Yalin Wang
email: ylwang@math.ucla.edu

Xiaotian Yin

Jie Zhang

Xianfeng Gu

Tony F Chan

Paul M Thompson

Shing-Tung Yau

Brain Mapping with the Ricci Flow Conformal Parameterization and Multivariate Statistics on Deformation Tensors

By solving the Yamabe equation with the discrete surface Ricci flow method, we can conformally parameterize a multiple boundary surface by a multi-hole disk. The resulting parameterizations do not have any singularities and they are intrinsic and stable. For applications in brain mapping research, first, we convert a cortical surface model into a multiple boundary surface by cutting along selected anatomical landmark curves. Secondly, we conformally parameterize each cortical surface using a multi-hole disk. Inter-subject cortical surface matching is performed by solving a constrained harmonic map in the canonical parameter domain. To map group differences in cortical morphometry, we then compute a manifold version of Hotelling's T 2 test on the Jacobian matrices. Permutation testing was used to estimate statistical significance. We studied brain morphology in 21 patients with Williams Syndrome (WE) and 21 matched healthy control subjects with the proposed method. The results demonstrate our algorithm's potential power to effectively detect group differences on cortical surfaces.

Introduction

Surface-based modeling is valuable in brain imaging to help analyze anatomical shape, to detect abnormalities of cortical surface folding, and to statistically combine or compare 3D anatomical models across subjects. Even so, a direct mapping between two 3D surfaces from different subjects is challenging to compute. Often, higher order correspondences must be enforced between specific anatomical points, curved landmarks, or subregions lying within the two surfaces. This is often achieved by first mapping each of the 3D surfaces to canonical parameter spaces such as a sphere [START_REF] Fischl | High-resolution inter-subject averaging and a coordinate system for the cortical surface[END_REF][START_REF] Bakircioglu | Landmark matching on brain surfaces via large deformation diffeomorphisms on the sphere[END_REF] or a planar domain [START_REF] Leow | Brain structural mapping using a novel hybrid implicit/explicit framework based on the level-set method[END_REF]. A flow, computed in the parameter space of the two surfaces [START_REF] Thompson | Growth patterns in the developing human brain detected using continuummechanical tensor mapping[END_REF][START_REF] Davatzikos | Spatial normalization of 3D brain images using deformable models[END_REF], then induces a correspondence field in 3D. This flow can be constrained using anatomic landmark points or curves, by constraining the mapping of surface regions represented implicitly using level sets [START_REF] Leow | Brain structural mapping using a novel hybrid implicit/explicit framework based on the level-set method[END_REF], or by using currents to represent anatomical variation [START_REF] Durrleman | Inferring brain variability from diffeomorphic deformations of currents: An integrative approach[END_REF] Feature correspondence between two surfaces can be optimized by using the L 2 -norm to measure differences in curvature profiles or convexity [START_REF] Fischl | High-resolution inter-subject averaging and a coordinate system for the cortical surface[END_REF] or by using mutual information to align scalar fields of various differential geometric parameters defined on the surface [START_REF] Wang | Automated surface matching using mutual information applied to riemann surface structures[END_REF]. Artificial neural networks may also be used to rule out or favor certain types of feature matches [START_REF] Pitiot | Learning object correspondences with the observed transport shape measure[END_REF]. Finally, correspondences may be determined by using a minimum description length (MDL) principle, based on the compactness of the covariance of the resulting shape model [START_REF] Davies | A minimum description length approach to statistical shape modeling[END_REF]. Anatomically homologous points can then be forced to match across a dataset. Thodberg [START_REF] Thodberg | Minimum description length shape and appearance models[END_REF] identified problems with early MDL approaches and extended them to an MDL appearance model, when performing unsupervised image segmentation.

All oriented surfaces have conformal structures. The conformal structure is, in some respects, more flexible than the Riemannian metric but places more restrictions on the the surface morphology than the topological structure. The Ricci flow method can conformally map an open boundary surface to a multi-hole disk [START_REF] Wang | Brain surface conformal parameterization with the Ricci flow[END_REF]. Compared with other conformal parameterization methods [START_REF] Hurdal | Cortical cartography using the discrete conformal approach of circle packings[END_REF][START_REF] Angenent | Conformal geometry and brain flattening[END_REF][START_REF] Gu | Genus zero surface conformal mapping and its application to brain surface mapping[END_REF][START_REF] Wang | Brain surface conformal parameterization using Riemann surface structure[END_REF], the Ricci flow method can handle cortical surfaces with complicated topologies without singularities. The continuous Ricci flow conformally deforms a Riemannian metric on a smooth surface such that the Gaussian curvature evolves like a heat diffusion process. In the discrete case, with the circle packing metric, the Ricci flow can be formulated in a variational setting and solved by the Newton method [START_REF] Wang | Brain surface conformal parameterization with the Ricci flow[END_REF].

