterized by a lipid core covered by a thin fibrous cap (thickness < 65/um).l o r > These unstable plaques are very prone to rupture or fissure, especially in the

Morphology/structure Activity/'function

Cap thickness I jpid core size Stenosis Remodelling Color

Collagen content vs. lipid content, mechanical stability

Calcification burden and pattern Shear stress

Inflammation (macrophage density) Endothelial denudation or dysfunction Plaque oxidative stress

Superficial platelet aggregation/fibrin deposition

Rate of apoptosis

Angiogenesis, intraplaque hemorrhage, leaking vasa vasorum

Matrix-digesting enzyme activity (MM I') Certain microbial agents (HSP60, C. Pneumoniae)

Adapted from ret. H

Table 1-1 O v e r v i e w of m a r k e r s for plaque vulnerability, c a t e g o r i z e d into morphological or functional markers.

s h o u l d e r s o f t h e fibrous cap, with s u b s e q u e n t e x p o s u r e o f the t h r o m b o g e n i c lipid c o r e t o t h e f l o w i n g b l o o d , r e s u l t i n g in t h r o m b o s i s . H o w e v e r , different types o f v u l n e r a b l e p l a q u e exist. C o r o n a r y t h r o m b o s i s m a y o c c u r from o t h e r lesions like p l a q u e e r o s i o n and calcified n o d u l e s , a l t h o u g h to a lesser frequency than c a p r u p t u r e . I n a r e c e n t p u b l i c a t i o n , N a g h a v i i't a/, s u m m a r i z e d t h e c h a r a c t e r i s t i c s o f a t h e r o s c l e r o t i c lesions t h a t r e s u l t e d in v a s c u l a r o c c l u s i o n and o t h e r clinical s y m p t o m s (table 1-1).u

IMAGING OF THE VULNERABLE PLAQUE

S e v e r a l i m a g i n g t e c h n i q u e s a r e currently available for t h e d e t e c t i o n o f s t e n o s i s a n d p l a q u e s , r a n g i n g f r o m n o n i n v a s i v e t o c a t h e t e r b a s e d i n v a s i v e s y s t e m s , u s i n g e l e c t r o -m a g n e t i c o r u l t r a s o u n d waves.13"18 For non-invasive imaging, the radiation w h i c h is minimally

a b s o r b e d by t i s s u e c a n b e u t i l i z e d . I n figure 1-2, t h e a b s o r p t i o n s p e c t r u m o f w a t e r for e l e c t r o - m a g n e t i c w a v e s is p l o t t e d . F r o m this g r a p h it is clear that for X-rays, y-rays a n d r a d i o w a v e s t h e a b s o r p t i o n c o e f f i c i e n t is smaller t h a n 1 cm"' a n d t h e r e f o r e t h e s e are very s u i t a b l e for i m a g i n g t h r o u g h c e n t i m e t r e s o f tissue. X-rays h a v e b e e n utilized for m o r e t h a n h u n d r e d years for n o n - i n v a s i v e imaging. T h e c o n t r a s t is b a s e d o n d i f f e r e n c e s in a b s o r p t i o n for t h e X-rays by t h e t i s s u e . H o w e v e r , d u e t o t h e l o w a b s o r p t i o n d i f f e r e n c e s b e t w e e n b l o o d a n d vascular wall c o m p o n e n t s , highly a b s o r b i n g c o n t r a s t agents h a v e to b e i n j e c t e d t o visualize t h e l u m e n . C o n s e q u e n t l y , a n g i o g r a p h y visualizes, albeit with a g o o d r e s o l u t i o n , t h e v a s c u l a r l u m e n b u t is n o t able to i m a g e t h e v a s c u l a r wall and its c o n t e n t s . D u e t o t h e fact t h a t v u l n e r a b l e p l a q u e s are o f t e n h e m o d y n a m i c a l l v insignificant, they a r e difficult t o d e t e c t with angiography.v>~" Still, a n g i o g r a p h y w a s the gold standard for c o r o n a r y i m a g i n g l o r d e c a d e s . C o m p u t e d t o m o g r a p h y o f m u l t i d i r e c t i o n a l X-ray p r o j e c t i o n s (CT) a l l o w s 3 D v i s u a l i z a t i o n o f m o r p h o l o g i c s t r u c t u r e s . H o w e v e r , d u e t o limited r e s o l u t i o n ( u p t o 0.6 x 0.75 m m ) a n d limited contrast, a l t h o u g h m u c h b e t t e r than for X-ray p r o j e c t i o n i m a g i n g , only c a l c i f i c a t i o n s c a n b e clearly d e t e c t e d . 2I F o r t h e m o r e e n e r g e t i c p a r t o f t h e

e l e c t r o - m a g n e t i c s p e c t r u m , t h e i m a g i n g techniques like P E T a n d S P E C T a r e h a m p e r e d by t h e i r l o w r e s o l u t i o n ( a p p r o x i m a t e l y 3-10 m m ) . ~

A t t h e o t h e r side o f t h e s p e c t r u m , radio w a v e s in c o m b i n a t i o n with a high m a g n e t i c field are u s e d t o n o n - i n v a s i v e l y i m a g e tissues. In this so called nuclear m a g n e t i c r e s o n a n c e i m a g i n g ( M R I ) , r a d i o w a v e s are u s e d t o excite t h e m a g n e t i c field i n d u c e d split g r o u n d state o f h y d r o g e n a t o m s in t h e t i s s u e . A f t e r excitation, r a d i o w a v e s are e m i t t e d w h i c h can b e c h a r a c t e r i z e d t h r e e p a r a m e t e r s : t h e signal s t r e n g t h , w h i c h d e p e n d s o n t h e d e n s i t y o f t h e p r o t o n s , t h e t i m e T , n e e d e d for r e c o v e r y o f t h e e x c i t e d spins t o the e q u i l i b r i u m , w h i c h d e p e n d s o n t h e s p i n - l a t t i c e i n t e r a c t i o n and t h e d e c a y t i m e T7 o f t h e R F signal, w h i c h

d e p e n d s o n the s p i n - s p i n i n t e r a c t i o n . T h e s e p a r a m e t e r s are tissue specific a n d t h e r e f o r e c a n b e u s e d t o d i f f e r e n t i a t e t h e tissue c o m p o n e n t s . T h u s M R I h a s t h e p o t e n t i a l t o d i s t i n g u i s h a t h e r o s c l e r o t i c p l a q u e a n d t o d e t e r m i n e its c o m p o s i t i o n a n d m i c r o a n a t o m y2' .

