192 resultados para Constant hysteresis
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Impedance cardiography is an application of bioimpedance analysis primarily used in a research setting to determine cardiac output. It is a non invasive technique that measures the change in the impedance of the thorax which is attributed to the ejection of a volume of blood from the heart. The cardiac output is calculated from the measured impedance using the parallel conductor theory and a constant value for the resistivity of blood. However, the resistivity of blood has been shown to be velocity dependent due to changes in the orientation of red blood cells induced by changing shear forces during flow. The overall goal of this thesis was to study the effect that flow deviations have on the electrical impedance of blood, both experimentally and theoretically, and to apply the results to a clinical setting. The resistivity of stationary blood is isotropic as the red blood cells are randomly orientated due to Brownian motion. In the case of blood flowing through rigid tubes, the resistivity is anisotropic due to the biconcave discoidal shape and orientation of the cells. The generation of shear forces across the width of the tube during flow causes the cells to align with the minimal cross sectional area facing the direction of flow. This is in order to minimise the shear stress experienced by the cells. This in turn results in a larger cross sectional area of plasma and a reduction in the resistivity of the blood as the flow increases. Understanding the contribution of this effect on the thoracic impedance change is a vital step in achieving clinical acceptance of impedance cardiography. Published literature investigates the resistivity variations for constant blood flow. In this case, the shear forces are constant and the impedance remains constant during flow at a magnitude which is less than that for stationary blood. The research presented in this thesis, however, investigates the variations in resistivity of blood during pulsataile flow through rigid tubes and the relationship between impedance, velocity and acceleration. Using rigid tubes isolates the impedance change to variations associated with changes in cell orientation only. The implications of red blood cell orientation changes for clinical impedance cardiography were also explored. This was achieved through measurement and analysis of the experimental impedance of pulsatile blood flowing through rigid tubes in a mock circulatory system. A novel theoretical model including cell orientation dynamics was developed for the impedance of pulsatile blood through rigid tubes. The impedance of flowing blood was theoretically calculated using analytical methods for flow through straight tubes and the numerical Lattice Boltzmann method for flow through complex geometries such as aortic valve stenosis. The result of the analytical theoretical model was compared to the experimental impedance measurements through rigid tubes. The impedance calculated for flow through a stenosis using the Lattice Boltzmann method provides results for comparison with impedance cardiography measurements collected as part of a pilot clinical trial to assess the suitability of using bioimpedance techniques to assess the presence of aortic stenosis. The experimental and theoretical impedance of blood was shown to inversely follow the blood velocity during pulsatile flow with a correlation of -0.72 and -0.74 respectively. The results for both the experimental and theoretical investigations demonstrate that the acceleration of the blood is an important factor in determining the impedance, in addition to the velocity. During acceleration, the relationship between impedance and velocity is linear (r2 = 0.98, experimental and r2 = 0.94, theoretical). The relationship between the impedance and velocity during the deceleration phase is characterised by a time decay constant, ô , ranging from 10 to 50 s. The high level of agreement between the experimental and theoretically modelled impedance demonstrates the accuracy of the model developed here. An increase in the haematocrit of the blood resulted in an increase in the magnitude of the impedance change due to changes in the orientation of red blood cells. The time decay constant was shown to decrease linearly with the haematocrit for both experimental and theoretical results, although the slope of this decrease was larger in the experimental case. The radius of the tube influences the experimental and theoretical impedance given the same velocity of flow. However, when the velocity was divided by the radius of the tube (labelled the reduced average velocity) the impedance response was the same for two experimental tubes with equivalent reduced average velocity but with different radii. The temperature of the blood was also shown to affect the impedance with the impedance decreasing as the temperature increased. These results are the first published for the impedance of pulsatile blood. The experimental impedance change measured orthogonal to the direction of flow is in the opposite direction to that measured in the direction of flow. These results indicate that the impedance of blood flowing through rigid cylindrical tubes is axisymmetric along the radius. This has not previously been verified experimentally. Time frequency analysis of the experimental results demonstrated that the measured impedance contains the same frequency components occuring at the same time point in the cycle as the velocity signal contains. This suggests that the impedance contains many of the fluctuations of the velocity signal. Application of a theoretical steady flow model to pulsatile flow presented here has verified that the steady flow model is not adequate in calculating the impedance of pulsatile blood flow. The success of the new theoretical model over the steady flow model demonstrates that the velocity profile is important in determining the impedance of pulsatile blood. The clinical application of the impedance of blood flow through a stenosis was theoretically modelled using the Lattice Boltzman method (LBM) for fluid flow through complex geometeries. The impedance of blood exiting a narrow orifice was calculated for varying degrees of stenosis. Clincial impedance cardiography measurements were also recorded for both aortic valvular stenosis patients (n = 4) and control subjects (n = 4) with structurally normal hearts. This pilot trial was used to