Ординатура / Офтальмология / Английские материалы / Automated Image Detection of Retinal Pathology_Jelinek, Cree_2009

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which can be found in the literature as early as 1879 [25]. The principal objective of this parameter is to provide sensitivity to general arterial narrowing, while reducing the impact of refractive variation through normalization by the venous diameter. Confirmation of the insensitivity of AVR to refraction has been reported by Wong et al. [24].

Stokoe and Turner [25] drew attention to the importance of calculating the AVR from measurements of arterial and venous diameters at comparable orders of division in their respective vascular trees, and also highlighted the practical difficulty of achieving this, not least because the more peripheral retinal arteries and veins tend to be dissociated. In order to overcome some of these problems, the AVR for a single eye has commonly been calculated by a technique based on work originated by Parr and Spears [26; 27], and subsequently modified by Hubbard [28], in which diameter measurements of a series of arteries or veins are combined into an equivalent diameter of the central retinal artery or vein, respectively. The ratio of these equivalent central vessel diameters can then be calculated to yield the AVR.

Parr and Spears derived an empirical formula relating vessel diameters at an arterial bifurcation, based on measurements from a sample of red-free monochrome retinal photographs of normotensive adults [26]. Their approach was guided by the observation that the ratio of areas of the daughter vessels to that of the parent generally decreased with increasing asymmetry of the bifurcation, suggesting a general form of an expression relating the diameters. A computer search algorithm was used to determine the parameters based on a least-squares criterion, yielding a relationship giving the parent arterial diameter

q

da0 = 0:87da22 + 1:01da21 0:22da1 da2 10:76 (10.1)

where da1 and da2 are the diameters of the larger and smaller daughter vessels respectively, all measured in mm. An equivalent formula for the veins was later derived by Hubbard by a similar approach, giving the parent venous diameter as

q

dv0 = 0:72dv22 + 0:91dv21 + 450:05 (10.2)

where dv1 and dv2 are defined in the same way as for the arteries, also measured in mm.

In order to yield the central vessel equivalent diameter from a series of arterial diameter measurements, Hubbard [28] proposed a simplified pairing of vessels, compared to the original Parr and Spears technique that involved reconstructing the actual arterial tree [27]. In the simplified scheme, the largest vessel is paired with the smallest, the next largest with the next smallest and so on, irrespective of the bifurcations actually observed. The parent vessel diameters are calculated by the appropriate formula, and are carried together with any odd remaining vessel to the next order of division where the pairing procedure is repeated. The process is continued until a diameter estimate for the single central vessel has been achieved. This process is illustrated in Figure 10.1(a), where measured arterial vessels [27] are shown in the left-hand column, and the diameters of subsequent orders of vessels are calculated by

the Parr and Spears empirical formula, eventually yielding the equivalent diameter of the central retinal artery, dcra.

The process is repeated separately for the venous tree, yielding the equivalent diameter of the central retinal vein, dcrv. Hence the arterial to venous ratio is given by

In a previously unpublished analysis, we have compared the diameter relationships predicted at an arterial bifurcation by the empirical Parr and Spears formula with those suggested theoretically in an optimum bifurcation by Murray’s Law [29], as discussed in the following section. In perfectly symmetrical bifurcations, the Parr and Spears formula consistently gives rise to a parent diameter in the region of 2.2% greater than that indicated by Murray’s Law, but more importantly, this relationship appears to be maintained within a tolerance of better than 0:5% of parent diameter over a wide range of bifurcations, the only exceptions being cases of extreme asymmetry. This consistency between the empirical Parr and Spears approach and the theoretical treatment by Murray should not be unexpected, bearing in mind that the Parr and Spears formula was derived from images of healthy normotensive subjects. It suggests that the AVR calculated by the Parr, Spears and Hubbard technique might be sensitive not only to general arterial narrowing, but also to deviations from the optimal bifurcation geometry predicted by Murray’s Law.

The Parr and Spears technique depends on measurement of all vessel diameters being undertaken at a consistent location in the vascular tree. One approach to achieve this involves an annular grid, consisting of concentric rings centered on the optic disc, superimposed on a retinal image [28]. Diameter measurements are taken from all vessels traversing a measurement zone between the concentric rings, as illustrated in Figure 10.1(b), before being combined by the method described earlier to yield their central vessel equivalent diameters, from which the AVR can be calculated.

