X-Ray Imaging of Coronary Stentstion procedures, X-ray imaging has generally been employed for this purpose [3], and still is the method of choice today. The use of X-rays allows for

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Progress in Biomedical Research

Introduction

During the past decades, minimally invasive techniqueshave been developed to an amazing degree of perfec-tion, and have replaced open surgery as the routinetreatment in many cardiological applications. Catheter-based surgery is greatly beneficial to the patientbecause it minimizes peripheral damage to tissue, whilethe miniaturized tools employed may even increase theworking precision at the actual target site [1,2]. In order to take full advantage of these benefits, corre-spondingly precise information about location and cur-rent status of the target lesion has to be obtained byequally minimal- or non-invasive methods during allstages of the intervention. This information is vital toformulating the diagnosis, guiding the course of theintervention, and finally determining the success of theprocedure. From the beginning of vascular catheteriza-tion procedures, X-ray imaging has generally beenemployed for this purpose [3], and still is the methodof choice today. The use of X-rays allows for higherresolution and more free access to the patient thanmagnetic resonance imaging (MRI), and interferes

hardly or even not at all with the interventional instru-mentation in situ, as intravascular ultrasound imaging(IVUS) devices would do. Furthermore, roentgenogramshave long been well-acquainted companions to physi-cians and provide routine diagnostic information fornearly all parts of the body in a way equivalent — or,in fact, complementary — to visual examination.X-ray image formation is based on physical processesthat differ from conventional optics. However, this factnot only provides for the generic information availablethrough X-ray imaging, but also leads to resolutionlimits of this method that differ from accustomedoptical limitations. The effects of these limits areespecially likely to occur when very small structuresare viewed, which certainly ranks coronary stentsamong the most challenging objects for imaging. It isthe intention of this article to describe the informa-tion encompassed in X-ray images, as well as thelimitations to be expected. Based on the processesinvolved in image formation, consequences for thepractical imaging of coronary stents will be drawn

X-Ray Imaging of Coronary Stents

R. SCHMIEDL, M. SCHALDACHDepartment of Biomedical Engineering, University of Erlangen-Nuremberg, Germany

Summary

Accurate imaging of vessels and vessel implants is an essential prerequisite for the guidance of interventional pro-cedures and the assessment of their early and late outcome. Physicians, physicists, and technicians have long beenfamiliar with X-ray imaging as well as developing this technique into a well-established routine method with gen-eral applicability and acceptance. However, the degree of quantitative precision required to meet the potential ofcurrent cardiovascular interventional equipment is a challenge even for present-day fluoroscopy systems, espe-cially with such delicate structures as coronary stents. This article investigates the capability of X-ray imaging ina very general approach based on the physical foundations of the method. Factors affecting the success of theimaging process are the mechanisms that determine contrast formation and spatial resolution, but also aspects ofimage perception and interpretation. The survey of both the information content and the inherent limitations of X-ray imaging implies practical consequences for the qualitative imaging of coronary stents, and may even help toidentify and eliminate possible systematic changes to quantitative data induced by structures below the resolutionlimit of the instrument.

Key Words

X-ray, angiography, stent, imaging artifacts

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At the entrance of this assembly, a filter (F) is installedthat may be conceived as an array of tiny lead pipes ofless than a tenth of a millimeter in diameter each, withthe pipe axes oriented towards the tube (T). This filtereffectively absorbs rays that enter from lateral direc-tions, i.e., rays that must have undergone scattering.Scatter radiation would otherwise make the imagehazy and dull, as it bears a smooth intensity pattern thatwould no longer comply with simple projection rules.Conversely, unscattered X-rays entering from the tubedirection may freely pass through the pipes, and arefinally absorbed below in a thin fluorescent layer (L)that converts them into visible light. This light instant-ly provides the input pattern for the subsequent imageintensifier tube (II). Image amplification starts withone more conversion, this time into photoelectrons,which are electrostatically accelerated and focusedonto a fluorescent screen (S). There, they are recon-verted into visible light of greatly increased intensity.At long last, this screen image may be viewed eitherdirectly or using a video camera (C). The latter is com-mon practice today, allowing the physician to freelymove the detector as well as to reproduce the image on

and discussed as examples. Although they are of greatpractical significance, considerations concerning radi-ation safety are not within the scope of this article. Fora recent and thorough discussion of safety relatedissues covering biological effects, personnel exposure,shielding, etc., the reader is referred to Ref. [4].

Principles of the X-Ray Imaging Process

Instrumental SetupThe components of a typical fluoroscopy system areschematically depicted in Figure 1 [5]. X-rays are gen-erated in a vacuum tube (T) by irradiating a metalanode with electrons accelerated by a voltage U. Thetube is housed by a shielding that allows X-rays to exitonly through a window (W). The window defines theangular width and energetic quality of the radiation bymeans of adjustable shutters and filter foils, respec-tively. The rays then traverse the table and the patient(P), where they are partially scattered or absorbed. Asa consequence, the remaining rays now bear a shadowimage of the illuminated volume, and project this pat-tern onto the detector assembly (D).

Figure 1. A fluoroscopy system (left) and details of the detector assembly (right) in a schematic view. The flow of X-rays andvisible light is indicated by dashed lines, while thin full lines represent sample trajectories of electrons. See text for a descrip-tion of individual components.

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any number of screens, store it digitally, or apply elec-tronic image enhancement or quantification.