corroborate the results of the LBM. Results from both investigations showed that the decay time constant for impedance has potential in the assessment of aortic valve stenosis. In the theoretically modelled case (LBM results), the decay time constant increased with an increase in the degree of stenosis. The clinical results also showed a statistically significant difference in time decay constant between control and test subjects (P = 0.03). The time decay constant calculated for test subjects (ô = 180 - 250 s) is consistently larger than that determined for control subjects (ô = 50 - 130 s). This difference is thought to be due to difference in the orientation response of the cells as blood flows through the stenosis. Such a non-invasive technique using the time decay constant for screening of aortic stenosis provides additional information to that currently given by impedance cardiography techniques and improves the value of the device to practitioners. However, the results still need to be verified in a larger study. While impedance cardiography has not been widely adopted clinically, it is research such as this that will enable future acceptance of the method.
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With rising environmental alarm, the reduction of critical aircraft emissions including carbon dioxides (CO2) and nitrogen oxides (NOx) is one of most important aeronautical problems. There can be many possible attempts to solve such problem by designing new wing/aircraft shape, new efficient engine, etc. The paper rather provides a set of acceptable flight plans as a first step besides replacing current aircrafts. The paper investigates a green aircraft design optimisation in terms of aircraft range, mission fuel weight (CO2) and NOx using advanced Evolutionary Algorithms coupled to flight optimisation system software. Two multi-objective design optimisations are conducted to find the best set of flight plans for current aircrafts considering discretised altitude and Mach numbers without designing aircraft shape and engine types. The objectives of first optimisation are to maximise range of aircraft while minimising NOx with constant mission fuel weight. The second optimisation considers minimisation of mission fuel weight and NOx with fixed aircraft range. Numerical results show that the method is able to capture a set of useful trade-offs that reduce NOx and CO2 (minimum mission fuel weight).
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Track defects cause profound effects to the stability of railway wagons; normally such problems are modeled for cases of wagons running at constant speed. Brake/traction torque adversely affect the wheel-rail contact characteristics but they are not explicitly considered in most of the wagon-track interaction simulation packages. This research developed a program that can simulate the longitudinal behaviour of railway wagon dynamics under the actions of braking or traction torques. This paper describes the mathematical formulation of modelling of a full wagon system using a fixed coordinate reference system. The effect of both the lateral and the vertical track geometry defects to the dynamics of wagons is reported; sensitivity of traction/brake state is analysed through a series of numerical examples.
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THEATRE: The New Dead: Medea Material. By Heiner Muller. Stella Electrika in association with La Boite Theatre Company, Brisbane, November 19. THERE has been a lot of intensity in independent theatre in Brisbane during the past year, as companies, production houses and producers have begun building new programs and platforms to support an expansion of pathways within the local theatre ecology. Audiences have been exposed to works signalling the diversity of what Brisbane theatre makers want to see on stage, from productions of new local and international pieces to new devised works, and the results of residencies and development programs. La Boite Theatre Company closes its inaugural indie season with a work that places it at the contemporary, experimental end of the spectrum. The New Dead: Medea Material is emerging director Kat Henry's interpretation of Heiner Muller's 1981 text Despoiled Shore Medea Material Landscape with Argonauts. Start of sidebar. Skip to end of sidebar. End of sidebar. Return to start of sidebar. Muller is known for his radical adaptations of historical dramas, from the Greeks to Shakespeare, and for deconstructed texts in which the characters - in this case, Medea - violently reject the familial, cultural and political roles society has laid out for them. Muller's combination of deconstructed characters, disconnected poetic language and constant references to aspects of popular culture and the Cold War politics he sought to abjure make his texts challenging to realise. The poetry entices but the density, together with the increasing distance of the Cold War politics in the texts, leaves contemporary directors with clear decisions to make about how to adapt these open texts. In The New Dead: Medea Material, Henry works with some interesting imagery and conceptual territory. Lucinda Shaw as Medea, Guy Webster as Jason and Kimie Tsukakoshi as King Creon's daughter Glauce, the woman for whom Jason forsakes his wife Medea, each reference different aspects of contemporary culture. Medea is a bitter, drunken, satin-gowned diva with bite; Jason - first seen lounging in front of the television with a beer in an image reminiscent of Sarah Kane's in-yer-face characterisation of Hippolytus in Phaedra's Love - has something of the rock star about him; and Glauce is a roller-skating, karaoke-singing, pole-dancing young temptress. The production is given a contemporary tone, dominated by Medea's twisted love and loss, rather than by any commentary on her circumstances. Its strength is the aesthetic Henry creates, supported by live electro-pop music, a band stage that stands as a metaphor for Jason's sea voyage, and multimedia that inserts images of the story unfolding beyond these characters' speeches as sorts of subconscious flashes. While Tsukakoshi is engaging throughout, there are moments when Shaw and Webster's performances - particularly in the songs - are diminished by a lack of clarity. The result is a piece that, while slightly lacking in its realisation at times, undoubtedly flags Henry's facility as an emerging director and what she wants to bring to the Brisbane theatre scene.
