Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

Velocity and Concentration field of discharge from a boat propeller

Two-stroke outboard boat engines using total loss lubrication deposit a significant proportion of their lubricant and fuel directly into the water. The purpose of this work is to document the velocity and concentration field characteristics of a submerged swirling water jet emanating from a propeller in order to provide information on its fundamental characteristics. Measurements of the velocity and concentration field were performed in a turbulent jet generated by a model boat propeller (0.02 m diameter) operating at 1500 rpm and 3000 rpm. The measurements were carried out in the Zone of Established Flow up to 50 propeller diameters downstream of the propeller. Both the mean axial velocity profile and the mean concentration profile showed self-similarity. Further, the stand deviation growth curve was linear. The effects of propeller speed and dye release location were also investigated.

Decentred optical axes and aberrations along principal visual field meridians

Suggestions that peripheral imagery may affect the development of refractive error have led to interest in the variation in refraction and aberration across the visual field. It is shown that, if the optical system of the eye is rotationally symmetric about an optical axis which does not coincide with the visual axis, measurements of refraction and aberration made along the horizontal and vertical meridians of the visual field will show asymmetry about the visual axis. The departures from symmetry are modelled for second-order aberrations, refractive components and third-order coma. These theoretical results are compared with practical measurements from the literature. The experimental data support the concept that departures from symmetry about the visual axis in the measurements of crossed-cylinder astigmatism J45 and J180 are largely explicable in terms of a decentred optical axis. Measurements of the mean sphere M suggest, however, that the retinal curvature must differ in the horizontal and vertical meridians.

Component reliability estimations without field data

Maintenance activities in a large-scale engineering system are usually scheduled according to the lifetimes of various components in order to ensure the overall reliability of the system. Lifetimes of components can be deduced by the corresponding probability distributions with parameters estimated from past failure data. While failure data of the components is not always readily available, the engineers have to be content with the primitive information from the manufacturers only, such as the mean and standard deviation of lifetime, to plan for the maintenance activities. In this paper, the moment-based piecewise polynomial model (MPPM) are proposed to estimate the parameters of the reliability probability distribution of the products when only the mean and standard deviation of the product lifetime are known. This method employs a group of polynomial functions to estimate the two parameters of the Weibull Distribution according to the mathematical relationship between the shape parameter of two-parameters Weibull Distribution and the ratio of mean and standard deviation. Tests are carried out to evaluate the validity and accuracy of the proposed methods with discussions on its suitability of applications. The proposed method is particularly useful for reliability-critical systems, such as railway and power systems, in which the maintenance activities are scheduled according to the expected lifetimes of the system components.

Mild systemic hypoxia and photopic visual field sensitivity

Purpose: Flickering stimuli increase the metabolic demand of the retina,making it a sensitive perimetric stimulus to the early onset of retinal disease. We determine whether flickering stimuli are a sensitive indicator of vision deficits resulting from to acute, mild systemic hypoxia when compared to standard static perimetry. Methods: Static and flicker visual perimetry were performed in 14 healthy young participants while breathing 12% oxygen (hypoxia) under photopic illumination. The hypoxia visual field data were compared with the field data measured during normoxia. Absolute sensitivities (in dB) were analysed in seven concentric rings at 1°, 3°, 6°, 10°, 15°, 22° and 30° eccentricities as well as mean defect (MD) and pattern defect (PD) were calculated. Preliminary data are reported for mesopic light levels. Results: Under photopic illumination, flicker and static visual field sensitivities at all eccentricities were not significantly different between hypoxia and normoxia conditions. The mean defect and pattern defect were not significantly different for either test between the two oxygenation conditions. Conclusion: Although flicker stimulation increases cellular metabolism, flicker photopic visual field impairment is not detected during mild hypoxia. These findings contrast with electrophysiological flicker tests in young participants that show impairment at photopic illumination during the same levels of mild hypoxia. Potential mechanisms contributing to the difference between the visual fields and electrophysiological flicker tests including variability in perimetric data, neuronal adaptation and vascular autoregulation, are considered. The data have implications for the use of visual perimetry in the detection of ischaemic/hypoxic retinal disorders under photopic and mesopic light levels.