I n p a t i e n t s , M R I is able t o identify u n s t a b l e p l a q u e s in t h e aorta.2 4 H o w e v e r , t h e

r e s o l u t i o n of M R I , w h i c h is a p p r o x i m a t e l y 0.4 m m i n - p l a n e r e s o l u t i o n with a 3 - m m slice

GENERAL INTRODUCTION

Frequency [Hz]

FIGURE 1-2 The absorption coefficient of water as a function of the frequency of the electro magnetic waves. Note the logarithmic scales and the regions in which the absorption coefficient is less than 1 cm"1: Radio waves, visible light, X

and y rays.

thickness,2526 and the imaging time (several minutes) limit its application for the detection

of the specific morphological characteristics of unstable plaques in coronary arteries.2

Tn the visible part of the electro-magnetic spectrum, the absorption by water is also low (figure 1 -2). However, in this part the scattering of the light by the tissue constituents hampers the utilisation of these electro-magnetic waves for non-invasive imaging. Using fiber-optics, light can be used in catheter based systems for intravascular imaging. In angioscopy, via a coherent bundle of optical fibers, an intra-luminal image is obtained while the blood is removed with flushing saline or C O , gas.28 Angioscopy is a

straight-forward imaging technique that only provides information on the morphology of the endo-luminal surface and is therefore, like angiography, unable to identify the extent of an atherosclerotic plaque into the vessel wall. In some cases, angioscopy can indirectly detect the position of a fibroatheromatous plaque.2'' The yellow color intensity of plaque

determined by angioscopy can indicate the prevalence of thrombosis on the plaque and thus be a marker of plaque vulnerability.1" Finally, the plaque cap thickness is a determinant

of plaque color and quantitative colorimetry might be useful for the detection of vulnerable plaques.''Instead of electro-magnetic waves, also acoustic waves can be used for medical imaging. In ultrasound (US) imaging, the intensity of back-reflected acoustic pulses is depicted as a function of the time of flight. The contrast of US imaging is based on differences in the acoustic impedance of the different tissue layers. Both the axial resolution and the attenuation of the US in tissue are proportional to the frequency of the US waves

(figure 1 -3). Therefore, for high resolution imaging of the arterial wall, the I S signals of frequencies around 311 MI 1/ have t< > be delivered and detected intravascular. This intravascular ultrasound (IVUS) imaging, which lias an axial resolution of approximately 100 fivn, currently represents the gold standard in the assessment of atherosclerotic disease. [VI S facilitated in-depth understanding of coronary artery disease. like arterial remodelling and therapeutic strategies like stent implantation and coronary brachv ihcrapv. [VUS imaging, although being able to image the vascular wall, is limited in specifically identifying lipid-rich plaques, thus the contrast and the res. >lution are not suitable for directly detecting the vulnerable plaque.

I sing a sophisticated analysis of the I S signals obtained during systole, the local mechanical properties can be assessed. This so called elastography can distinguish the weaker and stiffer regions in the arterial wall and therefore can identify the vulnerable plaque. Intravascular elastography is a unique tool to assess lesion composition and vulnerability, '; S(' which has proven to detect vulnerable plaques in v i t r ov With the

development of three-dimensional elastography, palpography, in vivo identification of weak spots over the full length of human coronary arteries has become possible."

An entirely different approach to deteel plaque vulnerability is the measurement of the temperature of the arterial wall, which may be increased by the local inflammation. With a precise thermography catheter, the heal or metabolic activity can be localised and correlated with plaques at high risk to rupture or thrombosis. Indeed, an increased thermal heterogeneity within human atherosclerotic coronan arteries was observed in patients

SE"

CL Q o — w E 5, o. 0) D 10 0.1 10 0 1 Tomography: SPECT & PET

US: 3-5 Mhz US: 7.5-20 Mhz . ^ 20-40 Mhz ^ C^ 1 10 100 Depth \prr\] 1 10 100 Depth [mm] 1000

Figure 1-3 Axial (depth) resolution and obtainable imaging depth for I S imaging

devices with different frequencies compared with other imaging techniques as SPECT, PET, CT, MR1. I S, OCT and (confocal) microscopy C)M .

GENERAL IXTRODI O K >\

w i t h u n s t a b l e a n g i n a a n d a c u t e m y o c a r d i a l i n f a r c t i o n , s u g g e s t i n g t h a t it m a y be related to t h e p a t h o g e n e s i s .4" H o w e v e r , t h e spatial r e s o l u t i o n ( a p p r o x i m a t e l y 0.5 m m ) and t h e

p o t e n t i a l in v i v o u n d e r e s t i m a t i o n o f h e a t p r o d u c t i o n locally in h u m a n a t h e r o s c l e r o t i c p l a q u e d u e t o t h e " c o o l i n g effect" o f c o r o n a r y b l o o d flow41 currently limits the applicability

o f this t e c h n i q u e .