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Rationale, aims and objectives: Patient preference for interventions aimed at preventing in-hospital falls has not previously been investigated. This study aims to contrast the amount patients are willing to pay to prevent falls through six intervention approaches. ----- ----- Methods: This was a cross-sectional willingness-to-pay (WTP), contingent valuation survey conducted among hospital inpatients (n = 125) during their first week on a geriatric rehabilitation unit in Queensland, Australia. Contingent valuation scenarios were constructed for six falls prevention interventions: a falls consultation, an exercise programme, a face-to-face education programme, a booklet and video education programme, hip protectors and a targeted, multifactorial intervention programme. The benefit to participants in terms of reduction in risk of falls was held constant (30% risk reduction) within each scenario. ----- ----- Results: Participants valued the targeted, multifactorial intervention programme the highest [mean WTP (95% CI): $(AUD)268 ($240, $296)], followed by the falls consultation [$215 ($196, $234)], exercise [$174 ($156, $191)], face-to-face education [$164 ($146, $182)], hip protector [$74 ($62, $87)] and booklet and video education interventions [$68 ($57, $80)]. A ‘cost of provision’ bias was identified, which adversely affected the valuation of the booklet and video education intervention. ----- ----- Conclusion: There may be considerable indirect and intangible costs associated with interventions to prevent falls in hospitals that can substantially affect patient preferences. These costs could substantially influence the ability of these interventions to generate a net benefit in a cost–benefit analysis.
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This thesis investigates the coefficient of performance (COP) of a hybrid liquid desiccant solar cooling system. This hybrid cooling system includes three sections: 1) conventional air-conditioning section; 2) liquid desiccant dehumidification section and 3) air mixture section. The air handling unit (AHU) with mixture variable air volume design is included in the hybrid cooling system to control humidity. In the combined system, the air is first dehumidified in the dehumidifier and then mixed with ambient air by AHU before entering the evaporator. Experiments using lithium chloride as the liquid desiccant have been carried out for the performance evaluation of the dehumidifier and regenerator. Based on the air mixture (AHU) design, the electrical coefficient of performance (ECOP), thermal coefficient of performance (TCOP) and whole system coefficient of performance (COPsys) models used in the hybrid liquid desiccant solar cooing system were developed to evaluate this system performance. These mathematical models can be used to describe the coefficient of performance trend under different ambient conditions, while also providing a convenient comparison with conventional air conditioning systems. These models provide good explanations about the relationship between the performance predictions of models and ambient air parameters. The simulation results have revealed the coefficient of performance in hybrid liquid desiccant solar cooling systems substantially depends on ambient air and dehumidifier parameters. Also, the liquid desiccant experiments prove that the latent component of the total cooling load requirements can be easily fulfilled by using the liquid desiccant dehumidifier. While cooling requirements can be met, the liquid desiccant system is however still subject to the hysteresis problems.
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This paper discusses control strategies adapted for practical implementation and efficient motion of underwater vehicles. These trajectories are piecewise constant thrust arcs with few actuator switchings. We provide the numerical algorithm which computes the time efficient trajectories parameterized by the switching times. We discuss both the theoretical analysis and experimental implementation results.