Corona ions from overhead transmission voltage powerlines : effect on DC e-field and ambient particle concentration levels

Along with their essential role in electricity transmission and distribution, some powerlines also generate large concentrations of corona ions. This study aimed at comprehensive investigation of corona ions, vertical dc e-field, ambient aerosol particle charge and particle number concentration levels in the proximity of some high/sub-transmission voltage powerlines. The influence of meteorology on the instantaneous value of these parameters, and the possible existence of links or associations between the parameters measured were also statistically investigated. The presence of positive and negative polarities of corona ions was associated with variation in the mean vertical dc e-field, ambient ion and particle charge concentration level. Though these variations increased with wind speed, their values also decreased with distance from the powerlines. Predominately positive polarities of ions were recorded up to a distance of 150 m (with the maximum values recorded 50 m downwind of the powerlines). At 200 m from the source, negative ions predominated. Particle number concentration levels however remained relatively constant (103 particle cm-3) irrespective of the sampling site and distance from the powerlines. Meteorological factors of temperature, humidity and wind direction showed no influence on the electrical parameters measured. The study also discovered that e-field measurements were not necessarily a true representation of the ground-level ambient ion/particle charge concentrations.

Inferior field loss increases rate of falls in older adults with glaucoma

PURPOSE: To examine the visual predictors of falls and injurious falls among older adults with glaucoma. METHODS: Prospective falls data were collected for 71 community-dwelling adults with primary open-angle glaucoma, mean age 73.9 ± 5.7 years, for one year using monthly falls diaries. Baseline assessment of central visual function included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from monocular Humphrey Field Analyser plots. Rate ratios (RR) for falls and injurious falls with 95% confidence intervals (CIs) were based on negative binomial regression models. RESULTS: During the one year follow-up, 31 (44%) participants experienced at least one fall and 22 (31%) experienced falls that resulted in an injury. Greater visual impairment was associated with increased falls rate, independent of age and gender. In a multivariate model, more extensive field loss in the inferior region was associated with higher rate of falls (RR 1.57, 95%CI 1.06, 2.32) and falls with injury (RR 1.80, 95%CI 1.12, 2.98), adjusted for all other vision measures and potential confounding factors. Visual acuity, contrast sensitivity, and superior field loss were not associated with the rate of falls; topical beta-blocker use was also not associated with increased falls risk. CONCLUSIONS: Falls are common among older adults with glaucoma and occur more frequently in those with greater visual impairment, particularly in the inferior field region. This finding highlights the importance of the inferior visual field region in falls risk and assists in identifying older adults with glaucoma at risk of future falls, for whom potential interventions should be targeted. KEY WORDS: glaucoma, visual field, visual impairment, falls, injury

Designing and evaluating mobile multimedia user experiences in public urban places : Making sense of the field