T h e r e a r e t w o f a c t o r s t h a t h a m p e r t h e d e t e c t i o n o f t h e v u l n e r a b l e p l a q u e using t h e a b o v e d e s c r i b e d t e c h n i q u e s : t h e y are e i t h e r (1) en face i m a g i n g t e c h n i q u e s , w h i c h are n o t a b l e t o s h o w t h e d e p t h r e s o l v e d m o r p h o l o g y ( a n g i o s c o p y , t h e r m o g r a p h y ) or (2) h a v e a r e s o l u t i o n t h a t d o e s n o t p e r m i t detailed i m a g i n g ( I V U S , M R I a n d C T ) . T h e n e e d f o r a high r e s o l u t i o n i m a g i n g t e c h n i q u e that can d e t e c t u n s t a b l e c o r o n a r y a t h e r o s c l e r o t i c p l a q u e s b e f o r e t h e y b e c o m e clinically significant is p a r a m o u n t . T h i s i m a g i n g lacuna c o u l d be filled by optical c o h e r e n c e t o m o g r a p h y ( O C T ) . I n t r a v a s c u l a r O C T may plav an i m p o r t a n t role in g u i d i n g t h e r a p e u t i c i n t e r v e n t i o n s , d i a g n o s i n g a t h e r o s c l e r o s i s a n d r e s e a r c h i n g t h e c a u s e s o f c o r o n a r y artery d i s e a s e .

OCT

S i n c e its i n t r o d u c t i o n in t h e early 1990s, O C T has b e c o m e a p o w e r f u l m e t h o d f o r i m a g i n g t h e i n t e r n a l s t r u c t u r e o f b i o l o g i c a l s y s t e m s a n d m a t e r i a l s .4 2 O C T is a n a l o g o u s t o

B - m o d e u l t r a s o u n d , e x c e p t t h a t it uses light r a t h e r t h a n s o u n d . W h e r e a s in u l t r a s o u n d t h e l o c a t i o n o f r e f l e c t i n g o b j e c t is d e t e r m i n e d by m e a s u r i n g e c h o delay t i m e s , in O C T d e p t h r e s o l v e d m e a s u r e m e n t o f t h e b a c k s c a t t e r e d light is a c h i e v e d t h r o u g h l o w - c o h e r e n c e i n t e r f e r o m e t r y . T h e h e a r t o f the O C T s e t u p is a M i c h e l s o n i n t e r f e r o m e t e r (figure 1-4); light e m i t t e d by a light s o u r c e is split by a b e a m splitter in t w o b e a m s . O n e is d i r e c t e d i n t o t h e r e f e r e n c e a r m a n d is r e f l e c t e d by a t r a n s l a t i n g r e f e r e n c e m i r r o r . T h e o t h e r b e a m is d i r e c t e d i n t o t h e s a m p l e a r m a n d is reflected b y a tissue s a m p l e . T h e b a c k reflected b e a m s r e c o m b i n e a t t h e b e a m s p l i t t e r a n d are g u i d e d to a d e t e c t o r . It is i m p o r t a n t to n o t e t h a t i n t e r f e r e n c e b e t w e e n t h e t w o light b e a m s will o n l y b e d e t e c t e d w h e n t h e difference in o p t i c a l p a t h l e n g t h s travelled by the light in b o t h a r m s is less t h a n t h e so-called c o h e r e n c e l e n g t h o f t h e light s o u r c e . T h i s p h e n o m e n o n is used t o d e t e r m i n e t h e o p t i c a l p a t h l e n g t h t h e light h a s travelled in t h e s a m p l e a r m : if i n t e r f e r e n c e is o b s e r v e d while s c a n n i n g t h e p a t h l e n g t h in t h e r e f e r e n c e a r m (i.e. m o v i n g t h e r e f e r e n c e m i r r o r ) , the back scattered light f r o m d i f f e r e n t p o s i t i o n s w i t h i n t h e s a m p l e (i.e. in d e p t h ) c a n b e m e a s u r e d ( ' c o h e r e n c e g a t i n g ' ) . C o n s e q u e n t l y , t h e axial r e s o l u t i o n is directly related t o the c o h e r e n c e length ( / ) o f the light s o u r c e (with a c e n t e r w a v e l e n g t h Xr), w h i c h is i n v e r s e l y related t o t h e b a n d w i d t h

(ZlA) o f t h e light s o u r c e ( e q u a t i o n 1-1).

TTAA

reference arm m

-Is RM BS

*->

EH

sample a n d

Figure 1-4 A schematic drawing of an OCT setup. Light emitted by a light source (Is) is split by a beam splitter (BS) into two beams, travelling through the reference arm or the sample arm. Via mirror (m), the light in the sample arm, is focused into a sample (S) using a lens (L). In the reference arm, the light is directed to a translating reference mirror (RM). Back reflected light from both arms is recombined by the beam splitter (BS) and the interference signal is monitored bv the detector (d).

The transverse resolution for O C T imaging is determined by the focused spot size, as in microscopy. In contrast to conventional microscopy, the lateral resolution is decoupled from the axial resolution. Furthermore, OCT provides cross-sectional images of structure below the tissue surface in analogy to histopathology. Standard-resolution O C T can achieve axial resolutions of 10-15 /urn.

In accordance with the terminology of ultrasound imaging, a measurement of reflectivity vs. depth is called an scan. The O C T image, or B-scan, is constructed from adjacent A-scans, with the reflectivity now plotted as a grey or color scale. The contrast of an O C T image is determined by differences in the optical properties (e.g. scattering and absorption) of different tissue layers and their components. T h e imaging depth is also determined by the optical properties of the tissue. Using wavelengths in the near infrared, where hemoglobin and melanin absorption arc low and scattering is reduced, permits imaging depths of up to 2 mm in tissues.43-4"1 Although this depth is shallow compared with other

clinical imaging techniques like US (figure 1-3), the image resolution of O C T is 1 to 2 orders of magnitude better than conventional ultrasound imaging, magnetic resonance imaging or computed tomography. Recently, using state-of-the-art lasers as light sources,

GENERAL INTRODUCTION

ultrahigh-resolution imaging with axial r e s o l u t i o n s as fine as 1— 2ium h a s b e e n d e m o n s t r a t e d

(table 1-2).