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Purpose: This paper investigates whether Socially Responsible Investment (SRI) is less sensitive to market downturns than conventional investments; the legal implications for fund managers and trustees; and possible legislative reforms to allow conventional funds more scope to invest in SRI. ----- ----- Design/methodology/approach: The paper uses the market model to estimate betas over the past 15 years for SRI funds and conventional investment funds during economic downturns, as distinct from during more ‘normal’ (non-recessionary) economic times. ----- ----- Findings: The beta risk of SRI, both in Australia and internationally, increases more than that of conventional investment during economic downturns. Traditional fund managers and trustees in Australia are therefore likely to breach their fiduciary duties if they go long - or remain long - in SRI funds during economic downturns, unless relevant legislation is reformed. ----- ----- Research limitations/implications: The methodology assumes that alpha and beta in the market model are constant. This is the subject of ongoing research. Second, it categorises the state of the market into ‘normal’ economic conditions and downturns using dummy variables. More sophisticated techniques could be used in future research. ----- ----- Practical implications: The current law would prevent conventional funds from investing in SRI. If SRI is viewed as socially desirable, useful legislative reforms could include explicitly overriding the common law to allow conventional funds to invest in SRI; introducing a 150% tax deduction or investment allowance for SRI; and allowing SRI sub-funds to obtain Deductible Gift Recipient status from the Australian Tax Office and other taxation authorities. ----- ----- Originality/value: The accurate assessment of risk in SRIs is an area which, despite its serious legal implications, is yet to be subjected to rigorous empirical investigation. Keywords - SRI, market model, GARCH, trust fund, fiduciary duties, market downturns, Australia.
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Common mode voltage generated by a power converter in combination with parasitic capacitive couplings is a potential source of shaft voltage in an AC motor drive system. In this paper, a three-phase motor drive system supplied with a single-phase AC-DC diode rectifier is investigated in order to reduce shaft voltage in a three-phase AC motor drive system. In this topology, the common mode voltage generated by the inverter is influenced by the AC-DC diode rectifier because the placement of the neutral point is changing in different rectifier circuit states. A pulse width modulation technique is presented by a proper placement of the zero vectors to reduce the common mode voltage level, which leads to a cost effective shaft voltage reduction technique without load current distortion, while keeping the switching frequency constant. Analysis and simulations have been presented to investigate the proposed method.
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Previous research has suggested that perceptual-motor difficulties may account for obese children's lower motor competence; however, specific evidence is currently lacking. Therefore, this study examined the effect of altered visual conditions on spatiotemporal and kinematic gait parameters in obese versus normal-weight children. Thirty-two obese and normal-weight children (11.2 ± 1.5 years) walked barefoot on an instrumented walkway at constant self-selected speed during LIGHT and DARK conditions. Three-dimensional motion analysis was performed to calculate spatiotemporal parameters, as well as sagittal trunk segment and lower extremity joint angles at heel-strike and toe-off. Self-selected speed did not significantly differ between groups. In the DARK condition, all participants walked at a significantly slower speed, decreased stride length, and increased stride width. Without normal vision, obese children had a more pronounced increase in relative double support time compared to the normal-weight group, resulting in a significantly greater percentage of the gait cycle spent in stance. Walking in the DARK, both groups showed greater forward tilt of the trunk and restricted hip movement. All participants had increased knee flexion at heel-strike, as well as decreased knee extension and ankle plantarflexion at toe-off in the DARK condition. The removal of normal vision affected obese children's temporal gait pattern to a larger extent than that of normal-weight peers. Results suggest an increased dependency on vision in obese children to control locomotion. Next to the mechanical problem of moving excess mass, a different coupling between perception and action appears to be governing obese children's motor coordination and control.
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Triggered by the continuing global financial crisis, most public administration systems internationally are reviewing their ability to meet public expectations in more challenging strategic environments, while satisfying the pressure from their political masters to drive down the costs of public administration. Consequently public sector organizations are under constant pressure to reform to meet not only the global economic challenges, but the need for more responsive government (Brown et al 2003). Doyle et al (2000) propose that organizational change is seldom well managed, but that the public sector faces greater difficulty in implementing corporate change than the private sector because of its unique environment, e.g. the need to deliver bureaucratically impartial outcomes. The scale of the changes required, and the constraints imposed by the context within which these changes need to occur, have intensified the need for capable public sector leadership and management. The types of capability required now extend beyond those typically required in public organizations through the efficiency drive of new public management. Acquiring these capabilities remains a key issue for public organizations. One challenge for public management, then, is leadership and management quality, including the need to recruit externally to refresh, re-energize and change the sector and its individual organizations as well as develop advanced skills among existing senior executives.