The majority of the world’s population now lives in cities (United Nations, 2008) resulting in an urban densification requiring people to live in closer proximity and share urban infrastructure such as streets, public transport, and parks within cities. However, “physical closeness does not mean social closeness” (Wellman, 2001, p. 234). Whereas it is a common practice to greet and chat with people you cross paths with in smaller villages, urban life is mainly anonymous and does not automatically come with a sense of community per se. Wellman (2001, p. 228) defines community “as networks of interpersonal ties that provide sociability, support, information, a sense of belonging and social identity.” While on the move or during leisure time, urban dwellers use their interactive information communication technology (ICT) devices to connect to their spatially distributed community while in an anonymous space. Putnam (1995) argues that available technology privatises and individualises the leisure time of urban dwellers. Furthermore, ICT is sometimes used to build a “cocoon” while in public to avoid direct contact with collocated people (Mainwaring et al., 2005; Bassoli et al., 2007; Crawford, 2008). Instead of using ICT devices to seclude oneself from the surrounding urban environment and the collocated people within, such devices could also be utilised to engage urban dwellers more with the urban environment and the urban dwellers within. Urban sociologists found that “what attracts people most, it would appear, is other people” (Whyte, 1980, p. 19) and “people and human activity are the greatest object of attention and interest” (Gehl, 1987, p. 31). On the other hand, sociologist Erving Goffman describes the concept of civil inattention, acknowledging strangers’ presence while in public but not interacting with them (Goffman, 1966). With this in mind, it appears that there is a contradiction between how people are using ICT in urban public places and for what reasons and how people use public urban places and how they behave and react to other collocated people. On the other hand there is an opportunity to employ ICT to create and influence experiences of people collocated in public urban places. The widespread use of location aware mobile devices equipped with Internet access is creating networked localities, a digital layer of geo-coded information on top of the physical world (Gordon & de Souza e Silva, 2011). Foursquare.com is an example of a location based 118 Mobile Multimedia – User and Technology Perspectives social network (LBSN) that enables urban dwellers to virtually check-in into places at which they are physically present in an urban space. Users compete over ‘mayorships’ of places with Foursquare friends as well as strangers and can share recommendations about the space. The research field of Urban Informatics is interested in these kinds of digital urban multimedia augmentations and how such augmentations, mediated through technology, can create or influence the UX of public urban places. “Urban informatics is the study, design, and practice of urban experiences across different urban contexts that are created by new opportunities of real-time, ubiquitous technology and the augmentation that mediates the physical and digital layers of people networks and urban infrastructures” (Foth et al., 2011, p. 4). One possibility to augment the urban space is to enable citizens to digitally interact with spaces and urban dwellers collocated in the past, present, and future. “Adding digital layer to the existing physical and social layers could facilitate new forms of interaction that reshape urban life” (Kjeldskov & Paay, 2006, p. 60). This methodological chapter investigates how the design of UX through such digital placebased mobile multimedia augmentations can be guided and evaluated. First, we describe three different applications that aim to create and influence the urban UX through mobile mediated interactions. Based on a review of literature, we describe how our integrated framework for designing and evaluating urban informatics experiences has been constructed. We conclude the chapter with a reflective discussion on the proposed framework.

Useful field of view predicts driving in the presence of distracters

Purpose. The Useful Field of View (UFOV(R)) test has been shown to be highly effective in predicting crash risk among older adults. An important question which we examined in this study is whether this association is due to the ability of the UFOV to predict difficulties in attention-demanding driving situations that involve either visual or auditory distracters. Methods. Participants included 92 community-living adults (mean age 73.6 +/- 5.4 years; range 65-88 years) who completed all three subtests of the UFOV involving assessment of visual processing speed (subtest 1), divided attention (subtest 2), and selective attention (subtest 3); driving safety risk was also classified using the UFOV scoring system. Driving performance was assessed separately on a closed-road circuit while driving under three conditions: no distracters, visual distracters, and auditory distracters. Driving outcome measures included road sign recognition, hazard detection, gap perception, time to complete the course, and performance on the distracter tasks. Results. Those rated as safe on the UFOV (safety rating categories 1 and 2), as well as those responding faster than the recommended cut-off on the selective attention subtest (350 msec), performed significantly better in terms of overall driving performance and also experienced less interference from distracters. Of the three UFOV subtests, the selective attention subtest best predicted overall driving performance in the presence of distracters. Conclusions. Older adults who were rated as higher risk on the UFOV, particularly on the selective attention subtest, demonstrated poorest driving performance in the presence of distracters. This finding suggests that the selective attention subtest of the UFOV may be differentially more effective in predicting driving difficulties in situations of divided attention which are commonly associated with crashes.