Signal Flow in X-Ray ImagingIn order to analyze image formation, it is instructive toexamine more closely the flow of signals involved inthe imaging process. As is well known, the stream ofX-rays that emerges from the tube consists of singleradiation quanta, or photons, each carrying some fixedamount of energy. Most of these photons are absorbedwithin the patient and just take effect as undesired ion-izing radiation. This energetic load to the patient isquantified in terms of the absorbed dose, which isdefined as the amount of energy imparted by radiationper mass. Obviously, it is vital to keep the patient doseas low as reasonably achievable ("ALARA" principle[5]). Routine use of an image intensifier within theimaging chain has significantly reduced dose require-ments and has eventually approached the fundamentaldosage limits as determined by the noise level of themeasurement: In a random stream of single entities,this noise level is governed by Poisson statistics anddepends directly on the (square root of the) number ofentities measured. Now, each X-ray photon that isabsorbed in the fluorescent layer (L) creates on theorder of 103 visible photons, the mean number varyingaccording to the X-photon energy. With a conversionefficiency of about 10 %, these visible photons releasesome 102 photoelectrons into the intensifier tube, eachof which in turn produces some 103 visible photons onthe output screen (S). Obviously, the number of entitiescarrying information is lowest at the fluorescent layer(L), which makes the noise level at this stage deter-mine the noise level of the final image. Current fluo-roscopy systems therefore strive for the goal of con-stant image quality at the lowest possible patient doseby adjusting the latter in order to keep the entrancedose to the detector at a constant level.Much instrumental development has focused on improv-ing the conversion efficiency, durability, and linearity ofthe components of the imaging chain. For the purposesof this article, today's instruments may be consideredapproximately ideal in these respects. The intensity ofthe light emitted from the image intensifier screen (S)well reproduces the radiation collected by the detector.To be precise, the screen intensity is proportional to theradiation dose (rather than to the number of photons),since in the initial fluorescence conversion event each X-ray photon is "weighted" according to its energy.

Key QuestionsBasically, from a very general point of view, an X-rayimage consists of different grey shades forming shapesthat correspond to the parts being imaged. This patternis presented to the observing physician for the purposeof giving a correct diagnosis. Therefore, in order toanalyze the process of X-ray imaging, the followingissues have to be dealt with:• What are the mechanisms that cause different grey

tones (contrast) to occur in the image?• Concerning shapes, what is the minimum size (res-

olution) that will still be imaged correctly?• Of all the information displayed in the image, what

kind is most suitable for recognition (perception) bythe physician?

Fundamentals of Image Formation I: Contrast

Extinction of X-RaysContrast in the X-ray pattern may be caused by anylocal effect that attenuates the amount of radiationtransmitted from the tube into the detector. In the rangeof X-ray energies typically employed in angiography(using voltages up to about 120 kV), the relevanteffects are scattering and absorption, which both arebased on the interaction between the X-ray photonsand the electrons within the irradiated specimen. Scattering events will change the direction of the pho-ton, and may or may not be accompanied by some lossin photon energy (termed inelastic or Compton scatter-ing vs. elastic or Rayleigh scattering, respectively).The probability of such events is mainly determined bythe number of electrons available per volume anddepends only slightly on photon energy.In an absorption event, the photon energy is complete-ly transferred to an electron which is thereby releasedfrom its bound state within an atom. Such a process isclearly limited to photon energies above a thresholdgiven by the binding energy of the electron. Withincreasing photon energy, therefore, additional elec-trons from the more tightly bound inner shells of theatoms become available for absorption events, whichgives rise to sharp "absorption edges" in the energydependence. Apart from that, the overall probability ofabsorption decreases strongly with increasing photonenergy, and increases with atomic number.Extinction of radiation by either of these mechanismsentails that, per distance x traversed, a well-definedfraction of all photons is lost from the direct path.

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involved has to be gathered, too. Generally, the X-rayspectrum as obtained from an electron-irradiated anodeis a sum of two components, termed "bremsstrahlung"and "characteristic radiation". Quanta of the former are emitted whenever electronsare decelerated in the electric field of the target nuclei.Therefore, such photons can carry any amount of ener-gy up to the full kinetic energy of the primary elec-trons. The energy spectrum is continuous and decreas-es almost linearly to zero at the primary electron ener-gy, as illustrated schematically by the dashed curve inFigure 3a [6]. Of all these photons, however, onlythose transmitted through the exit window of the tubewill be available for imaging. From the extinctioncurves in Figure 2, it is clear that the window willremove predominantly lower-energy quanta from theinitial distribution, causing the final shape of the spec-trum to be a broad peak as indicated by the full line inFigure 3a. On the other hand, characteristic radiation originatesfrom within single target atoms that have been ionizedby direct electron collision. This will provide only pho-tons at few well-defined energies, giving rise to narrowbut intense peaks that are characteristic of the emittingatom (Fig. 3a). However, in practice, this radiation isgenerally excluded from discussion, which may be jus-tified by two practical arguments: On the one hand,characteristic radiation depends not only on the anodematerial but may even strongly vary with minorchanges in acceleration voltage, especially when thisvoltage is only slightly above the ionization threshold(around 70 kV). The contribution of this component,therefore, is generally hard to predict. Fortunately, onthe other hand, the lines of the most common anodematerials W and Re are located near 60 keV, which isclose to the center of the broad continuum peak understandard angiographic conditions. Thus, to a greatextent, the information these lines convey is alreadycontained in the continuum radiation image. For prac-tical calculations, it is therefore sufficient to describethe spectrum approximately by the bremsstrahlungcomponent only, which will allow for at least a goodquantitative estimate of the contrast caused by a givenobject.