45

VASCULAR APPLICATION O F O C T

T o d a t e , O C T i m a g i n g is r o u t i n e l y u s e d in o p h t h a l m o l o g y ,4 6'1 b u t has g r e a t p o t e n t i a l

as a n ' o p t i c a l b i o p s y ' t o o l in o t h e r fields o f m e d i c i n e , i.e. g a s t r o - e n t e r o l o g y ,4 8"5

d e r m a t o l o g y ,M urology,5 2'5 4 gynaecology,"'"' a n d cardiology."''' A p a r t from a p p l i c a t i o n as a

d i a g n o s t i c t o o l , O C T can also b e u s e d for feedback d u r i n g surgical p r o c e d u r e s '1" e.g. in

laser a b l a t i o n o f t i s s u e s ,, x a n d for g u i d a n c e in c l e a r i n g a totally o c c l u d e d vessel."'9 I n

c a r d i o l o g y , O C T c o u l d b e u s e d t o d e t e c t a n d analyze a t h e r o s c l e r o t i c l e s i o n s , d u e to its capacity o f high r e s o l u t i o n i m a g i n g o f superficial s t r u c t u r e s . A s P a s t e r k a m p et al. s t a t e , t h i c k n e s s o f t h e c a p as well as t h e size a n d c o m p o s i t i o n o f t h e u n d e r l y i n g a t h e r o m a t o u s lipid c o r e , are m a j o r c o n t r i b u t o r s t o p l a q u e vulnerability, a n d O C T is t h e o n l y i m a g i n g m o d a l i t y c a p a b l e o f m e a s u r i n g this c a p t h i c k n e s s .6 0 By accurately m e a s u r i n g t h e c a p

t h i c k n e s s , O C T c o u l d b e a t o o l i n d e t e c t i o n o f r u p t u r e - p r o n e v u l n e r a b l e p l a q u e s .6 i r'2

I n 1 9 9 6 , B r e z i n s k i et al. w e r e t h e first t o r e p o r t t h e u s e o f O C T for i m a g i n g v a s c u l a r pathology.6 1 , 6 3 T h i s g r o u p also d e v e l o p e d d e v e l o p m e n t o f an e x p e r i m e n t a l c a t h e t e r for in

vivo imaging.6 4 T h e c a t h e t e r - b a s e d i m a g e s w e r e p r o v e n t o identify p l a q u e s b o t h in vitro,65 a n d in vivo.1'''-'' I n a n in vitro e x p e r i m e n t , Y a b u s h i t a et al. d e m o n s t r a t e d the abilitv o f O C T t o d e t e c t d i f f e r e n t types o f a t h e r o s c l e r o t i c l e s i o n s , d e f i n e d as fibrous, fibrocalcific a n d lipid-rich a t h e r o m a ' s .6" U s i n g a p r o t o t y p e c a t h e t e r , J a n g et al. r e c e n t l y s h o w e d t h a t in vivo i n t r a c o r o n a r y O C T a p p e a r s t o b e feasible a n d safe.6" W i t h O C T they i d e n t i f i e d m o s t

a r c h i t e c t u r a l features d e t e c t e d by I V U S a n d s u g g e s t e d t h a t O C T may p r o v i d e a d d i t i o n a l detailed s t r u c t u r a l i n f o r m a t i o n . l i g h t s o u r c e SLD SLD AF Ti:Al203 "k ( n m ) 825 1300 1300 800 Ak ( n m ) - 2 5 - 50 - 60 - 100 - 250 Pm ,x ( m W ) - 5 - 5 - 2 0 - 1000 /c (Mm) - 12 - 15 - 12 - 1 - 3 d\ ( m m ) 0 . 5 - 1.0 1.0-2.0 1.0-2.0 0 . 5 - 1.5

T a b l e 1-2 O v e r v i e w of light sources and their specifications. T h e c e n t e r wavelength (A) is proportional to the imaging depth (d). The bandwidth of the light source (AX) is inversely proportional to the coherence length (/.). The maximal power (P|llaJ is also given. SLD: super luminescent diode; AF: autofluorescent fiber; T i : A l , 0 . : titanium sapphire laser

SCOPE OF THIS THESIS

Currently, the interpretation of vascular O C T images is based on the qualitative interpretation of the O C T images, without further quantitative data analysis of the O C T signals. In this thesis, the possibilities of quantitative analysis of vascular O C T signals are explored for the identification of vulnerable plaques. To distinguish the constituents of these plaques, reflection spectroscopy on components will be performed, furthermore, the effect of the light source, with consequently the effect of axial resolution and contrast, on the O C T data analysis is studied.

In CHAPTER 2 we explore the possibility to extract quantitative data from the O C T image, i.e. the attenuation coefficient (ju ). Subsequently, the algorithm for measurement of fx is applied to O C T images of human atherosclerotic tissue and the possibility of discrimination of plaque components, based on the quantitative basis is explored. The results are presented in CHAPTER 3. A comparison between two O C T setups, operating with different light sources (and thus different contrast and resolution), the effect on quantitative measurement is presented in CHAPTER 4 as well as the correlation between O C T and histology. To determine the effect of the surrounding tissue and to further quantify the optical properties precisely, ,a and the index of refraction (n) was measured in isolated vessel wall and plaque components (CHAPTER 5). The dependence on temperature of /u and n, important to relate in vitro and /'// vivo measurements, was also determined. In CHAPTER 6, the measurement of// is applied to living, apoptotic and necrotic cells. Since the morphological changes during necrosis and apoptosis would result in changes of ji , enabling detection of cellular death using OCT. Finally, in CI IAPTER 7 a general discussion on the role of vascular O C T is given.