Tensor-based morphometry is widely used in computational anatomy as a means to understand shape variation between structural brain images. Techniques based on Riemannian manifolds to compare deformation tensors or strain matrices were introduced in [START_REF] Commowick | Incorporating statistical measures of anatomical variability in atlasto-subject registration for conformal brain radiotherapy[END_REF][START_REF] Pennec | Riemannian elasticity: A statistical regularization framework for non-linear registration[END_REF][START_REF] Arsigny | Log-Euclidean metrics for fast and simple calculus on diffusion tensors[END_REF]. In [START_REF] Lepore | Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors[END_REF], the full deformation tensors were used in the context of tensor-based morphometry. In a conformal parameterization, the original metric tensor is preserved up to a constant. The conformal parametrization provides an ideal framework to apply tensor based morphometry on surfaces, to help understand shape variation between structural brain images.

In this paper, we use the Ricci flow method to compute a conformal mapping between cortical surfaces and a multi-hole surface. Then we compute a direct cortical surface correspondence by computing a constrained harmonic map on the parameter domain. We apply multivariate statistics to the Jacobian matrices to study cortical surface variation between a group of patients with Williams syndrome (WS) and a group of healthy control subjects. WS is a genetic disorder in which the cortex develops abnormally, but the scope and type of systematic differences is unknown [START_REF] Thompson | Abnormal cortical complexity and thickness profiles mapped in Williams syndrome[END_REF]. In our experimental results, we identified several significantly different areas on the left and right cortical surfaces between WS patients and control subjects.

Ricci Flow Conformal Parameterization

In this section, we introduce the theory of Ricci flow in the continuous setting, and then generalize it to the discrete setting.

Ricci Flow on Continuous Surfaces

Riemannian Metric and Gaussian Curvature All the concepts used here may be found, with detailed explanations, in [START_REF] Guggenheimer | Differential Geometry[END_REF]. Suppose S is a C 2 smooth surface embedded in R 3 with local parameters (u 1 , u 2 ). Let r(u 1 , u 2 ) be a point on S and dr = r 1 du 1 + r 2 du 2 be the tangent vector defined at that point, where r 1 , r 2 are the partial derivatives of r with respect to u 1 and u 2 , respectively. The Riemannian metric or the first fundamental form is:

< dr, dr >= < r i , r j > du i du j , i, j = 1, 2. ( 1
)
The Gauss map G : S → S 2 from the surface S to the unit sphere S 2 maps each point p on the surface to its normal n(p). The Gaussian curvature K(p) is defined as the Jacobian of the Gauss map. Intuitively, it is the ratio between the infinitesimal area of the image of the Gauss map and the infinitesimal area on the original surface.

The total curvature of a compact surface is determined by the topology of the surface: S KdA + ∂S k g ds = 2πχ(S), where ∂S is the boundary of the surface S, k g is the geodesic curvature, and χ(S) is the Euler characteristic of the surface (an integer).

Conformal deformation

Let S be a surface embedded in R 3 . S has a Riemannian metric induced from the Euclidean metric of R 3 , denoted by g. Suppose u : S → R is a scalar function defined on S. It can be verified that ḡ = e 2u g is also a Riemannian metric on S, and angles measured by g are equal to those measured by ḡ. We say ḡ is a conformal deformation from g. Figure 1 shows that a conformal deformation maps infinitesimal circles to infinitesimal circles and preserves their intersection angles.

When the Riemannian metric is conformally deformed, curvatures will also be changed accordingly. Suppose g is changed to ḡ = e 2u g, the Gaussian curvature will become K = e -2u (-∆ g u+K), where ∆ g is the Laplacian-Beltrami operator under the original metric g. The geodesic curvature will become k = e -u (∂ r u + k), where r is the tangent vector orthogonal to the boundary. Smooth Surface Ricci Flow Suppose S is a smooth surface with a Riemannian metric g. The Ricci flow deforms the metric g(t) according to the Gaussian curvature K(t) (induced by g(t) itself), where t is the time parameter

dg ij (t) dt = -2K(t)g ij (t). ( 2
)
If we replace the metric in Eq. 2 with g(t) = e 2u(t) g(0), then the Ricci flow can be simplified as du(t)/dt = -2K(t), which states that the metric should change according to the curvature. The Ricci flow can be easily modified to compute a metric with a user-defined curvature K : du(t)/dt = 2( K -K). The resulting metric g(∞) will induce the user-defined curvature K.

The Ricci flow has been proven to converge. For surfaces with non-positive and positive Euler numbers, the proofs were given by Hamilton [START_REF] Hamilton | The Ricci flow on surfaces. Mathematics and general relativity[END_REF] and Chow [START_REF] Chow | The Ricci flow on the 2-sphere[END_REF] respectively. For a closed surface, if the total area is preserved during the flow, the Ricci flow will converge to a metric such that the Gaussian curvature is constant everywhere.

Ricci Flow on Discrete Surfaces

In engineering fields, smooth surfaces are often approximated by simplicial complexes (triangle meshes). Key concepts, such as the metric, curvature, and conformal deformation in the continuous setting can be generalized to the discrete setting. We denote a triangle mesh as Σ, the mesh boundary as ∂Σ, a vertex set as V , an edge set as E, and a face set as F . e ij represents the edge connecting vertices v i and v j , and f ijk denotes the face formed by v i , v j , and v k . Discrete Riemannian Metric and Gaussian Curvature A Riemannian metric on a mesh Σ is a piecewise constant metric with cone singularities at vertices.