Visual sensitivity loss in the central thirty degrees of visual field is associated with diabetic peripheral neuropathy

Aims/hypothesis: Impaired central vision has been shown to predict diabetic peripheral neuropathy (DPN). Several studies have demonstrated diffuse retinal neurodegenerative changes in diabetic patients prior to retinopathy development, raising the prospect that non-central vision may also be compromised by primary neural damage. We hypothesise that type 2 diabetic patients with DPN exhibit visual sensitivity loss in a distinctive pattern across the visual field, compared with a control group of type 2 diabetic patients without DPN. Methods: Increment light sensitivity was measured by standard perimetry in the central 30 degree of visual field for two age-matched groups of type 2 diabetic patients, with and without neuropathy (n=40/30). Neuropathy status was assigned using the neuropathy disability score. Mean visual sensitivity values were calculated globally, for each quadrant and for three eccentricities (0-10 degree , 11-20 degree and 21-30 degree ). Data were analysed using a generalised additive mixed model (GAMM). Results: Global and quadrant between-group visual sensitivity mean differences were marginally but consistently lower (by about 1 dB) in the neuropathy cohort compared with controls. Between-group mean differences increased from 0.36 to 1.81 dB with increasing eccentricity. GAMM analysis, after adjustment for age, showed these differences to be significant beyond 15 degree eccentricity and monotonically increasing. Retinopathy levels and disease duration were not significant factors within the model (p=0.90). Conclusions/interpretation: Visual sensitivity reduces disproportionately with increasing eccentricity in type 2 diabetic patients with peripheral neuropathy. This sensitivity reduction within the central 30 degree of visual field may be indicative of more consequential loss in the far periphery.

Performance evaluation of onsite wastewater treatment : field sampling and preliminary evaluation of results