Calculating Image ContrastThe decisive quantity for image contrast is the intensi-ty at the output screen. Since each photon contributesto this intensity according to its energy, the number of

For a parallel beam of photons, such a decrease in inten-sity I is mathematically described by Beer's Law [6],

Figure 2. Energy dependence of the X-ray extinction lengthλ for selected homogeneous materials. 1 eV (electron Volt)corresponds to the amount of energy acquired by an elec-tron at 1 V acceleration voltage, 1 eV = 1.6 ⋅ 10-19 J.

(1)

where I0 stands for the intensity at x = 0, and λ is acharacteristic extinction length denoting the distancerequired for a decrease to 1/e ≈ 37 %. The extinctionlength is inversely proportional to the probability of anextinction event, and thus is a function of atomic num-ber, material density, and photon energy. Tabulatedvalues of λ are reproduced in Figure 2 for selectedorganic and metallic materials. Note that the extinctionlength may vary between different materials by up tothree orders of magnitude in the energy range most rel-evant to angiography. From data like those presented inFigure 2, it is straightforward to determine the attenu-ation of transmitted intensity, or extinction, that agiven object will bring about at a given photon energy.

The X-Ray SpectrumIn order to assess the total contrast of the object, inaddition to extinction data, information on the rangeand spectral distribution of the photon energies

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photons, N(E), has to be weighted by the photon ener-gy E in order to render the screen effect correctly.Figure 3b displays the resulting "effective tube spec-trum" which has its maximum at slightly higher ener-gies than the photon distribution in Figure 3a.Introducing an object into the X-ray path will lead toextinction of radiation in an energy-dependent waydetermined by the extinction length λ(E) (see Figure 2)and the object thickness D, as described by Equation 1.The total screen intensity IS may then be calculated bysumming up contributions from all energies E,

reduces the overall intensity level (note the scaling fac-tor applied to the effective tube spectrum for plotting).Only 4 % of the intensity without object is retained inthis example, which means that 96 % of the total radi-ation dose is lost within the "patient". Adding a layerof iron that represents an 80 µm stent strut hardlyaffects the transmitted spectrum at all. Covering bothsides of the iron foil with 9 µm Au, however, results ina much greater spectral change that visually indicatesenhanced contrast. In order to provide a quantitative measure of the con-trast C between an "object" and the surrounding"background", the following expression is calculated:

Figure 3. (a) Approximate energy distribution of X-ray photons at 95 kV electron acceleration voltage, as emitted from a W anode, and subsequently filtered by an X-ray tube exit window consisting of a 3 mm Al layer plus a 0.2 mm Cu foil. Theintensity of the characteristic W radiation (Kα and Kβ lines) is not necessarily to scale. (b) Spectral contributions to the screenintensity for the imaging of a "stent strut" (iron foil) with and without a gold "marker" layer. The effective tube spectrum hasbeen reduced by a factor of 15 for plotting.

(2)

where the first two factors of the integrand describe theapproximate tube spectrum shown in Figure 3a, i.e., alinear decrease down to the maximum energy Emax

combined with attenuation according to the extinctionlength λW(E) and thickness DW of the exit window. Theeffective tube spectrum in Figure 3b is accordinglygiven by the first three factors of the integrand. As an example, a typical situation for the imaging of acoronary stent is shown in Figure 3b. The objectassumed consists of 150 mm soft tissue, representing anot too oblique view through a normal-weight patient[7].1 Again, extinction removes predominantly lower-energy radiation from the spectrum, and greatly

(3)

1 The air in the lungs as well as elsewhere in the imaging path canbe validly neglected in these considerations due to its low andessentially constant density.

where IO and IB denote the screen intensity within theobject and background area, respectively. The use of apercentage quantity is recommended because of theeye's capability to adapt to varying illumination condi-tions, and by the way this renders the missing constantfactor in Equation 2 irrelevant. Normalizing to the sumrather than to the larger of the two intensities yields a

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This consideration is of quite general validity, becausethe mean image intensifier dose is just the quantity thatis always regulated to a pre-set value. In angiographicimages, therefore, the "background" which is formedby thorax tissue of comparatively little contrast isbrought to exactly this mean dose level by the imagequality control loop. Although the precise numericalvalue of course depends on all the parameters men-tioned above, practically useful parameter combina-tions will always end up with a similar noise levelunless the dose is significantly increased. Therefore, apicture element generally should display more thanabout 10 % contrast in order to be classified as repre-senting an object distinct from the background.

Fundamentals of Image Formation II: Resolution

General ConsiderationsUnlike visible light, X-rays cannot be focused by anoptical lens. The only feasible way to transfer spatialinformation by means of X-rays is therefore to projecta shadow image using radiation from a point source.Although such a geometric projection from a pointsource ideally has no inherent restrictions on resolu-tion, real devices are made up of non-ideal componentsthat introduce characteristic resolution limits. When trying to quantify resolution, however, one soonrealizes that there is virtually no measure of resolutionthat is independent of contrast. In common parlance,"low resolution" denotes a blurred image, which meansthat the screen intensity at any location is partiallyspread out over its neighborhood and averaged withcontributions spread back from the surroundings. Inmost cases, averaging is incomplete, so that, after all,the contrast detection limit determines whether or notany remaining structure can be found in the blurredimage. This limit, in turn, depends on the length scaleof the measurement, as can be seen by continuing thetrain of thought outlined in the previous section: If thelength scale of interest is given by two picture ele-ments rather than by a single one (with all imagingconditions unchanged), the intensity level of a "2 × 2"area will be determined by 22 ⋅ 130 = 520 photons, witha noise level of 23 photons or only 4.4 %. In thisimage, therefore, a "2 × 2" object of 7 % contrast isdetectable, whereas a "1 × 1" object of the same con-trast is not (see Figure 4). Conversely, taking anotherimage with just four times the dose (or equivalently,adding up four independent images of the previous dose)