The edge lengths of a mesh Σ are sufficient to define the Riemannian metric, l : E → R + , as long as for each face f ijk , the edge lengths satisfy the triangle inequality:

l ij + l jk > l ki .
The discrete Gaussian curvature K i on a vertex v i ∈ Σ can be computed from the angle deficit, where θ jk i represents the corner angle attached to vertex v i in the face f ijk . The discrete Gaussian curvatures are determined by the discrete metrics. And the total discrete curvature is, similar to the smooth case, a topological invariant:

K i = 2π -f ijk ∈F θ jk i , v i ∈ ∂Σ π -f ijk ∈F θ jk i , v i ∈ ∂Σ (3) v 1 v 2 v 3 φ 12 φ 23 φ 31 γ 1 γ 2 γ 3 θ 1 θ 2 θ 3 (
vi∈V K i = 2πχ(M ).

Discrete Conformal Deformation

In the discrete setting, conformal deformation is carried out using the concept of circle packing metric, which was introduced by Thurston in [START_REF] Thurston | Geometry and Topology of Three-Manifolds[END_REF].

By approximating infinitesimal circles using circles with finite radii, a circle packing metric of Σ can be denoted as (Γ, Φ), where Γ is a vertex function, Γ : V → R + , which assigns a radius γ i to the vertex v i ; Φ is an edge weight function, Φ : E → [0, π 2 ], which assigns an acute angle (i.e. weight) Φ(e ij ) to each edge e ij . Figure 2 illustrates the circle packing metric. Each vertex v i has a circle whose radius is γ i . For each edge e ij , the intersection angle φ ij is defined through two circles around v i and v j , which either intersect or are tangent.

Two circle packing metrics (Γ 1 , Φ 1 ) and (Γ 2 , Φ 2 ) on the same mesh are conformally equivalent if Φ 1 ≡ Φ 2 . A conformal deformation of a circle packing metric only modifies the vertex radii and preserves the intersection angles of the edges.

Discrete Surface Ricci Flow

Suppose (Σ, Φ) is a weighted mesh with an initial circle packing metric. Similar to the smooth setting, if we set k = ( K1 , K2 , • • • , Kn ) T to be the user-defined target curvature, the discrete Ricci flow can be defined as :

du i (t) dt = ( Ki -K i ), (4)
The Discrete Ricci flow can be formulated in the variational setting; namely, it is a negative gradient flow of a special energy form. Let (Σ, Φ) be a weighted mesh with spherical (Euclidean or hyperbolic) background geometry. For arbitrary two vertices v i and v j , the following symmetric relation holds: ∂K i /∂u j = ∂K j /∂u i . Let ω = n i=1 K i du i be a differential one-form [START_REF] Weitraub | Differential Forms: A Complement to Vector Calculus[END_REF]; the symmetric relation guarantees that this one-form is closed (curl free) in the metric space: dω = 0. Then by Stokes theorem, the following integration is path independent:

f (u) = u u0 n i=1 ( Ki -K i )du i , (5)
where n is the number of vertices, u i = log(γ i ), γ i is the radius associated with edge i, and u 0 is an arbitrary initial metric. The above integration (Eq. 5) is called the discrete Ricci energy, which is welldefined. The discrete Ricci energy has been proved to be strictly convex (i.e., its Hessian is positive definite) in [START_REF] Chow | Combinatorial Ricci flows on surfaces[END_REF]. The global minimum uniquely exists, which gives the desired discrete metric that induces k. The discrete Ricci flow is the negative gradient flow of this energy, and it converges to the global minimum.

As in [START_REF] Wang | Brain surface conformal parameterization with the Ricci flow[END_REF], the discrete surface Ricci flow method was used to solve the Yamabe equation [START_REF] Wang | Brain surface conformal parameterization with the Ricci flow[END_REF] and conformally map an open boundary cortical surface to a multi-hole disk.

Multivariate Statistics on Deformation Tensors

Derivative Map

Suppose φ : S 1 → S 2 is a map from the surface S 1 to the surface S 2 . In order to simplify the formulation, we use the isothermal coordinates of both surfaces for the arguments. Let (u 1 , v 1 ), (u 2 , v 2 ) be the isothermal coordinates of S 1 and S 2 respectively. The Riemannian metric of S i is represented as

g i = e 2λi (du 2 i + dv 2 i ), i = 1, 2.
On the local parameters, the map φ can be represented as φ(u 1 , v 1 ) = (φ 1 (u 1 , v 1 ), φ 2 (u 1 , v 1 )). The derivative map of φ is the linear map between the tangent spaces, dφ : T M (p) → T M (φ(p)), induced by the map φ. In the local parameter domain, the derivative map is the Jacobian of φ, dφ = ∂φ1 ∂u1 ∂φ1 ∂v1 ∂φ2 ∂u1 ∂φ2 ∂v1 .