GENERAL INTRC «DUCTION

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Q U A N T I T A T I V E M E A S U R E M E N T O F

A T T E N U A T I O N C O E F F I C I E N T S O F WEAKLY

SCATTERING MEDIA USING OPTICAL

C O H E R E N C E T O M O G R A P H Y

Dirk J. Faber, Freek J. van der Meer,

Maurice C.G. Aalders, and Ton G. van Leeuwen

MODELING THE O C T SIGNAL

F

r o m c a l i b r a t e d , w e a k l y s c a t t e r i n g t i s s u e p h a n t o m s (2-6 m m " ' ) , w e e x t r a c t t h e a t t e n u a t i o n c o e f f i c i e n t w i t h a n a c c u r a c y o f Ü.8 m m ' f r o m O C T d a t a in t h e clinically relevant 'fixed f o c u s ' g e o m e t r y . T h e data are analyzed u s i n g a single scattering m o d e l and a recently d e v e l o p e d d e s c r i p t i o n o f t h e confocal p o i n t spread f u n c t i o n ( P S F ) . We verify t h e validity o f t h e single s c a t t e r i n g m o d e l by a q u a n t i t a t i v e c o m p a r i s o n w i t h a multiple scattering m o d e l , and validate the use o f t h e P S F o n the calibrated s a m p l e s . I m p l e m e n t a t i o n o f this m o d e l for existing O C T s y s t e m s will b e straightforward. L o c a l i z e d quantitative m e a s u r e m e n t o f the a t t e n u a t i o n coefficient o f different tissues can significantly i m p r o v e t h e clinical value o f O C T .

1. I N T R O D U C T I O N

T h e clinical value o f O p t i c a l C o h e r e n c e T o m o g r a p h y ( O C T )1 d e p e n d s o n high i m a g i n g

s p e e d t o p r o v i d e real t i m e in vivo i m a g i n g ,2 high spatial r e s o l u t i o n t o r e s o l v e small t i s s u e

s t r u c t u r e s ,3 a n d sufficient c o n t r a s t t o d i s c r i m i n a t e b e t w e e n t h o s e s t r u c t u r e s . C o n t r a s t in

O C T images originates from differences in reflectivity o f different tissues, which are c a u s e d by their variation in (complex) refractive i n d e x n. U n f o r t u n a t e l y , c o n t r a s t is limited b e c a u s e for m o s t tissues n only ranges from 1.3 t o 1.4. L o c a l i z e d m e a s u r e m e n t o f t h e a t t e n u a t i o n coefficient// can p r o v i d e additional i n f o r m a t i o n , and may increase the clinical p o t e n t i a l o f O C T by a l l o w i n g q u a n t i t a t i v e d i s c r i m i n a t i o n b e t w e e n different tissue t y p e s .

T h e a t t e n u a t i o n coefficient c a n b e m e a s u r e d f r o m t h e O C T signal by fitting a m o d e l r e l a t i o n to this signal from a r e g i o n o f i n t e r e s t in a n O C T i m a g e . C u r r e n t l y , t w o m o d e l s are available. W i d e l y used4-''-6 is t h e s o - c a l l e d single s c a t t e r i n g m o d e l , w h i c h a s s u m e s t h a t

only light that has b e e n b a c k s c a t t e r e d o n c e c o n t r i b u t e s t o t h e O C T signal. A m o d e l t a k i n g i n t o a c c o u n t multiple scattering was i n t r o d u c e d by T h r a n e eta/, and has recently b e e n u s e d

to extract optical properties of atherosclerotic lesions'1 and human skin'.

Focusing optics in the sample arm suppress the detection of light scattered from outside the focal volume, similar to confocal microscopy. In clinically used probes and catheters, the optical components of the sample arm are fixed. Therefore, for quantitative extraction of//, the confocal properties of the O C T system have to be taken into account,

i.e. the change of the ()CT signal with increasing distance between the probed location in

the tissue and location of the focus."'" We have recently derived a general expression for the confocal axial point spread function (PSF) for single mode fiber (SMF) based O C T systems.12 The major advantage of this PSF is that it is described by one parameter only,

the Rayleigh length, which can easily be determined experimentally.

In this paper we investigate the steps necessary to extract fx from O C T images of weakly scattering non-absorbing samples. This method provides a template that can be applied to other ranges of /x . In section 2, we discuss the general principles of non-linear least squares fitting and introduce test statistics to judge the significance of the best fit values. In section 3 we establish criteria for choosing an appropriate model for the O C T signal, and proceed to choose a model for weakly scattering media using calibrated samples. Section 4 investigates the range of validity of our PSF in scattering media. Section 5 combines these results to extract the attenuation coefficient from calibrated samples, in the clinically more relevant situation of a fixed focus. Section 6 discusses implications and limitations of this study.

2. CURVE FITTING

Discrimination of different tissues based on differences in their attenuation coefficient //_ requires its accurate measurement from O C T data. This is done by defining a functional relationship between the O C T signal as a function of depth and a , and then fitting this model to a region of interest in an O C T image. The curve fitting algorithms and statistics used throughout this paper can be found in textbooks.1'1 4 Suppose we fit a model / w i t h

Madjustable parameters a.to /Vdata points (.v.,v. ± Ay). The maximum likelihood estimate

of the model parameters a is found by minimizing the quantity X2 given by:

A

^=1

yi-f{*üa\...a

M

)

2

CT: (2-1)

i.e. by minimizing the sum of squared, weighted, residuals. It is appropriate to use the measurement errors for weighting, i.e. O = Ay, for experimental data. For non-linear models the ^-minimization is an iterative process, implemented by the Levenberg-Marquardt method. The number of degrees of freedom {dof) of the fit is defined as N—M. To judge the significance of the best fit values of the parameters a., uncertainty estimates

MODELING Ti ii-OCT SIGNAL

o f t h e s e values p l u s s o m e g o o d n e s s - o f - f i t statistics h a v e t o b e calculated. N o t e t h a t o f t e n u n i f o r m w e i g h t i n g is u s e d , i.e. each data p o i n t is a s s i g n e d e q u a l w e i g h t in the c u r v e fitting (G = 1 in e q u a t i o n 2-1).