more symmetric expression and follows common prac-tice in optics as well as in communications technology[5]. By this definition, zero contrast corresponds toequal screen intensities, while 100 % contrast meanscomplete extinction within the object area. In the aboveexample, the background is provided by the tissue layeralone, and contrast values of 3.4 % and 12.2 % result forthe bare and the gold covered steel object, respectively.This quantifies the efficacy of a thin gold layer to pro-duce X-ray contrast, i.e., to serve as an X-ray marker.

Contrast LimitationsAs stated, current angiographic equipment does notpresent the intensifier output screen image directly, butrecords this image electronically and transfers it to aviewing screen. By electronic amplification in thecourse of this transfer, contrast and brightness of theresulting image may be freely adjusted, so that onemight expect that in principle any non-zero contrastcould be made manifest. However, the noise in theimage is amplified just as much as the signal. Thismeans that the signal intensity has a fixed percentageuncertainty that the object contrast must exceed inorder to become visible. The contrast limit is thereforeultimately determined by the X-ray photon statisticsthat govern the noise level, and can be estimated in thefollowing way: The image intensifier dose commonly recommended for asingle image of documentational quality is D = 100 nGy(nano Gray, 1 Gy = 1 J/kg) when using a 17 cmentrance field [8]. As this dose is measured in terms ofradiation energy per mass of body tissue rather than ofdetector material, the corresponding amount of energyis most easily calculated by assuming body tissueabsorption characteristics for the detector, too, and byusing infinite thickness to ensure 100 % absorption. Atan irradiated area A, the absorbed energy is related tothe dose via E = D ⋅ A ⋅ λ ⋅ ρ, where λ and ρ denoteextinction length and density of the hypothetical "bodytissue" detector, respectively. For an average photonenergy of around 60 keV, Figure 2 gives λ ≈ 5 cm. Thisresults in a total energy of 1.1 ⋅ 10−7 J, which is equiv-alent to roughly 1.2 ⋅ 107 photons of 60 keV beingabsorbed in the detector. If the picture is formed fromindependent elements about 0.5 mm in size (this num-ber will be accounted for in the next section), each ele-ment within the circular illuminated area will thenreceive about 130 photons, with a standard deviation of1301/2 = 11.4 photons, or 8.8 % noise level.

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would render even the smaller object visible, although theinstrument certainly has not been changed. Obviously the"resolution" that characterizes the imaging capabilities ofa given fluoroscopy system is by no means a rigorous"ultimate limit", but rather denotes the "critical lengthscale" of the progressive contrast loss in the imaging ofsmaller objects. In the context of projection, one technical remark isrequired to avoid possible confusion. As is clear fromFigure 1, the projected pattern will always be larger thanthe original object, with the sizes scaling as the distancesfrom the point source. By varying these distances, magni-fication factors ranging from little above 1 up to morethan 2 can be achieved in practice. Correspondingly, how-ever, resolution limits imposed by devices external to theprojecting beam will yield variable apparent resolutionsin the object plane. For the sake of simplicity, therefore,all resolution data given in the following account willrefer to the projected image at the entrance plane of thedetector rather than to the object. This will allow descrip-tion of all the different effects in a consistent way, whileresults may readily be re-scaled to the actual object size.

Critical Length Scales for Contrast TransferThe overall resolution of a fluoroscopy system is deter-mined by a number of individual contributions related tothe specific amount of blurring induced by each of itscomponents. To start right within the X-ray tube [(T) inFigure 1], the non-zero size of the X-ray emitting spotwill cause the shadow of a sharp object edge to form acontinuous transition. The width of this transition in theprojected image is given by the size of the electron-irra-diated spot scaled according to the distances of detectorand tube from the object edge. At a projection magnifi-cation of 1.5, for example, a 0.5 mm spot size wouldsmear out a sharp edge across 0.25 mm in the detectorplane. However, it should be noted that the specifiedspot size actually denotes the outer tailing of the electrondistribution, while most of the radiation is emitted fromwell nearer to the center of the spot. Thus, actually mostof the change in the image concentrates around the cen-ter of the estimated transition width, resulting in consid-erably (of the order of 50 %) less significant widening. During projection itself, spatial information can bedegraded by photon scattering, which contributes tothe image to an extent determined by the filter array[(F) in Figure 1]. With the pipes of the filter being offinite width and length, X-rays will pass through a pipeeven if they enter from a direction slightly deviatingfrom the pipe axis, i.e., after a small angle scatteringevent at a laterally shifted object position. However,supposing that the pipe height is 8 times the pipe diam-eter, the average object area from which photons willhave a nonzero chance to pass, the filter will have aradius of 1/8 of the object-to-filter distance, which is alength well within the centimeter range and large com-pared to typical object structures. Therefore, the scat-tered component is sampled from so wide an area that,in effect, it merely adds up to an additional homoge-neous "background" signal.2

By itself, the filter array (F) does not degrade resolu-tion in a strict sense. However, the absorbing walls ofthe filter pipes inevitably introduce a regular patterninto the projected image, e.g., a 40 per mm periodicity.As this pattern is generated only just before the X-raysare absorbed, it cannot be blurred by the previouseffects. Yet it certainly is an undesired addition thatshould not be present in the final image, and thus evencreates a need for further blurring.