Let the position vector of S 1 be r(u 1 , v 1 ). Denote the tangent vector fields as

∂ ∂u1 = ∂r ∂u1 , ∂ ∂v1 = ∂r ∂v1
. Because (u 1 , v 1 ) are isothermal coordinates, ∂ ∂u1 and ∂ ∂v1 only differ by a rotation of π/2. Therefore, we can construct an orthonormal frame on the tangent plane on S 1 as {e -λ1 ∂ ∂u1 , e -λ1 ∂ ∂v1 }. Similarly, we can construct an orthonormal frame on S 2 as {e -λ2 ∂ ∂u2 , e -λ2 ∂ ∂v2 }. The derivative map under the orthonormal frames is represented as

dφ = e λ2-λ1 ∂φ1 ∂u1 ∂φ1 ∂v1 ∂φ2 ∂u1 ∂φ2 ∂v1
.

In practice, smooth surfaces are approximated by triangle meshes. The map φ is approximated by a simplicial map, which maps vertices to vertices, edges to edges and faces to faces. The derivative map dφ is approximated by the linear map from one face [v 1 , v 2 , v 3 ] to another one [w 1 , w 2 , w 3 ]. First, we isometrically embed the triangle [v 1 , v 2 , v 3 ],[w 1 , w 2 , w 3 ] onto the plane R 2 , the planar coordinates of the vertices of v i , w j are denoted using the same symbol v i , w j . Then we explicitly compute the linear matrix for the derivative map dφ,

dφ = [w 3 -w 1 , w 2 -w 1 ][v 3 -v 1 , v 2 -v 1 ] -1 .
In our work, we use multivariate statistics on deformation tensors [START_REF] Lepore | Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors[END_REF], but adapt the concept to surface tensors. Let J be the derivative map and define the deformation tensors as S = (J T J) 1/2 . Instead of analyzing shape change based on the eigenvalues of the deformation tensor, we consider a new family of metrics, the "Log-Euclidean metrics" [START_REF] Arsigny | Log-Euclidean metrics for fast and simple calculus on diffusion tensors[END_REF]. These metrics make computations on tensors easier to perform, as they are chosen such that the transformed values form a vector space, and statistical parameters can then be computed easily using standard formulae for Euclidean spaces.

We apply Hotelling's T 2 test on the log-Euclidean space of the deformation tensors. Given two groups of n-dimensional vectors S i , i = 1, ..., p, T j , j = 1, ..., q, we use the Mahalanobis distance M to measure the group mean difference,

M = (log S -log T )Σ -1 (log S -log T )
where S and T are the means of the two groups and Σ is the combined covariance matrix of the two groups.

Experimental Results

We tested our algorithm on brain anatomic surfaces extracted from 3D MRI scans of a group of 21 WS individuals and a group of 21 healthy control subjects. The cerebral cortex and landmark data are the same ones used in [START_REF] Thompson | Abnormal cortical complexity and thickness profiles mapped in Williams syndrome[END_REF]. We tested our algorithm with different landmark sets. The first set included four selected landmark curves per hemisphere: the Central Sulcus, Superior Temporal Sulcus, Primary Intermediate Sulcus and Middle Frontal Control Line. A second set of constraint curves included seven selected landmark curves (the three new landmarks are the Precentral Sulcus, Paracentral Sulcus and Subparietal Sulcus). After we cut a cortical surface open along the selected landmark curves, the cortical surface becomes topologically equivalent to an open boundary genus 3 (4 landmarks) or genus 6 (7 landmarks) surface. So the cortical surface can be conformally mapped to a multi-hole disks with 4 and 7 boundaries, respectively. Examples of cortical surfaces with landmark curves overlaid (after cuts introduced) and their parameterization results are shown in Figure 3.

Because of the shape difference between different cortices, the centers and the radii of the inner circles are different. By computing a constrained harmonic map from each individual conformal map to a canonical multi-hole disk in the parameter domain, we can easily compute a direct surface correspondence between each of the cortical surfaces [START_REF] Wang | Brain surface conformal parameterization with the Ricci flow[END_REF]. Currently, the reference canonical multi-hole disk is arbitrarily chosen. For landmark curve matching, we guaranteed the matching of both curve ends. For other parts, we match curves based on unit speed parameterization on both curves.

Based on the surface matching results, the Jacobian matrices were computed as described in Section 3. For each point on the cortical surface, we ran permutation test with 5000 random assignments of subjects to groups to estimate the statistical significance of the areas with group differences in surface morphometry. Figure 4 and 5 illustrates our experimental results. We compared left and right cortical surface morphology between 21 control subjects and 21 WS patients with mappings constrained by a total of 4 and 7 selected landmark curves. Different sets of landmarks were used as anchors to evaluate the impact of the choice of anatomical constraints on the results. The significance maps, for the left and right hemispheres, show group differences at the voxel level, between WS patients and control subjects. Mappings with 4 and 7 selected landmark curves were computed. We detected few significant shape differences between left and right cortical surfaces (i.e., anatomical asymmetries) in both the control group and the WS group. Even so, we did find significant shape differences for both left and right cortical surfaces between WS and control subjects. We also found the regions with differences detected at the voxel level were consistent for the mappings computed with 4 and 7 selected landmark curves. However, detection power was not as high as expected in regions around the landmarks. Our future research will examine the statistics in the vicinity of the chosen landmarks, and multiple comparison correction methods, for example based on controlling the false discovery rate, will be used to assess the overall significance of the group differences.