N e x t t o t h e b e s t e s t i m a t e s , the s t a n d a r d e r r o r o f e a c h fitted p a r a m e t e r is c a l c u l a t e d . If t h e s t a n d a r d e r r o r is small a n d t h e p a r a m e t e r is c h a n g e d a little, t h e c u r v e will fit m u c h w o r s e (i.e. higher %2). T h e m a g n i t u d e o f t h e w e i g h t s <X therefore influences the ' e l b o w r o o m ' of t h e p a r a m e t e r . C o n s e q u e n t l y , w h e n t h e s t a n d a r d e r r o r is t o be u s e d as a reliable e s t i m a t e o f t h e u n c e r t a i n t y of the fit p a r a m e t e r , w e i g h t i n g with the m e a s u r e m e n t e r r o r s is essential. F r o m t h e s t a n d a r d e r r o r s , 9 5 % c o n f i d e n c e i n t e r v a l s (c.i.) a r e calculated w h i c h a r e m o r e insightful as u n c e r t a i n t y e s t i m a t e s : if t h e fitting is r e p e a t e d o n a n o t h e r data set f r o m t h e s a m e s a m p l e , t h e b e s t fit value o f t h e p a r a m e t e r is e x p e c t e d t o fall w i t h i n this c.i. 9 5 o u t o f a 100 times. So-called p a r a m e t e r d e p e n d e n c i e s ( b e t w e e n 0 and 1) are also calculated: a value (very) close t o 1 indicates t h a t t h e fit d o e s n o t d e p e n d heavily o n the p a r a m e t e r , a n d m a y p o i n t t o o v e r - p a r a m e t e r i z a t i o n (i.e. a c h a n g e in t h e p a r a m e t e r c a n be c o m p e n s a t e d for b y c h a n g i n g the o t h e r p a r a m e t e r s ) .

N o t e t h a t a small c.i. c a n also b e f o u n d w h e n a b e s t fit d o e s n o t follow t h e d a t a v e r y well, for e x a m p l e d u e to an i n a p p r o p r i a t e m o d e l . T h e c o r r e l a t i o n coefficient R2 ( b e t w e e n 0

a n d 1) is calculated for e a c h fit. A R2 close to 1 indicates t h e b e s t fit c o m e s close t o t h e d a t a

p o i n t s . Arbitrarily, a R2> 0 . 8 is a s s u m e d as r e a s o n a b l e . H o w e v e r , a fit u s i n g physically

u n r e a l i s t i c p a r a m e t e r values can also h a v e a h i g h R2. T h e %2- m i n i m i z a t i o n ' a s s u m e s ' t h a t

the w e i g h t e d residuals have a G a u s s i a n d i s t r i b u t i o n and h a v e the s a m e s t a n d a r d d e v i a t i o n a l o n g t h e b e s t fit c u r v e ; a n d t h a t t h e d e v i a t i o n o f a p o i n t from t h e c u r v e is n o t c o r r e l a t e d t o t h e d e v i a t i o n from t h e n e x t o r p r e v i o u s p o i n t . T h e s e a s s u m p t i o n s a r e t e s t e d u s i n g a S h a p i r o - F r a n c i a t e s t and a r u n s - t e s t . T h e S h a p i r o - F r a n c i a t e s t c o m p u t e s t h e c o r r e l a t i o n coefficient W b e t w e e n a n o r m a l d i s t r i b u t i o n a n d t h e d i s t r i b u t i o n o f t h e w e i g h t e d r e s i d u -als, a n d it is i n t e r p r e t e d in t h e s a m e way as R2. T h e r u n s - t e s t c o m p a r e s the o b s e r v e d

n u m b e r o f r u n s (a series o f c o n s e c u t i v e data p o i n t s either a b o v e o r b e l o w t h e c u r v e ) to the e x p e c t e d n u m b e r o f r u n s . A g a i n arbitrary, W > 0.8 a n d p - v a l u e o f t h e r u n s t e s t pm n s > 0.05 are c o n s i d e r e d a c c e p t a b l e . T h e a s s u m p t i o n o f i n d e p e n d e n t s c a t t e r o f t h e w e i g h t e d residuals is a priori v i o l a t e d d u e t o l o w pass filtering (either in h a r d w a r e o r software) in the O C T data a c q u i s i t i o n , o r p o s s i b l e speckle a v e r a g i n g6 p r i o r to fitting. W h e n necessary, this

is d e a l t w i t h bv u s i n g e a c h ;/'th p o i n t o f t h e data set in t h e fitting, w h e r e // c o r r e s p o n d s to the n u m b e r o f p o i n t s in t h e d u r a t i o n o f t h e a v e r a g i n g t i m e o f t h e filters. If all p o i n t s are u s e d in the fit, p is d i s r e g a r d e d . All c u r v e fitting a l g o r i t h m s a n d statistical analysis a l g o r i t h m s a r e i m p l e m e n t e d in L a b V I E W 7. T h e a l g o r i t h m s w e r e v e r i f i e d against commercially available c u r v e fitting software (Microcal Origin 6.0, Microcal Software, Inc.).

3. C H O O S I N G A M O D F L FOR T H E O C T SIGNAL.

T h e m a i n q u e s t i o n in c h o o s i n g a m o d e l for t h e O C T signal is: c a n m u l t i p l e scattering effects b e i g n o r e d ? Since i m a g i n g d e p t h s generally d o n o t exceed = 1 m m , this may well be

justified for weakly scattering media ("T < 6 mm ' for the samples used in this paper). We

first compare the single scattering model4-'1,6 to a multiple scattering model using the same

calibrated scattering samples with m ranging from 2 mm to 6 mm"1 described in ref. 15

and used in a similar analysis in ref. 8. The experiments are performed under the condition of dynamic focusing (i.e. the focal plane coincides with the probing location) such that the influence of the confocal properties during the depth scan is constant.

In OCT, interference between the light returning from the sample arm and the reference arm takes place only when the path length difference between both arms is matched within the coherence length of the light source (coherence gating). In the following, the O C T signal i{z) refers to the amplitude of the interference signal, and we define z = 0 at the sample interface. Ideally, z is the probing depth in the sample but the term 'location of the coherence gate in the sample' is more accurate. In the single scattering model, only light that has been backscattered once contributes to the O C T signal and the OCT signal is given by Beer's law:

/(z)cc Jexp(-2/j,z) (2-2)

T h e factor 2 accounts for round trip attenuation, the square root appears because the detector current is proportional to the sample field rather than intensity.