Figure 4. Contrast detection limits in a noisy image. In thetest pattern (a), the contrast of the top, middle, and bottomtriplet of squares is 10 %, 7 %, and 18 %, respectively. At a9 % noise level (b), the small squares in the upper and mid-dle set end up near and below the detection limit, respec-tively. However, larger objects of even the lower contraststill show up clearly against the noise, as do the smallsquares of higher contrast. The size of the small squares hasbeen chosen so as to match the "independent picture ele-ment" of the noise image.

2 Precisely this component is responsible for the increasing amountof grey veil at higher tube voltages, since scattering events prevailat higher photon energies.

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bution to the former and generally corresponds to aconsiderably smaller distance, as shown by the valuesquoted above. From that, it becomes clear that objectssmaller than the "resolution limit" may still show up inthe final image, although their specific intensity levelwill have spread out into and mixed with the intensityof all the surrounding area within the reach of the esti-mated critical length.

Fundamentals of Image Formation III: Perception

The last step in the imaging chain — and in somerespects, the most decisive one — is perception of themonitor image by the physician. This process is gov-erned by the "technical" aspects of the human sense ofsight as well as by more "non-technical" aspects of theinterplay between eye and brain giving rise to objectperception and interpretation [5]. Some of theseaspects will be highlighted now.

"Technical" AspectsThe considerations on contrast and image noise present-ed above relate to single shot X-ray images.Nevertheless, images are also commonly obtained aspart of a time series, e.g., within the time span of a videoframe. However, it is well known that the eye is not ableto perceive individual frames at such speed (which ofcourse was chosen for exactly that reason). What is"measured" by the retina therefore corresponds rather tothe time average of a number of frames, governed by atime constant of the order of 0.2 seconds [5]. Since theresulting retina image is thus defined by a larger dosethan the single video frame, the apparent noise level willcorrespondingly decrease. Provided that the object doesnot move or change, this will improve the minimumdetectable contrast, and will most probably make it pos-sible to detect more details in a frame series than in anysingle frame of this series. Conversely, this effect mayalso be exploited the other way round in pursuit of theALARA principle, as it allows one to use a reduceddose per frame during pulsed fluoroscopy withoutapparent loss in image quality. This is a common rec-ommendation in practice [8]. In a similar way, the visual acuity may also affect theinformation transfer. If individual picture elements onthe viewing screen cannot be resolved, they will mergeinto an average intensity. Consequently, the apparentresolution will degrade, although the same merging ofelements will make the image look less noisy. Yet this

In the fluorescent layer (L), each X photon releases ashower of visible photons which are no longer con-strained to a specific direction. The effective photo-cathode area illuminated by a single shower thereforedepends on the average spreading of the visible pho-tons, for which the thickness of the absorbing layergives an approximate (rather, upper) limit in the low0.1 mm range. Like the visible photons, the photoelectrons are alsoemitted almost isotropically into the intensifier tube (II),but the electrostatic lens formed by the electric fieldswithin the tube forces the electrons to re-focus on theexit screen (S). However, aberrations of such a lens areinherently larger than those of an optical lens. Blurringcaused by the aberrations corresponds to a width ofabout 0.2 - 0.3 mm in the detector entrance plane. Finally, in the last stage of the detector assembly theimage on the screen (S) is recorded by a camera and dig-itized into a 512 × 512 or 1024 × 1024 grid. While noperceptible image distortion is caused by the granularityof the screen phosphorus or by the camera optics, thedigital recording introduces a "hard limit" on resolution,because all information possibly contained within a dig-ital picture cell ("pixel") is replaced by the cell's averageintensity. As the image intensifier allows changing of themagnification of the screen image within certain limits,the area in the detector plane that corresponds to a singlecell will vary accordingly. Using a 17 cm entrance fieldand a 1024 × 1024 grid, for example, yields an effectivepixel size of 17 cm / 1024 ≈ 0.17 mm. With all of these components degrading resolutionindependently from each other, the overall criticallength of contrast transfer, or overall blurring width,may be regarded as a total position uncertainty, andaccordingly may be computed by quadratic addition ofall the independent contributions. Taking only the lowestnumbers given, one arrives at a best estimate of 0.3 mm,but standard image intensifier quality and camera pixelresolution render a value of at least 0.5 mm more real-istic, especially for older fluoroscopic systems. Asalready stated, this length denotes a minimum sizeobjects should have in order to be imaged without sig-nificant contrast loss. With regard to blurring, it canalso be regarded as the minimum distance that must liebetween two points for their intensity levels not to bemixed into each other. Still in other words, it stands forthe effective size of the smallest independent pictureelement. This must not be confused with the pixel ofthe digital viewing monitor, which is just one contri-

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should not be a matter of concern in practice, sincethese effects may be readily controlled by proper siz-ing and positioning of the viewing screen.