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This paper describes a novel probabilistic approach to incorporating odometric information into appearance-based SLAM systems, without performing metric map construction or calculating relative feature geometry. The proposed system, dubbed Continuous Appearance-based Trajectory SLAM (CAT-SLAM), represents location as a probability distribution along a trajectory, and represents appearance continuously over the trajectory rather than at discrete locations. The distribution is evaluated using a Rao-Blackwellised particle filter, which weights particles based on local appearance and odometric similarity and explicitly models both the likelihood of revisiting previous locations and visiting new locations. A modified resampling scheme counters particle deprivation and allows loop closure updates to be performed in constant time regardless of map size. We compare the performance of CAT-SLAM to FAB-MAP (an appearance-only SLAM algorithm) in an outdoor environment, demonstrating a threefold increase in the number of correct loop closures detected by CAT-SLAM.
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This paper proposes the use of the Bayes Factor as a distance metric for speaker segmentation within a speaker diarization system. The proposed approach uses a pair of constant sized, sliding windows to compute the value of the Bayes Factor between the adjacent windows over the entire audio. Results obtained on the 2002 Rich Transcription Evaluation dataset show an improved segmentation performance compared to previous approaches reported in literature using the Generalized Likelihood Ratio. When applied in a speaker diarization system, this approach results in a 5.1% relative improvement in the overall Diarization Error Rate compared to the baseline.
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Intrinsically photosensitive retinal ganglion cells (ipRGC) signal environmental light level to the central circadian clock and contribute to the pupil light reflex. It is unknown if ipRGC activity is subject to extrinsic (central) or intrinsic (retinal) network-mediated circadian modulation during light entrainment and phase shifting. Eleven younger persons (18–30 years) with no ophthalmological, medical or sleep disorders participated. The activity of the inner (ipRGC) and outer retina (cone photoreceptors) was assessed hourly using the pupil light reflex during a 24 h period of constant environmental illumination (10 lux). Exogenous circadian cues of activity, sleep, posture, caffeine, ambient temperature, caloric intake and ambient illumination were controlled. Dim-light melatonin onset (DLMO) was determined from salivary melatonin assay at hourly intervals, and participant melatonin onset values were set to 14 h to adjust clock time to circadian time. Here we demonstrate in humans that the ipRGC controlled post-illumination pupil response has a circadian rhythm independent of external light cues. This circadian variation precedes melatonin onset and the minimum ipRGC driven pupil response occurs post melatonin onset. Outer retinal photoreceptor contributions to the inner retinal ipRGC driven post-illumination pupil response also show circadian variation whereas direct outer retinal cone inputs to the pupil light reflex do not, indicating that intrinsically photosensitive (melanopsin) retinal ganglion cells mediate this circadian variation.