T h e contribution of multiple scattering to the O C T signal has been described by Thrane et al. hollowing their terminology, the O C T signal for dynamic focusing is expressed as the root mean square heterodyne signal current:

1

/ -v x 2exp(-// -)[l-exp(-// z)]

r

,

v

,->wf

i(z) oc exp(-2/Az) +

1V / s / L

,

I V

^

/ J

+[ 1 - exp(-7i,z)]--4

w~ Wi

T h e last two terms under the square root describe the contribution due to multiple scattering. I lere, ws I wj = ll + [2WQ/po{z)]~ ) where ir, and ir are the 1 / e intensity radii of the

p r o b e beam with and without scattering, respectively, w.is the 1/e intensity radius at the focusing lens andpnis the lateral coherence length, given by: PQ(Z)- yj3///5z(AQ/x0nm \nf'jz),

where Xlt is the center wavelength of the light source, ƒ is the focal length of the objective

lens and 0 s is the root-mean-square scattering angle. Note that /u^ in equation 2-3 is the

(2-3)

MODELING THE O C T SIGNAL

s c a t t e r i n g coefficient. F o r n o n a b s o r b i n g s a m p l e s as u s e d in this p a p e r ,"s—/^t- F o r t h e

e p o x v s a m p l e s A l - E l , t h e a t t e n u a t i o n coefficient /J.I i n c r e a s e s f r o m ~2 mm"' to ~7 m m '; n = l .55. T h e s c a t t e r i n g a n i s o t r o p y g = 0.75 w h i c h m e a n s that e q u a t i o n 3 is slightly o u t s i d e o f the range o f validity o f small-angle forward scattering. H o w e v e r , in ref. 8 g o o d a g r e e m e n t b e t w e e n e q u a t i o n 2 - 3 a n d e x p e r i m e n t w a s f o u n d u s i n g t h e e x a c t s a m e s a m p l e s , at 1300 n m . 0 ^ in e q u a t i o n 2-2 is a p p r o x i m a t e l y g i v e n by "v (2(1 -g)) = 0 . 7 1 .

T h e S M F ( F i b e r c o r e , S M 7 5 0 , m o d e field d i a m e t e r 5.3 m m . ) b a s e d O C T s e t u p u s e d i n t h e e x p e r i m e n t s i n c l u d e s a T i r S a p p h i r e laser ( F e m t o l a s e r s , A.n = 8 0 0 n m , AX = 125 n m

F W H M ) . R e f e r e n c e m i r r o r a n d the f o c u s i n g lens in t h e s a m p l e a r m are m o u n t e d o n t w o v o i c e c o i l t r a n s l a t o r s ( Q u i c k S c a n V102.2L, Physik I n s t r u m e n t e ) . Scan s p e e d w a s 1 A -s c a n / -s . D y n a m i c r a n g e wa-s 111 d B . T h e d e t e c t o r c u r r e n t i-s d e m o d u l a t e d u -s i n g a l o c k - i n amplifier and l o w - p a s s filtered in software p r i o r t o s t o r a g e . All data a c q u i s i t i o n software is w r i t t e n in L a b V I E W 6. T h e c o l l i m a t i n g lens a n d f o c u s i n g lens in t h e s a m p l e a r m are b o t h E d m u n d O p t i c s A c h r o m a t s P 4 5 - 7 9 3 , f = 2 5 m m , N A = 0 . 0 8 . C h r o m a t i c a b e r r a t i o n e x p r e s s e d as m a x . - m i n . effective focal l e n g t h is 10 /xva in t h e b a n d w i d t h o f o u r light s o u r c e . D e p t h o f focus in air is 1 2 6 ± 6 / a n ( c o r r e s p o n d i n g t o 2 x Rayleigh l e n g t h m e a s u r e d in air). T h e lateral resolution ( d e t e r m i n e d by t h e s p o t size o f the focused s a m p l e b e a m ) is a p p r o x i m a t e l y 7 fxm. We r e c o r d e d O C T i m a g e s o f e p o x y s a m p l e s A l - E l . O C T i m a g e s c o n t a i n e d 500 A-s c a n A-s o f 4 0 9 6 p o i n t A-s ( 0 . 2 4 , « m axial, 20 u r n lateral i n c r e m e n t ) . After i m a g i n g , a 6 x 6 pixel m o v i n g average filter ( a p p r o x i m a t e l y c o r r e s p o n d i n g to 1 c o h e r e n c e length) was applied t o the data t o r e d u c e s p e c k l e . N o t e t h a t this a v e r a g i n g r e d u c e d t h e s t a n d a r d d e v i a t i o n o f t h e data by a f a c t o r v6. A larger a v e r a g i n g k e r n e l w o u l d lead t o f u r t h e r r e d u c t i o n b u t also to u n d e s i r a b l e loss o f r e s o l u t i o n . T h e a v e r a g e a n d s t a n d a r d d e v i a t i o n o f 50 A - s c a n s w a s calculated for use in t h e c u r v e fitting. A l t h o u g h a v e r a g i n g m o r e A - s c a n s w o u l d yield a s m o o t h e r d a t a set for t h e fitting, for clinical O C T i m a g e s w e e x p e c t t o b e able t o use only t h e limited n u m b e r o f 5 0 - 1 0 0 A - s c a n s for a specific tissue r e g i o n .