Pattern Recognition and InterpretationIn general, the physical and neurophysiological aspectsof image perception are entwined functionally just aseye and brain are anatomically. Many features onlydevelop from the mutual interplay within the percep-tion network, and at varying stages of abstraction. Onesuch example, of particular significance for X-rayimaging, is the ability of the visual system to choosethe length scale of interest almost at will, and even tosuppress the perception of patterns on other scalesonce they have been identified as, e.g., "slowly varyingbackground" or "noise". Therefore, an extended objectof interest will be assigned a characteristic intensitylevel that is obtained by essentially an average takenacross the object's area, which in turn allows the aboveconsiderations on minimum detectable contrast versusobject size to be applied correspondingly. Another example intended to illustrate the interplay ofvisual input and observer's knowledge in the perceptionprocess is shown in Figure 5. The black-on-white patternpresented seems quite random at first and probably evensecond glance. On prolonged inspection, however, theblotches eventually make sense and may be interpreted

to depict a rider on horseback. It is most notable thatonce this shape has been identified, it will immediatelybe re-established when looking again at this image. Thisclearly demonstrates that a pattern that is expected orknown to occur in the image can be easily perceivedeven if it is heavily distorted. On the other hand, un-known or unexpected shapes are liable to be regarded asrandom noise at a far lower level of distortion. There is a vast number of further "non-technical" fac-tors that affect the processes of reading, understanding,and interpreting visual information. Among them arefundamental ones like general visual ability, state ofeducation or practical experience, or — much less easyto assess — comprehension, mental acuity, and evenimagination. Other factors depend rather on the givensituation, like eye adaptation time after illuminationchanges, fatigue of sense of sight after prolonged duty,or the presence of complications that force attention tobe focused on them. Susceptibility to each of theseinfluences may vary widely due to personal disposition,or physical condition even within one individual, andno attempt will be made here to claim enough under-standing of the physiological and neurological process-es involved to propose an imaging strategy that is opti-mized along such lines. Instead, the following discus-sion will focus on practical consequences for X-rayimaging that can be drawn from the general considera-tions presented above, with some emphasis on coro-nary stents.

Discussion

Imaging of Single Objects: Struts of a Coronary StentThe general condition for X-ray visibility an objectmust fulfil is to provide a level of contrast within thearea it is projected to that is sufficient to be detectedabove the noise level of the image. As a rule of thumb,about 10 % contrast will be required across the area ofan independent picture element, which is commonly ofthe order of 0.3 - 0.5 mm in diameter with currentinstrumentation. An object of larger diameter may bedetected at a correspondingly lower contrast, becausethe effective noise level decreases when short-scalevariations are averaged out. However, object size is notalways the length scale of interest: For example, whenthe borders of a large object have to be tracked downto a desired accuracy, the length scale to define theeffective noise will be just the tolerance allowed.Contrast requirements will increase accordingly, as is

Figure 5. Example illustrating the interplay between theinformation presented by the image and pattern-findingprocesses added by the observer during perception of theimage content [5].

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that lies far above the detection limit. In this way, areproducible pattern is established that is independentof a particular stent orientation and thus provides areliable base for imaging.

Imaging of Combined Objects: Angiography of aStented VesselIn principle, imaging of combined objects does notintroduce any fundamentally new feature apart fromthe obvious need to calculate the extinction by cumu-lating all contributions along the projection path.Again the resulting contrast may then be assessed byblurring the contrast of the ideal X-ray pattern on thescale of the critical resolution length. Trivial as thisissue may seem (and essentially is), it nevertheless pro-vides the key answer to a subtle problem that — para-doxically — arises from nothing other than sophisti-cated evaluation of X-ray images:Quantitative coronary angiography (QCA) allows thediameter of a vessel to be determined with an accuracythat is better than 0.1 mm. From the above considera-tions, however, it is clear that information of this spa-tial precision is not provided by the X-ray image, atleast not at normal image dose levels. Nevertheless, ifsome information on the object is known beforehand,the information content of the image that normally

common experience with precision measurements. Onthe other hand, the characteristic contrast of objects orstructures of a diameter smaller than the independentpicture element will be distributed throughout an areaof the size of the independent picture element, suchthat the contrast at a given point will be an averagecontrast sampled from a surrounding area of the samesize. Therefore, the contrast of a small structure willonly be sufficient if the 10 % limit is exceeded evenafter the area average has been performed. Taking the imaging of struts of a coronary stent as anexample, under idealized conditions a 12.2 % contrasthas been predicted earlier for a gold/iron combinationthat models the sandwich structure of a strut with a"marker" layer (see Figure 3b and related text). Beingtypically 100 µm wide and generally much longer thanthe critical length of 0.5 mm (or alternatively, 0.3 mm),the strut will occupy about 20 % (33 %) of the averag-ing area, which decreases the maximum contrastachieved to 2.5 % (4 %). Taking into account that theside walls of the strut are also covered with gold, cor-responding calculations predict that the total contrastwill peak at 4 % (6.3 %) after averaging. This is clear-ly not enough to allow detection of a single strut understandard imaging conditions. However, frequently another strut from the other sideof the stent tube will come up next to the first strut inthe projected image, thereby effectively doubling thepercentage of strut area within the blurring range, andthus also doubling the resulting contrast. Similarly,contrast is enhanced if the second strut lies just withinthe shadow of the first one, because now extinction isnearly doubled in this area ("nearly" because the sec-ond strut receives only radiation already attenuated bythe first strut). Strut-like features are therefore likely toreach the detection limit especially if the front andback sides of the stent tube appear "aligned" to eachother, while "random" orientation will rather producelower and diffuse contrast without discernible struc-tures. The situation is illustrated in Figure 6 for a seg-ment of a Tenax XR coronary stent (Biotronik,Germany), demonstrating that images calculated fromthe above considerations are found to match well toexperimental data. Figure 6 also shows that, whereasthe actual strut orientation is clearly a matter of chancenear the tube axis, the situation is by far better definedat the sides of the stent tube. Here, several struts accu-mulate within each other's blurring width in more orless the same orientation, resulting in a stable contrast

Figure 6. Effect of finite resolution on the appearance of asegment of the Tenax XR coronary stent. The upper andlower row correspond to a "near-aligned" and a "random"strut orientation, respectively. Left: Calculated ideal X-raypatterns; Middle: Same patterns but at limited resolutionand scaled to the experiment; Right: Experimental imagesobtained with a Siemens Neurostar Plus system providingabout 0.3 mm resolution.