Background The onsite treatment of sewage and effluent disposal within the premises is widely prevalent in rural and urban fringe areas due to the general unavailability of reticulated wastewater collection systems. Despite the seemingly low technology of the systems, failure is common and in many cases leading to adverse public health and environmental consequences. Therefore it is important that careful consideration is given to the design and location of onsite sewage treatment systems. It requires an understanding of the factors that influence treatment performance. The use of subsurface effluent absorption systems is the most common form of effluent disposal for onsite sewage treatment and particularly for septic tanks. Additionally in the case of septic tanks, a subsurface disposal system is generally an integral component of the sewage treatment process. Therefore location specific factors will play a key role in this context. The project The primary aims of the research project are: • to relate treatment performance of onsite sewage treatment systems to soil conditions at site; • to identify important areas where there is currently a lack of relevant research knowledge and is in need of further investigation. These tasks were undertaken with the objective of facilitating the development of performance based planning and management strategies for onsite sewage treatment. The primary focus of the research project has been on septic tanks. Therefore by implication the investigation has been confined to subsurface soil absorption systems. The design and treatment processes taking place within the septic tank chamber itself did not form a part of the investigation. In the evaluation to be undertaken, the treatment performance of soil absorption systems will be related to the physico-chemical characteristics of the soil. Five broad categories of soil types have been considered for this purpose. The number of systems investigated was based on the proportionate area of urban development within the Brisbane region located on each soil types. In the initial phase of the investigation, though the majority of the systems evaluated were septic tanks, a small number of aerobic wastewater treatment systems (AWTS) were also included. This was primarily to compare the effluent quality of systems employing different generic treatment processes. It is important to note that the number of different types of systems investigated was relatively small. As such this does not permit a statistical analysis to be undertaken of the results obtained. This is an important issue considering the large number of parameters that can influence treatment performance and their wide variability. The report This report is the second in a series of three reports focussing on the performance evaluation of onsite treatment of sewage. The research project was initiated at the request of the Brisbane City Council. The work undertaken included site investigation and testing of sewage effluent and soil samples taken at distances of 1 and 3 m from the effluent disposal area. The project component discussed in the current report formed the basis for the more detailed investigation undertaken subsequently. The outcomes from the initial studies have been discussed, which enabled the identification of factors to be investigated further. Primarily, this report contains the results of the field monitoring program, the initial analysis undertaken and preliminary conclusions. Field study and outcomes Initially commencing with a list of 252 locations in 17 different suburbs, a total of 22 sites in 21 different locations were monitored. These sites were selected based on predetermined criteria. To obtain house owner agreement to participate in the monitoring study was not an easy task. Six of these sites had to be abandoned subsequently due to various reasons. The remaining sites included eight septic systems with subsurface effluent disposal and treating blackwater or combined black and greywater, two sites treating greywater only and six sites with AWTS. In addition to collecting effluent and soil samples from each site, a detailed field investigation including a series of house owner interviews were also undertaken. Significant observations were made during the field investigations. In addition to site specific observations, the general observations include the following: • Most house owners are unaware of the need for regular maintenance. Sludge removal has not been undertaken in any of the septic tanks monitored. Even in the case of aerated wastewater treatment systems, the regular inspections by the supplier is confined only to the treatment system and does not include the effluent disposal system. This is not a satisfactory situation as the investigations revealed. • In the case of separate greywater systems, only one site had a suitably functioning disposal arrangement. The general practice is to employ a garden hose to siphon the greywater for use in surface irrigation of the garden. • In most sites, the soil profile showed significant lateral percolation of effluent. As such, the flow of effluent to surface water bodies is a distinct possibility. • The need to investigate the subsurface condition to a depth greater than what is required for the standard percolation test was clearly evident. On occasion, seemingly permeable soil was found to have an underlying impermeable soil layer or vice versa. The important outcomes from the testing program include the following: • Though effluent treatment is influenced by the physico-chemical characteristics of the soil, it was not possible to distinguish between the treatment performance of different soil types. This leads to the hypothesis that effluent renovation is significantly influenced by the combination of various physico-chemical parameters rather than single parameters. This would make the processes involved strongly site specific. • Generally the improvement in effluent quality appears to take place only within the initial 1 m of travel and without any appreciable improvement thereafter. This relates only to the degree of improvement obtained and does not imply that this quality is satisfactory. This calls into question the value of adopting setback distances from sensitive water bodies. • Use of AWTS for sewage treatment may provide effluent of higher quality suitable for surface disposal. However on the whole, after a 1-3 m of travel through the subsurface, it was not possible to distinguish any significant differences in quality between those originating from septic tanks and AWTS. • In comparison with effluent quality from a conventional wastewater treatment plant, most systems were found to perform satisfactorily with regards to Total Nitrogen. The success rate was much lower in the case of faecal coliforms. However it is important to note that five of the systems exhibited problems with regards to effluent disposal, resulting in surface flow. This could lead to possible contamination of surface water courses. • The ratio of TDS to EC is about 0.42 whilst the optimum recommended value for use of treated effluent for irrigation should be about 0.64. This would mean a higher salt content in the effluent than what is advisable for use in irrigation. A consequence of this would be the accumulation of salts to a concentration harmful to crops or the landscape unless adequate leaching is present. These relatively high EC values are present even in the case of AWTS where surface irrigation of effluent is being undertaken. However it is important to note that this is not an artefact of the treatment process but rather an indication of the quality of the wastewater generated in the household. This clearly indicates the need for further research to evaluate the suitability of various soil types for the surface irrigation of effluent where the TDS/EC ratio is less than 0.64. • Effluent percolating through the subsurface absorption field may travel in the form of dilute pulses. As such the effluent will move through the soil profile forming fronts of elevated parameter levels. • The downward flow of effluent and leaching of the soil profile is evident in the case of podsolic, lithosol and kransozem soils. Lateral flow of effluent is evident in the case of prairie soils. Gleyed podsolic soils indicate poor drainage and ponding of effluent. In the current phase of the research project, a number of chemical indicators such as EC, pH and chloride concentration were employed as indicators to investigate the extent of effluent flow and to understand how soil renovates effluent. The soil profile, especially texture, structure and moisture regime was examined more in an engineering sense to determine the effect of movement of water into and through the soil. However it is not only the physical characteristics, but the chemical characteristics of the soil also play a key role in the effluent renovation process. Therefore in order to understand the complex processes taking place in a subsurface effluent disposal area, it is important that the identified influential parameters are evaluated using soil chemical concepts. Consequently the primary focus of the next phase of the research project will be to identify linkages between various important parameters. The research thus envisaged will help to develop robust criteria for evaluating the performance of subsurface disposal systems.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Purpose: Flat-detector, cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. Methods: The rich sources of prior information in IGRT are incorporated into a hidden Markov random field (MRF) model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk (OAR). The voxel labels are estimated using the iterated conditional modes (ICM) algorithm. Results: The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom (CIRS, Inc. model 062). The mean voxel-wise misclassification rate was 6.2%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. Conclusions: By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. The rich sources of prior information in IGRT are incorporated into a hidden Markov random field model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk. The voxel labels are estimated using iterated conditional modes. The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom. The mean voxel-wise misclassification rate was 6.2\%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