10.2.2Bifurcation geometry

The geometry of bifurcating vessels may have a significant impact on the hemodynamics of the vascular network. Important parameters characterizing the geometry of an arterial bifurcation are the bifurcation angle y, defined as the internal angle between the daughter vessels, and the junction exponent x, defined by the relationship

where d0 and d1, d2 are the diameters of the parent and daughter vessels respectively. Early work by Murray [29; 30] predicted that optimum values of both the junction exponent and bifurcation angle should exist, minimizing the power required to maintain circulation through the bifurcation (including losses due to viscous drag, and the metabolic energy to maintain the blood and tissue volume). Murray indicated that the optimum value of the junction exponent is 3, generally referred to as Murray’s Law. Sherman [31] and LaBarbera [32], based on data from a variety of other workers, have shown that with the exception of the very largest vessels, healthy arteries

(b)

FIGURE 10.1

Measurement of AVR by Parr, Spears, and Hubbard technique: (a) derivation of central retinal arterial (CRA) equivalent diameter, and (b) measurement of vessels in zone defined by a predetermined annular grid.

d0 d1

l0

d2

FIGURE 10.2

A generalized vascular segment and bifurcation.

and veins appear to follow Murray’s Law reasonably well. Conversely, deviations from the Murray optima have been observed in diseased coronary arteries [33].

Zamir [34; 35] extended Murray’s approach to consider asymmetry in bifurcating vessels, together with alternative optimization criteria. In the general bifurcation illustrated in Figure 10.2, nondimensional parameters can be defined for the asymmetry ratio

d2

a = 2 (10.5)

d12

and the ratio of vessel cross-sectional areas, sometimes referred to as expansion ratio

From Murray’s principal hypothesis that the diameter of a vessel is proportional to the cube root of the flow that the vessel is intended to carry, it can be shown that

where d1 is the diameter of the larger daughter vessel. Experimental data from measurements of retinal vessels [36] appear to be consistent with these theoretical ratios, albeit with some scatter of observed data around the theoretical values.

From the above ratios, theoretical optimum branching angles can be predicted given the asymmetry ratio and taking into account specific optimization criteria. Four such criteria have been considered [34–37]: lumen surface, lumen volume, pumping power, and endothelial drag. The spread observed in data from retinal bifurcations

suggests that more than one optimality criterion may be involved, although some bias in favor of the principles of minimum lumen volume and pumping power has been observed [36]. In general, for a given optimality criterion, the optimum bifurcation angle y depends on both the junction exponent x and also the asymmetry ratio a [37], but for reasonably symmetrical bifurcations (say a > 0:4) obeying Murray’s Law, the optimum angle y for a bifurcation is approximately constant at 75 degrees.

It is generally believed that the endothelium plays an important role in the maintenance of optimal geometry at bifurcations. Inhibition of endothelial nitric oxide in vitro has been shown to cause deviations in the junction exponent from optimum values [38], and observations in the retina from young normal subjects have shown acute alteration of bifurcation geometry when synthesis of endothelial nitric oxide was suppressed by infusion of NG-mono-methyl-L-arginine (L-NMMA) [39]. Accordingly, it has been hypothesised that deviations from optimal bifurcation geometry are associated with endothelial dysfunction. Given that impairment of endothelial function has been found in the early stages of atherosclerosis [40], speculation has arisen that altered bifurcation geometry may even precede clinical presentation of cardiovascular disease.

It has been noted that the junction exponent is not an ideal parameter to characterize the optimality of diameter relationships at a bifurcation, since it is poorly behaved in the presence of measurement noise [41]. For this reason, an alternative parameter based on mean nondimensional daughter diameter, corrected for the effects of asymmetry, was used in a recent study [41] as a more robust surrogate for junction exponent.

10.2.3Vessel length to diameter ratios

The length to diameter ratio (LDR) of a vessel segment is typically measured between consecutive bifurcations, represented by l0=d0 in Figure 10.2. The LDR will tend to increase in value in the presence of general arterial narrowing, as well as rarefaction, both of which are associated with increased peripheral vascular resistance and hypertension [42]. Furthermore, the LDR, like the AVR, is robust to variability in refraction by virtue of its nondimensionality.

A practical issue arises in the measurement of LDR from typical retinal images. Since the length of a vessel segment is measured between consecutive bifurcations, a risk exists that a measurement of LDR may vary, depending on the ability to detect a bifurcation involving a very small daughter vessel branching from a larger parent. This, in turn, is likely to be affected by image quality, increasing scatter in L/D measurements, and reducing reproducibility. In order to minimize any association between L/D measurements and image quality, it is necessary to establish criteria to reject small daughter vessels close to the threshold of imaging or visualization, so that these are not regarded as terminating vessel segments undergoing LDR measurement.