Conclusions and Future Work

We applied the Ricci flow conformal parameterization for brain cortical surface registration. Based on the derivative map between two matching surfaces, a multivariate statistic on the Jacobian matrices was used to study surface morphometry in WS. Experimental results suggest that the significantly different areas were consistent with respect to the choice of landmark constraints and the algorithm has the potential to detect systematic surface abnormalities associated with disease. In the future, we will further study other possible statistics on the Jacobian matrices and find the optimal statistics for analyzing deformations computed using our Ricci flow conformal parameterization-based surface matching method. We will also validate our algorithm on larger databases of anatomical models.

Fig. 1 .

 1 Fig. 1. Properties of Conformal Mapping: Conformal mappings transform infinitesimal circles to infinitesimal circles and preserve the intersection angles among the circles. Here, infinitesimal circles are approximated by finite ones.

Fig. 2 .

 2 Circle Packing Metric (a) Flat circle packing metric (b) Circle packing metric on a triangle.

Fig. 3 .

 3 Fig. 3. Cortical surfaces with landmark curves and their conformal parameterization results. The first row shows a cortex with 4 landmarks and the second row shows a cortex with 7 landmarks (one landmark is not visible in this view).

Fig. 4 .

 4 Fig. 4. Brain morphology study in 21 Williams Syndrome patients and 21 matched control subjects (intra group study).

Fig. 5 .

 5 Fig. 5. Brain morphology study in 21 Williams Syndrome patients and 21 matched control subjects (inter group study).


Ameet Shah

Arun Mrcophth

Sachdev

David Mrcophth

Coggon

PhD, DM, FMedSci Parwez Hossain
email: parwez@soton.ac.uk

PhD Frcophth Frcs

Geographic Variations in Microbial Keratitis: An analysis of the Peer-Reviewed Literature

Keywords: cornea, keratitis, corneal ulcer, infection, epidemiology

The epidemiology of microbial keratitis has been investigated in several studies by analysis of organisms cultured from corneal scrapes. However, a comparison of the frequency of different organisms causing keratitis in different parts of the world is lacking. We present a review incorporating an analysis of data from studies worldwide. The data provide a comparison of the frequency of culture-positive organisms found in different parts of the world. Associations between a country's gross national income (GNI) and types of causative organism are explored.

The highest proportion of bacterial corneal ulcers was reported in studies from North America, Australia, the Netherlands and Singapore. The highest proportion of staphylococcal ulcers was found in a study from Paraguay whilst the highest proportion of pseudomonas ulcers was reported in a study from Bangkok. The highest proportions of fungal infections were found in studies from India and Nepal. Spearman's correlation coefficient demonstrated statistically significant correlations between GNI and percentages of bacterial (0.85 (95% CI 0.68 to 0.91, p<0.0001), fungal (-0.81 (95% CI -0.90 to -0.66, p<0.0001) and streptococcal (-0.43 (95% CI -0.66 to -0.12, p=0.009) isolates.

INTRODUCTION

Microbial keratitis is a potentially serious corneal infection and a major cause of visual impairment worldwide. A conservative estimate of the number of corneal ulcers occurring annually in the developing world alone is 1.5-2 million.[1] Permanent visual dysfunction has been reported in a significant proportion of patients in both developing [2] and developed [3] countries. Srinivasan et al [4] comment that ulceration of the cornea in south India 'is a blinding disease of epidemic proportions'.

Various micro-organisms can cause microbial keratitis and predisposing risk factors vary from one geographic region to another. They include pre-existing corneal disease as well as other risk factors such as contact lens wear, surgical or non-surgical trauma and ocular surface disease. [5][6][7] There is limited comparative information on international patterns of causative organisms in microbial keratitis. With increasing rates of migration and international travel, an awareness of these geographical variations is relevant for clinicians treating microbial keratitis, and especially for those planning to work in regions where they have not previously practised. The aim of this review is to summarise the published literature that provides information on the worldwide variation in organisms causing microbial keratitis.

METHODS

Search Strategy

A systematic review of the current literature pertaining to the prevalence of causative organisms responsible for microbial keratitis was conducted. Pubmed searches were performed and verified in April 2009 by two independent investigators. The terms 'microbial keratitis', 'bacterial keratitis' and 'infectious keratitis' were entered into Pubmed. Only papers presenting data that were collected after 1 st January 1990 were examined, and the search was restricted to English Language and human studies. Only studies that cultured at least 50 organisms in total were included. Titles and abstracts were read and a judgement was made as to whether the paper provided culture results for microbial keratitis in a specified geographical location. If this was felt to be the case then a full text request was made to access the original published data.

Studies looking only at infections related to use of contact lenses were excluded, as were studies looking only at limited age groups.

Extraction and Recording of Data

Papers were read and information was abstracted on the following variables: number of patients in the study, time period of reporting, region, method by which organisms were isolated, method of culture, rate of positive cultures, and number of contact lens wearers in the study sample. These data were then entered then into a Microsoft Excel spread sheet.