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would identify the object may instead be used toincrease spatial precision: In the case of QCA, theobject is essentially a cylindrical volume that is filledwith a solution of contrast agent and is viewed perpen-dicular to the cylinder axis. Thus, the contrast changeacross the vessel diameter can be calculated theoreti-cally for ideal imaging conditions as well as for theactual resolution of a given instrument (Figure 7a,"artery"). In the resulting profile of the contrast onset,the position of the vessel edge is exactly known fromtheory, which changes the task of edge detection intodetermining the position of the onset region within theimage. However, looking for the onset pattern impliessampling data across a range equal to the predictedonset width. Due to this larger range, the correspond-ing noise level is substantially reduced-and thereby,positioning precision increased-as compared to sam-pling only across a range of the independent pictureelement, let alone the targeted tolerance width. In prac-tical terms, rather than matching a calculated onsetprofile to patterns in the image, an "edge detection"algorithm is applied to the image that is sensitive to thedesired kind of correlated changes. Results of this fil-tering algorithm are superimposed on the originalimage to present "sharpened" edges to the observingphysician as well as to the software that evaluatesquantitative angiographic data. The problem mentioned arises when the QCA systemis confronted with an object that has a non-cylindrical

contrast profile. While the edge of an artery is general-ly cylindrical to a good approximation even in anasymmetric stenosis, a stent provides an X-ray patternwith narrow regions of extreme contrast right at theedges. The "stent" curves in Figure 7 illustrate this forthe case of a "generalized" stent tube, which has beencalculated assuming an equivalent homogeneous mate-rial distribution across the tube surface in order tobecome independent of a peculiar strut configurationand orientation. Blurring the ideal patterns as in thereal image most obviously redistributes the narrowstent contrast into broad peaks, while the artery edgesare apparently less affected due to the smoother origi-nal profile. Therefore, the combined contrast will gen-erally display a significantly broader pattern with astent than without. Of course, the precise extent ofbroadening will depend on the actual artery and stentextinction, but calculations show that it will usually beof the order of the resolution width unless the contrastagent induces near full X-ray extinction around theartery center.3 Smaller but still significant effects arepredicted even for less visible stents, e.g., with puresteel struts only. Since the QCA system does not knowabout the presence of the stent, this will inevitablyresult in local overestimation of the lumen diameter by

Figure 7. (a) Calculated contrast profiles for a "generalized" stent tube and a cylindrical artery, as well as the resulting pro-file of the stented vessel. Thin and thick lines correspond to zero and 0.3 mm blurring width, respectively. (b) Visualization ofthe same effect using a more realistic stent pattern resembling the X-ray charateristics of the Tenax XR stent.

3 This condition is not equivalent to 100 % artery contrast on themonitor, but applies independently of the monitor's brightness andcontrast settings.

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obstruction of lumen measurements just around thestent center, which is usually located near the most crit-ical part of the lesion. The marker thickness is suchthat even at the ends of the stent, only the sides of thetube present a truly significant contrast, while theartery center is still comparatively open. At the resolu-tion capabilities of current instruments, the segmentside presents an elongated shape (Figure 6) that distin-guishes the marker blot from point-like noise which isprone to be filtered out either by the eye or if electron-ic image enhancement is applied. Moreover, the totalpattern is formed by a pair of blots connected by aregion of less contrast, which facilitates perception ascompared to a single blot. Still, as for any other metalstent, the side effects on quantitative angiography dis-cussed above apply, giving rise to the dumb-bell-likeappearance of a stented vessel that contains contrastagent (Figure 7). Finally, all the fundamental considerations presentedabove make a simple method seem feasible that shouldtheoretically allow for improvements in stent imagingunder almost any set of circumstances: It has beenestablished that the stent contrast contained in the X-ray pattern is blurred across the range of an indepen-dent image element, whereby the contrast decreasesdue to mixing with surrounding intensity and eventual-ly falls below the detection limit of the noise. Now, oneapproach that certainly will improve visibility is todecrease the noise; yet this requires higher dose levelswhich are undesired for obvious reasons. The alterna-tive idea therefore is to increase the contrast byincreasing the share of the stent pattern within the blur-ring range. Since the pattern originates from the stentlocation within the patient while the blurring is deter-mined mainly after the detector entrance, the idea canbe realized by increasing the size of the projected X-ray pattern on the detector entrance plane, in otherwords by retracting the detector assembly from thepatient as far as compatible with the required field ofview. Note that the total image dose should not beaffected by this maneuver. Although this setting meansusing the maximum entrance field of the image inten-sifier, which is commonly associated with larger aber-rations, these additional aberrations are well tolerateddue to the larger detector entrance pattern. A net bene-fit of increased contrast within the stent's blurringwidth is expected to result, which should bring agreater fraction of the stent pattern above the detectionlimit and thereby improve perceptibility.

about 1 - 2 times the resolution width for a stent withan X-ray opaque layer, and up to about half that valuefor a steel-only stent. This effect may even account fordeviations from the usual correlation between QCAand IVUS that have been reported to occur withinstented lesions [9], with the apparent underestimationby IVUS most probably being rather an actual overes-timation of the real lumen by QCA. Moreover, QCAwill not only yield a systematic error in a stentedregion, but may even obscure the problem's origin tothe physician because filtering the image for QCAtends to suppress small contrast changes along theartery that otherwise would signify the onset of thestent (like those in the blurred patterns of Figure 7b).Thus, it is left to the physician in charge to identify thisartificial broadening and to correctly interpret mea-sured results.