Peripheral refraction patterns out to large field angles

Purpose To investigate hyperopic shifts and the oblique (or 45-degree/135-degree) component of astigmatism at large angles in the horizontal visual field using the Hartmann-Shack technique. Methods The adult participants consisted of 6 hypermetropes, 13 emmetropes and 11 myopes. Measurements were made with a modified COAS-HD Hartmann-Shack aberrometer across T60 degrees along the horizontal visual field in 5-degree steps. Eyes were dilated with 1% cyclopentolate. Peripheral refraction was estimated as mean spherical (or spherical equivalent) refraction, with/against the rule of astigmatism and oblique astigmatism components, and as horizontal and vertical refraction components based on 3-mm major diameter elliptical pupils. Results Thirty percent of eyes showed a pattern that was a combination of type IV and type I patterns of Rempt et al. (Rempt F, Hoogerheide J, Hoogenboom WP. Peripheral retinoscopy and the skiagram. Ophthalmologica 1971;162:1Y10), which shows the characteristics of type IV (relative hypermetropia along the vertical meridian and relative myopia along the horizontal meridian) out to an angle of between 40 and 50 degrees before behaving like type I (both meridians show relative hypermetropia). We classified this pattern as type IV/I. Seven of 13 emmetropes had this pattern. As a group, there was no significant variation of the oblique component of astigmatism with angle, but about one-half of the eyes showed significant positive slopes (more positive or less negative values in the nasal field than in the temporal field) and one-fourth showed significant negative slopes. Conclusions It is often considered that a pattern of relative peripheral hypermetropia predisposes to the development of myopia. In this context, the finding of a considerable portion of emmetropes with the IV/I pattern suggests that it is unlikely that refraction at visual field angles beyond 40 degrees from fixation contributes to myopia development.

Pupil shape as viewed along the horizontal visual field

Purpose: Changes in pupil size and shape are relevant for peripheral imagery by affecting aberrations and how much light enters and/or exits the eye. The purpose of this study is to model the pattern of pupil shape across the complete horizontal visual field and to show how the pattern is influenced by refractive error. Methods: Right eyes of thirty participants were dilated with 1% cyclopentolate and images were captured using a modified COAS-HD aberrometer alignment camera along the horizontal visual field to ±90°. A two lens relay system enabled fixation at targets mounted on the wall 3m from the eye. Participants placed their heads on a rotatable chin rest and eye rotations were kept to less than 30°. Best-fit elliptical dimensions of pupils were determined. Ratios of minimum to maximum axis diameters were plotted against visual field angle. Results: Participants’ data were well fitted by cosine functions, with maxima at (–)1° to (–)9° in the temporal visual field and widths 9% to 15% greater than predicted by the cosine of the field angle . Mean functions were 0.99cos[( + 5.3)/1.121], R2 0.99 for the whole group and 0.99cos[( + 6.2)/1.126], R2 0.99 for the 13 emmetropes. The function peak became less temporal, and the width became smaller, with increase in myopia. Conclusion: Off-axis pupil shape changes are well described by a cosine function which is both decentered by a few degrees and flatter by about 12% than the cosine of the viewing angle, with minor influences of refraction.