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The depth of focus (DOF) can be defined as the variation in image distance of a lens or an optical system which can be tolerated without incurring an objectionable lack of sharpness of focus. The DOF of the human eye serves a mechanism of blur tolerance. As long as the target image remains within the depth of focus in the image space, the eye will still perceive the image as being clear. A large DOF is especially important for presbyopic patients with partial or complete loss of accommodation (presbyopia), since this helps them to obtain an acceptable retinal image when viewing a target moving through a range of near to intermediate distances. The aim of this research was to investigate the DOF of the human eye and its association with the natural wavefront aberrations, and how higher order aberrations (HOAs) can be used to expand the DOF, in particular by inducing spherical aberrations ( 0 4 Z and 0 6 Z ). The depth of focus of the human eye can be measured using a variety of subjective and objective methods. Subjective measurements based on a Badal optical system have been widely adopted, through which the retinal image size can be kept constant. In such measurements, the subject.s tested eye is normally cyclopleged. Objective methods without the need of cycloplegia are also used, where the eye.s accommodative response is continuously monitored. Generally, the DOF measured by subjective methods are slightly larger than those measured objectively. In recent years, methods have also been developed to estimate DOF from retinal image quality metrics (IQMs) derived from the ocular wavefront aberrations. In such methods, the DOF is defined as the range of defocus error that degrades the retinal image quality calculated from the IQMs to a certain level of the possible maximum value. In this study, the effect of different amounts of HOAs on the DOF was theoretically evaluated by modelling and comparing the DOF of subjects from four different clinical groups, including young emmetropes (20 subjects), young myopes (19 subjects), presbyopes (32 subjects) and keratoconics (35 subjects). A novel IQM-based through-focus algorithm was developed to theoretically predict the DOF of subjects with their natural HOAs. Additional primary spherical aberration ( 0 4 Z ) was also induced in the wavefronts of myopes and presbyopes to simulate the effect of myopic refractive correction (e.g. LASIK) and presbyopic correction (e.g. progressive power IOL) on the subject.s DOF. Larger amounts of HOAs were found to lead to greater values of predicted DOF. The introduction of primary spherical aberration was found to provide moderate increase of DOF while slightly deteriorating the image quality at the same time. The predicted DOF was also affected by the IQMs and the threshold level adopted. We then investigated the influence of the chosen threshold level of the IQMs on the predicted DOF, and how it relates to the subjectively measured DOF. The subjective DOF was measured in a group of 17 normal subjects, and we used through-focus visual Strehl ratio based on optical transfer function (VSOTF) derived from their wavefront aberrations as the IQM to estimate the DOF. The results allowed comparison of the subjective DOF with the estimated DOF and determination of a threshold level for DOF estimation. Significant correlation was found between the subject.s estimated threshold level for the estimated DOF and HOA RMS (Pearson.s r=0.88, p<0.001). The linear correlation can be used to estimate the threshold level for each individual subject, subsequently leading to a method for estimating individual.s DOF from a single measurement of their wavefront aberrations. A subsequent study was conducted to investigate the DOF of keratoconic subjects. Significant increases of the level of HOAs, including spherical aberration, coma and trefoil, can be observed in keratoconic eyes. This population of subjects provides an opportunity to study the influence of these HOAs on DOF. It was also expected that the asymmetric aberrations (coma and trefoil) in the keratoconic eye could interact with defocus to cause regional blur of the target. A dual-Badal-channel optical system with a star-pattern target was used to measure the subjective DOF in 10 keratoconic eyes and compared to those from a group of 10 normal subjects. The DOF measured in keratoconic eyes was significantly larger than that in normal eyes. However there was not a strong correlation between the large amount of HOA RMS and DOF in keratoconic eyes. Among all HOA terms, spherical aberration was found to be the only HOA that helped to significantly increase the DOF in the studied keratoconic subjects. Through the first three studies, a comprehensive understanding of DOF and its association to the HOAs in the human eye had been achieved. An adaptive optics system was then designed and constructed. The system was capable of measuring and altering the wavefront aberrations in the subject.s eye and measuring the resulting DOF under the influence of different combination of HOAs. Using the AO system, we investigated the concept of extending the DOF through optimized combinations of 0 4 Z and 0 6 Z . Systematic introduction of a targeted amount of both 0 4 Z and 0 6 Z was found to significantly improve the DOF of healthy subjects. The use of wavefront combinations of 0 4 Z and 0 6 Z with opposite signs can further expand the DOF, rather than using 0 4 Z or 0 6 Z alone. The optimal wavefront combinations to expand the DOF were estimated using the ratio of increase in DOF and loss of retinal image quality defined by VSOTF. In the experiment, the optimal combinations of 0 4 Z and 0 6 Z were found to provide a better balance of DOF expansion and relatively smaller decreases in VA. Therefore, the optimal combinations of 0 4 Z and 0 6 Z provides a more efficient method to expand the DOF rather than 0 4 Z or 0 6 Z alone. This PhD research has shown that there is a positive correlation between the DOF and the eye.s wavefront aberrations. More aberrated eyes generally have a larger DOF. The association of DOF and the natural HOAs in normal subjects can be quantified, which allows the estimation of DOF directly from the ocular wavefront aberration. Among the Zernike HOA terms, spherical aberrations ( 0 4 Z and 0 6 Z ) were found to improve the DOF. Certain combinations of 0 4 Z and 0 6 Z provide a more effective method to expand DOF than using 0 4 Z or 0 6 Z alone, and this could be useful in the optimal design of presbyopic optical corrections such as multifocal contact lenses, intraocular lenses and laser corneal surgeries.