Optimizing Stent ContrastConsidering that the ultimate purpose of X-ray imag-ing is to help provide a correct diagnosis, there are atleast two diagnostic questions that lead to conflictingcriteria for an optimized stent contrast: On the onehand, as an implant, the stent must allow the physicianto locate it in the body, which might be vital in choos-ing the appropriate technique for a subsequent inter-vention or even for recovering a stent in one of the rarecases it is lost from the balloon. Optimizing stent visi-bility even under adverse instrumental resolution ispossible by maximizing the extinction of the struts,i.e., by using X-ray opaque materials of high atomicnumber rather than steel. On the other hand, the defin-itive purpose of the stent is to maintain lumen patency,which is therefore the clinically important criterion ofsuccessful stent implantation. The stent thus must notimpede lumen measurements in the stented region,and, accordingly, should be visible as little as possible.On the whole, "optimum" visibility is largely a matterof personal preference of the physician and cannot beachieved by a single stent once and for all. In this respect, the Biotronik Tenax XR stent providesan interesting and unique balance between the con-flicting goals described. It is a stainless steel stentmade up of several circular segments where only thefirst and last segment bear an X-ray opaque markerlayer (9 µm Au) as described above. The entire surfaceof the stent is covered by a hemocompatible a-SiClayer that is essentially invisible to X-rays. From theviewpoint of X-ray imaging, this design minimizes

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Conclusion

X-ray imaging is an invaluable tool for non-invasivediagnostic purposes. Long acquaintance of both tech-nicians and physicians with the method has led tosophisticated and optimized equipment. However, vas-cular interventional techniques have only recently cre-ated the need to image increasingly fine structures in aquantitative way, with structures of only a tenth of amillimeter in size as provided by coronary stents beingcertainly among the most demanding objects for cur-rent imaging instrumentation. It should thus not be sur-prising that well-established procedures for imageenhancement which have been developed and opti-mized for anatomical structures will in general provedetrimental to the imaging of "unexpected" additionsand modifications to the vascular system; indeed theseprocedures were positively designed to suppressunwanted structures. Therefore, the physician performing interventionalprocedures should be aware of the limitations of cur-rent imaging devices, and should especially keep inmind the possibility of pitfalls induced by the sameimage enhancement procedures that have been proven— and will continue — to be helpful in so many rou-tine applications. In some cases, it may even be best toturn off electronic filtering entirely, which at least willshow the object pattern with as little modification aspossible (i.e., with only the blurring inherent to the res-olution). In particular, QCA results obtained fromstented vessels should be viewed with great care, sinceapparent broadening due to the stent contrast may eas-ily be misinterpreted as an enlarged lumen. If this hap-pens at the lesion site, it may result in overestimationof dilatation success; but if broadening concentratesaround X-ray opaque stent ends, it may be erroneouslyused as the reference diameter and will lead to a corre-sponding underestimation of lumen gain. Unfortunately, there is no obvious feature that would

indicate if the image is free from the discussed effects.Thus it is left to the physician's experience, acquain-tance with the fluoroscopy system, and knowledge ofthe patient's history to decide if a given X-ray imageallows one to trust one's eyes. For ultimately not theimage quality, nor noise level or any other single para-meter of the imaging chain will decide about the suc-cess of imaging, but only the percentage of correctdiagnoses enabled.

Acknowledgement

We gratefully acknowledge the support we receivedfrom the Angiography Department at Siemens AG,Medical Engineering (Forchheim, Germany), particu-larly its experimental data and helpful discussions.

References

[1] King SB. The development of interventional cardiology. JAm Coll Cardiol. 1998; 31(4B): 64B-88B.

[2] Kutryk MJB, Serruys P W. Cororary Stenting - CurrentPerspectives. Martin Dunitz, London: 1999.

[3] Forssmann W. The catheterization of the right side of theheart. Klin Wochenschr. 1929; 8: 2085.

[4] Limacher MC, Douglas P , Germano G, et al. Radiation safe-ty in the practice of cardiology. J Am Coll Cardiol. 1998;31(4): 892-913.

[5] Gebauer A, Lissner J, Schott O. Das Röntgenfernsehen.Georg Thieme Verlag, Stuttgart, 1974.

[6] Gerthsen C, Kneser HO, Vogel H. Physik. Springer Verlag,Berlin, 1982.

[7] DIN V 13273-7: Katheter für den medizinischen Bereich - Teil 7: Bestimmmung der Röntgenstrahlschwächung vonKathetern, Anforderungen und Prüfung. 1996.

[8] Serruys PW, Kutryk MJB. Handbook of Coronary Stents.Martin Dunitz, London, 2000: 307-312.

[9] Hoffmann R, Mintz GS, Popma JJ, et al. Overestimation ofacute lumen gain and late lumen loss by quantitative coronaryangiography (compared with intravascular ultrasound) instented lesions. Am J Cardiol. 1997; 80(10): 1277-1281.

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