With regard to the microorganisms cultured, the total numbers in each of the following categories were abstracted and recorded: gram positive organisms -staphylococcal species and streptococcal species; gram negative organisms -pseudomonus species; protozoa; fungi/yeasts -aspergillus species and candida species.

Classification of income levels and GNI subheading

The prevalence of different causative organisms was compared according to countries' gross national incomes (GNIs) (source = http://web.worldbank.org). Income groups were defined by 2007 GNI per capita, calculated using the World Bank Atlas method.[8] The groups distinguished were: low income, $935 or less; lower middle income, $936 -$3,705; upper middle income, $3,706 -$11,455; and high income, $11,456 or more.

Statistical analysis

Statistical analysis was performed using 'Analyse-it' version 2.20 software. Spearman's correlation coefficients were used to explore associations between:

1) prevalence of certain types of organism and GNI; and between 2) prevalence of contact lens wear and prevalence of pseudomonas.

RESULTS

3883 publications were identified through the preliminary Pubmed search. Of these, 37 papers met the inclusion criteria. One paper was excluded because it included a significant number of cases that the authors deemed to constitute an outbreak of suture-related infections.

[9] Twelve of the included papers were from the Indian subcontinent, 7 from North America and Canada, 6 from the Far East, 5 from Australasia, 4 from Europe, 2 from Africa (both from Ghana) and 1 from South America. The median GNI of the countries studied was $22685 (range $470 -$59880). The number of patients ranged from 73 to 3183. The time periods of study ranged from 3 -192 months, although three studies did not specify the study period. The proportion of keratitis patients with a recent history of contact lens wear was reported in only 22 studies and ranged from 0.33% (West Bengal [10]) to 50.3% (Paris[11]).

Three studies reported on only culture-positive cases and so appear to have 100% culturepositive rates in Table 1. In the remainder of the studies culture-positive rates ranged from 35% -86%.

Among studies which looked at non-bacterial as well as bacterial organisms, Los Angeles [12] and Adelaide [13] had the highest percentages of bacterial cases (95% in both), with Paraguay [14] having the highest percentage of staphylococcal species (79%), and Bangkok [15] the highest proportion of pseudomonal infections (55%). Tamil Nadu [16] had the highest percentage of streptococcal infections (47%). The highest percentage of protozoal infections (7%) was found in a study from Hong Kong. [5] Eastern India [10] had the highest proportion of corneal infections attributable to fungi (67%).

When considering those countries with a significant proportion of fungal ulcers (we have arbitrarily chosen a cut-off of 10% or more), East India also had the highest percentage of aspergillus (60% of all fungal cultures) whereas the highest percentage of fusarium (73% of all fungal cultures) was found in a study from Hyderabad [17].

Statistically significant correlations were found between Gross National Income and percentages of bacterial, fungal (see Figures 1 and2) and streptococcal isolates (data not shown). Spearman's correlation coefficient for prevalence of bacteria and GNI was 0.85 (95% CI 0.68 to 0.91, p<0.0001), for prevalence of fungi and GNI was -0.81 (95% CI -0.90 to -0.66, p<0.0001) and for prevalence of streptococci and GNI was -0.43 (95% CI -0.66 to -0.12, p=0.009). Surprisingly there was no statistically significant correlation between percentage of pseudomonal isolates and percentage of contact lens wearers.

DISCUSSION

We have found a wide variation in the causative organisms for microbial keratitis in different parts of the world. To some degree this variation is explained by economic factors as well as contact lens wear. A high proportion of bacterial ulcers were reported from centres in developed countries (North America, Australia, and Western Europe). In these countries, patients are far less likely to be agricultural workers, and so have a reduced risk of trauma from organic matter, which is known to be a risk factor for fungal infection. [28] A high percentage of staphylococcus species (79%) was recorded in the study from Paraguay

[14] although the reason for this is not clear. Of note, the authors comment that their patients have to make long journeys to their hospital. Thus, their data may reflect more severe cases of microbial keratitis.

The study from Tamil Nadu [16] found the highest proportion of streptococcus species (46.8%). The authors noted that this figure was only 18.5% in 1986 and suggest that the trend might represent a genuine change in the bacterial flora due to changes in the climate and environment.

The study from Bangkok [15] had the highest proportion of pseudomonas infections (55%).

Interestingly, this study did not have the highest proportion of contact lens wearers (only 24%). Other studies reported far higher proportions of contact lens wearers, for example 44% in a study from Taiwan [26] and 50% in the study from Paris [11]. When we compared the percentage of contact lens wearers with the percentage of pseudomonal infections (figure 4), the Spearman correlation coefficient was not statistically significant. Interestingly, Cohen et al. [39] at Wills Eye Hospital reported a decline in contact lens-related ulcers: during 1998 to 1991, contact lens wear accounted for 44% of all ulcers, but during 1992 to 1995, it accounted for only 30%. The authors speculated that their figures might reflect a reduction in the number of referrals to their unit due to the increased availability of fluoroquinolones in the community.