T h r e e different m o d e l s w e r e fit independently to t h e a v e r a g e A - s c a n s u s i n g t h e s t a n d a r d d e v i a t i o n as w e i g h t s : (1) t h e single s c a t t e r i n g m o d e l of e q u a t i o n 2-2 w i t h an a d d e d offset / and m u l t i p l i e r ^ . F o r each fit, / was fixed to the average noise level of t h e data set; A and (x w e r e t h e free r u n n i n g p a r a m e t e r s . M o d e l (II) is b a s e d o n e q u a t i o n 2 - 3 , with a d d e d offset /' a n d m u l t i p l i e r ^ . 0 s w a s fixed t o its t h e o r e t i c a l v a l u e a n d /'0was fixed to t h e average

n o i s e level o f the d a t a set, b u t w a s a l l o w e d t o vary if this i m p r o v e d the fit. A a n d ^r were

the free r u n n i n g p a r a m e t e r s . M o d e l (III) is the s a m e as I I , w i t h all p a r a m e t e r s /'0, A,/nt and 0 allowed to vary. F o r all m o d e l s , c o n v e r g e n c e o f t h e a l g o r i t h m is c h e c k e d by using different initial g u e s s v a l u e s for t h e m o d e l p a r a m e t e r s . I n all fits, e v e r y 2 0 ' t h data point w a s u s e d , c o r r e s p o n d i n g t o t h e r e s p o n s e t i m e o f t h e s o f t w a r e l o w - p a s s filter (see section 2).

T h e r e s u l t s o f t h e b e s t fit v a l u e s o f /<c, u s i n g m o d e l s I, I I a n d I I I are s u m m a r i z e d in

Fig. 2 - 1 . T h e e r r o r b a r s r e p r e s e n t t h e 9 5 % c o n f i d e n c e i n t e r v a l s o f t h e fitted /u^. T h e first c r i t e r i o n in c h o o s i n g a m o d e l is w h e t h e r o r n o t t h e b e s t fit v a l u e s o t t h e p a r a m e t e r s , and

their c.i. and dependency, are physically reasonable. Both model 1 and II give physically acceptable values for the attenuation coefficient and corresponding confidence intervals. In the fits of model II to samples C l - E l the offset Z(| was allowed to vary, because it reduced

X2 compared to fitting with fixed /(|. However, this causes larger confidence intervals of ,i/.

compared to model I because the fit is now not as 'tight': within the limits given bv the measurement errors, a change in ju can be compensated for to a larger extent bv a change in

A and /'0. The fits of model 111 did not yield phvsicallv possible values for 9 (which

tended to unrealistically large values, effectively annihilating the multiple scattering contributions). Both the offset /. and the multiple scattering contributions in equation 2-3 result in the O C T signal approachinga constant value, with increasing depth. Therefore, variation of iQ and 0.n has the same effect, fixing iQ to the noise level of the data set did

not resolve this problem. We conclude that model III does not model the O C T signal for this range of scattering coefficients, relatively low scattering anisotropv, and our measurement setup very well.

Both model I and II appear appropriate for describing the O C T signal. The goodness-of-fit of both models is judged by their Revalue which was 0.8 for sample Al and larger than 0.95 for samples Bl-F.1, for both models. Violations of the assumptions of non-linear least squares fitting are checked by judging W and the p-value of the runs-test. There is no evidence these models arc inappropriate since W' > 0.86 and p > 0.05 for all

E, 7 6 5 4 3 2 1 -0 //'J integtating sphere I B model I (eq. 2)

I I model II (eq. 3; 8,„.s fixed)

I I model III (eq. 3)

È

A1 B1 C1 Sample

D1 E1

Figure 2-1: comparison of attenuation coefficients extracted from epoxv samples Al-El using integrating sphere measurements (from ref [15]), and curve fitting using models I,II and III. The error bars represent 95% confidence intervals of the extracted fit parameter.

M( (DELING THE O C T SIGNAL

samples. Consequently, the model yielding the smallest value of fj should be chosen. By definition, variations in yf < 1 are not significant.13 A fit using a model with more

parame-ters (less dof likely has smaller %2 and an F-test can assess whether this reduction in y} is

worth the cost of having less dof. A comparison per sample shows that %2 is not reduced

between model I and II; whereas model II has an additional fit parameter for the larger scattering coefficients. Therefore the simpler model I is chosen.

We conclude that there is no evidence against using the single scattering model I for describing the O C T signal with depth, for/^ < 6 mm"1 and our measurement setup, and

we will use this model in the remainder of this paper, f o r other ranges o(/u the analysis outlined in this section should be repeated to establish the appropriate model.

4. MODELING OF THE CONFOCAL PSF

In clinically used probes and catheters, dynamic focusing is in general not possible, and the influence of the confocal point spread function on the O C T signal has to be accounted for to quantitatively extract attenuation coefficients. We have recently introduced a general expression for the PSF of single mode fiber based O C T systems. In this section, we investigate the range of validity of this expression in scattering media.

The axial confocal PSF for these OCT systems h(z) is given by:

z-zcf

{

Z

R )

2 > + 1

J

Here, Zcf is the position of the confocal gate and zR is the 'apparent' Rayleigh length

used to characterize the PSF. The Rayleigh length zn of a Gaussian beam is given by z =

nnof/XQ with CO the beam waist at the focus and XQ the center wavelength of the light

source. The apparent Rayleigh length is related to z0 through zR = az() where a is used to

distinguish specular reflection (0C=1) from diffuse reflection (a=2).1 2 This distinction is

based on theoretical grounds assuming single backscattering (or more generally, assuming the beam is not distorted prior to and after backscattering). The Rayleigh length of our system measured on a mirror in air is Z= 63 ± 3 /mi.

The PSF can be measured by moving a reflector through the focus of the sample beam and recording the detector output. F.quivalently, the reflector can be held at a fixed position

z while moving the focusing lens. In OCT, we can use the coherence gate to select a

'reflector' inside a sample. To systematically evaluate the PSF for specular and diffuse reflections inside scattering media, O C T images of the samples described below were recorded for 100 different positions of the confocal gate z as illustrated in Fig. 2-2(A). From each image the average A-scan was calculated (Fig. 2-2(15); red curves represent fits as discussed in section 5 below) and the average A-scans were combined to a data set shown