Trauma was a major risk factor for corneal infection in certain countries. In Paraguay [14], the percentage of cases with preceding trauma was 48%, in Eastern Nepal[19], 53%, in Madurai, South India[4], 65% and 83% in Eastern India[10] (most commonly from injury by the paddy or its stalk). The authors of this last study noted an increase in keratitis during harvesting season.

The above studies also addressed the frequency of self-medication prior to presentation at a tertiary referral unit. In the Madurai study, 20% of patients had been to a village healer and 87% had been started on topical medication, of whom 8% were on topical corticosteroids. In the study from Eastern India, 18% of patients had used medication before coming to clinic, and in the Paraguay study the proportion was 83%. Schwab [40] states that in some developing countries locally produced over-the-counter antibiotics may be cheaper compared to imported preparations and this may impact on the prompt use of appropriate therapy.

Access to these over-the-counter antibiotics is limited and individuals may be more inclined to go to local healers who are generally well respected but may instil harmful 'traditional' agents such as vegetable extracts, leaves, herbs, human urine or animal products or perform practices such as thermal cautery. Jeng and McLeod[41] commented on the emerging resistance of bacterial infections to fluoroquinolones. In addition to changes in resistance patterns, studies have also demonstrated changing patterns of causative organisms over time in a given geographical location. Varaprasathan et al.[42] reported that the proportion of S. pneumoniae and P. aeruginosa ulcers in Northern California had decreased over a 50 year period whilst that of S. marcescens had increased over the same period. Sun et al. [START_REF] Sun | Distribution and shifting trends of bacterial keratitis in north China (1989-98)[END_REF] reported a rise in the percentage of gram positive cocci in North China from 25% in 1991 to 70.8% in 1997, as well as a decrease in gram negative bacilli from 69% to 23.4% over a similar period. Leck et al.[16] have previously compared corneal ulcers in Ghana and South India, whilst Lam et al. [5] have discussed differences between Hong Kong, Europe and North America.

However, the present study is the first to present a worldwide comparison of corneal infections.

In interpreting this comparison, a number of limitations must be considered. Variations existed in the definition of microbial keratitis between studies. Lam et al, reporting on cases from Hong Kong [5], included patients with 'the clinical presentation of a corneal stromal infiltrate >1 mm 2 '. This differs from Srinivasan et al [4] who included patients with 'loss of the corneal epithelium with underlying stromal infiltration and suppuration associated with signs of inflammation with or without hypopyon'. There were variations in methods of culture. For example, one study [21] used Sheep's blood agar, Chocolate, Non-nutrient, Sabauroud, brainheart infusion and potato dextrose agar, whilst another [18] used only chocolate and Sabouraud media. Some studies did not specify the media used [17,22,23]. All studies included bacterial infections, but not all included fungal, protozoal and yeast organisms. The majority of studies looked at all cases of microbial keratitis whilst some looked only at patients requiring hospital admission (Wong et al. and Cheung et al. [3,31]). It is likely that in these studies, particularly virulent organisms will be over-represented. Finally, data are only available from centres that have conducted studies on microbial keratitis, limiting the coverage of certain regions of the world.

Despite these limitations, we have presented to our knowledge, for the first time, a worldwide overview of causative organisms in microbial keratitis demonstrating associations between specific types of microbial keratitis and national income.

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The Corresponding Author has the right to grant on behalf of all authors and does grant on behalf of all authors, an exclusive licence (or non exclusive for government employees) on a worldwide basis to the BMJ Publishing Group Ltd to permit this article (if accepted) to be published in BJO and any other BMJPGL products and sublicences such use and exploit all subsidiary rights, as set out in our licence (http://group.bmj.com/products/journals/instructions-for-authors/licenceforms).

Competing Interest: None declared.

Scatterplot to show

Figure 1 :Figure 2 :

 12 Figure 1: Scatterplot showing percentage of bacterial isolates in studies not looking exclusively at bacterial causes of microbial keratitis plotted against gross national income (US Dollars per capita)

Table 1 : Studies meeting criteria for inclusion in review

 1 paper did not specify the number of contact lens wearers. Instead they report on the number of isolates from contact lens wearers. The figure given in the table therefore represents the percentage of isolates retrieved from cases where CL wear was a risk factor †Estimated to be lower middle income ($936 to $3,705), value given in table is midpoint of this range

	Location of	GNI per capita	Time period	Number of	Proportion (%) of	Method of culture	Proportion (%) of
	study			patients	patients using contact		patients with
	(reference)	($)	(months)		lenses		positive cultures
	Africa
	Ghana(16)		24	290	unspecified	sheep's blood agar, Sabouraud broth, inhibitory	50
						mould agar, brain heart infusion broth, chocolate
						agar and cysteine tryptone agar
	Accra, Ghana(18)		unspecified	199	unspecified	chocolate, Sabouraud	64
	Indian
	Subcontinent
	Nepal(19)		36	447	unspecified	sheep's blood agar, chocolate, brain-heart	68
						infusion, Sabouraud
	Chittagong,		unspecified	151	unspecified	blood, chocolate,thioglycolate,Sabouraud	63
	Bangladesh(20)
	Tamil Nadu,		24	800	unspecified	sheep's blood agar, Sabouraud broth and	69
	India(16)					Sabouraud glucose agar, brain heart infusion
						broth, chocolate, cysteine tryptone agar
	West Bengal,		36	1198	0.33	blood, chocolate, potato dextrose agar, Sabouraud	68
	India(10)					dextrose
	New Delhi, India(2)		unspecified	100	2.0	blood, chocolate, thioglycolate, Sabouraud	65
	Madurai, India(4)		3	434	unspecified	sheep's blood agar, potato dextrose agar,	68
						chocolate, brain-heart infusion
	Hyderabad,		95	1092	unspecified	sheep's blood agar, chocolate, non-nutrient,
	India(21)					Sabouraud, brain-heart infusion, potato dextrose
						agar

* ** This paper presented data for 1995 and 2005, only 2005 data have been extracted in our study

Table 2 : Bacterial isolates by location

 2

	Location of study		Number of isolates (percentage of total isolates from that location)
			Gram +ve bacteria			Gram -ve bacteria
		Any	Staphylo	Streptococci Other	Any	Pseudomonas	O
			-cocci
	Africa
	Ghana	17(11.3)	4(2.7)	8(5.3)	5(3.3)	21(14.0)	21(14.0)
	Accra, Ghana	34(26.2)	18(13.8)	11(8.5)	5(3.8)	29(22.3)	17(13.1)
	Indian Subcontinent
	Nepal	136(38.0)	102(28.5)	31(8.7)	3(0.8)	21(5.9)	18(5.0)	3
	Chittagong, Bangladesh	27(21.3)	2(1.6)	23(18.1)	2(1.6)	39(30.7)	34(26.8)	5
	Tamil Nadu, India	178(33.1)	63(11.7)	110(20.4)	5(0.9)	57(10.6)	35(6.5)
	West Bengal, India	214(23.1)	174(18.8)	28(3.0)	12(1.3)	84(9.1)	63(6.8)
	New Delhi, India	35(53.8)	28(43.1)	2(3.1)	5(7.7)	17(26.2)	10(15.4)
	Madurai, India	132(40.6)	26(8.0)	76(23.4)	30(9.2)	35(10.8)	24(7.4)
	Hyderabad, India	198(50.9)	92(23.7)	60(15.4)	46(11.8)	45(11.6)	27(6.9)
	Tamil Nadu, India	814(34.0)	259(10.8)	492(20.6)	63(2.6)	325(13.6)	236(9.9)
	Hyderabad, India	80(67.2)	43(36.1)	27(22.7)	0(0)	13(10.9)	6(5.0)	7
	Delhi, India	223(30.6)	200(27.4)	10(1.4)	13(1.8)	152(20.9)	88(12.1)
	Riyadh, Saudi Arabia	130(73.9)	75(42.6)	26(14.8)	29(16.5)	45(25.6)	16(9.1)	29
	Baghdad, Iraq	88(37.3)	70(29.7)	15(6.4)	3(1.3)	74(31.4)	68(28.8)	6
	South America
	Asuncion, Paraquay	278(69.0)	210(52.1)	42(10.4)	226(56.	132 (32.8)	46(11.4)
					1)

Table 3 : Protozoa and fungal/yeast isolates by location

 3

	Location of study		Number of isolates
		Protozoa		Fungi and yeasts
		Any	Any	Aspergillus	Candida	Other
	Africa
	Ghana	1(0.7)	82(54.7)	19(12.7)	1(0.7)	62(41.3)
	Accra, Ghana	unspecified	65(50.0)	10(7.7)	1(0.8)	45(34.6)
	Indian Subcontinent
	Nepal	unspecified	200(55.9)	75(20.9)	9(2.5)	116(32.4)
	Chittagong, Bangladesh	unspecified	48(37.8)	24(18.9)	1(0.8)	23(18.1)
	Tamil Nadu, India	7(1.3)	296(55.0)	76(14.1)	0(0)	220(40.9)
	West Bengal. India	4(0.4)	623(67.4)	373(40.3)	7(0.8)	243(26.3)
	New Delhi, India	unspecified	13(20.0)	6(9.2)	0(0.0)	7(10.8)
	Madurai, India	3(0.9)	155(47.7)	25(7.7)	unspecified	116(35.7)
	Hyderabad, India	unspecified	146(37.5)	43(11.1)	2(0.5)	101(26.0)
	Tamil Nadu, India	33(1.4)	1176(49.1)	294(12.3)	unspecified	882(36.8)
	Hyderabad, India	3(2.5)	22(18.5)	5(4.2)	1(0.8)	16(13.4)
	Delhi, India	11(1.5)	358(49.1)	149(20.4)	30(4.1)	179(24.6)
	Riyadh, Saudi Arabia	unspecified	unspecified	unspecified	unspecified	unspecified
	Baghdad, Iraq	unspecified	74(31.4)	42(17.8)	4(1.7)	28(11.9)
	South America
	Asuncion, Paraquay	unspecified	209(51.9)	37(9.2)	4(1.0)	168(41.7)
	Far East
	Taipei, Taiwan	11(4.4)	34(13.5)	5(2.0)	10(4.0)	19(7.5)
	Taipei, Taiwan	unspecified	unspecified	unspecified	unspecified	unspecified