Estimation of the mechanical properties of the eye through the study of its vibrational modes

Measuring the eye's mechanical properties in vivo and with minimally invasive techniques can be the key for individualized solutions to a number of eye pathologies. The development of such techniques largely relies on a computational modelling of the eyeball and, it optimally requires the synergic interplay between experimentation and numerical simulation. In Astrophysics and Geophysics the remote measurement of structural properties of the systems of their realm is performed on the basis of (helio-)seismic techniques. As a biomechanical system, the eyeball possesses normal vibrational modes encompassing rich information about its structure and mechanical properties. However, the integral analysis of the eyeball vibrational modes has not been performed yet. Here we develop a new finite difference method to compute both the spheroidal and, specially, the toroidal eigenfrequencies of the human eye. Using this numerical model, we show that the vibrational eigenfrequencies of the human eye fall in the interval 100 Hz - 10 MHz. We find that compressible vibrational modes may release a trace on high frequency changes of the intraocular pressure, while incompressible normal modes could be registered analyzing the scattering pattern that the motions of the vitreous humour leave on the retina. Existing contact lenses with embebed devices operating at high sampling frequency could be used to register the microfluctuations of the eyeball shape we obtain. We advance that an inverse problem to obtain the mechanical properties of a given eye (e.g., Young's modulus, Poisson ratio) measuring its normal frequencies is doable. These measurements can be done using non-invasive techniques, opening very interesting perspectives to estimate the mechanical properties of eyes in vivo. Future research might relate various ocular pathologies with anomalies in measured vibrational frequencies of the eye.Comment: Published in PLoS ONE as Open Access Research Article. 17 pages, 5 color figure

Apparent mass of small children: Modelling

Mass-spring-damper models are widely available for quantifying the whole-body vibration characteristics of primates, human adolescents and human adults, but no models have previously been developed for small children. In this study a single degree of freedom, linear, mass-spring-damper with base support model was determined from the seated vertical apparent mass modulus function of each of eight small children of less than 18 kg in mass. A Differential Evolution optimisation algorithm was used in conjunction with a mean squared error measure and penalty functions to identify the optimal child model parameter values. The eight child models were characterised by a mean moving mass m1 of 8.5 kg, a mean body stiffness k1 of 21131 N/m and a mean damping coefficient c1 of 329 Ns/m. Comparison to the parameter values of similar models reported in the literature for Rhesus monkeys, Baboons, large children and adults suggests that the values obtained in the current study for small children are intermediate between the smaller primates and the larger humans. A regression analysis of the model parameters was performed as a function of subject mass for a data set consisting of the eight child models, twelve similar models for primates, and 60 similar models for large children and adults. The moving mass m1 of the group of models grew with a power exponent of approximately unity, the body stiffness k1 grew with a power exponent of approximately +1/2, the damping coefficient c1 grew with a power exponent of approximately +3/4 and the dimensionless damping ratio was independent of subject mass. The natural frequency of the models grew with a power exponent of approximately –1/4

Aerospace Medicine and Biology: A continuing supplement 180, May 1978

This special bibliography lists 201 reports, articles, and other documents introduced into the NASA scientific and technical information system in April 1978

Non-local first-order modelling of crowd dynamics: a multidimensional framework with applications

In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is provided. Within this common framework, two first-order mathematical models, along with related numerical solution techniques, are derived. The models are oriented to specific real world applications: a one-dimensional model of crowd-structure interaction in footbridges and a two-dimensional model of pedestrian flow in an underground station with several obstacles and exits. The noticeable heterogeneity of the applications demonstrates the significance of the physical framework and its versatility in addressing different engineering problems. The results of the simulations point out the key role played by the physiological and psychological features of human perception on the overall crowd dynamics.Comment: 26 pages, 17 figure

Review of Hyperspace by Michio Kaku (1994)

"There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact" Mark Twain-Life on the Mississippi This is a lovely book full of fascinating info on the evolution of physics and cosmology. Its main theme is how the idea of higher dimensional geometry created by Riemann, recently extended to 24 dimensions by string theory, has revolutionized our understanding of the universe. Everyone knows that Riemann created multidimensional geometry in 1854 but it is amazing to learn that he also was a physicist who believed that it held the key to explaining the fundamental laws of physics. Maxwell´s equations did not exist then and Riemann´s untimely death at age 39 prevented his pursuit of these ideas. Both he and his British translator Clifford believed that magnetic and electric fields resulted from the bending of space in the 4th dimension-more than 50 years before Einstein! The fourth dimension became a standard subject in the popular media for the next 50 years with several stories by HG Wells using it and even Lenin wrote about it. The American mathematician Hinton had widely publicized his idea that light is a vibration in the 4th spatial dimension. Amazingly, physicists and most mathematicians forgot about it and when Einstein was looking for the math needed to encompass general relativity 60 years later, he had never heard of Riemannian geometry. He spent 3 years trying to find the equations for general relativity and only after a math friend told him about Riemann was he able to complete his work. Riemann´s equations with four dimensional metric tensors describing every point in space were incorporated almost unchanged into relativity. And on and on it goes. Since this review I have written a great deal on the language games of math and science, uncertainty, incompleteness, the limits of computation etc., so those interested should find them useful since this volume like most science frequently wanders across the line into philosophy (scientism). Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019

A frequency weighting for the evaluation of steering wheel rotational vibration

The human perception of rotational hand-arm vibration has been investigated by means of a test rig consisting of a rigid frame, an electrodynamic shaker unit, a rigid steering wheel, a shaft assembly, bearings and an automobile seat. Fifteen subjects were tested while seated in a driving posture. Four equal sensation tests and one annoyance threshold test were performed using sinusoidal excitation at 18 frequencies in the range from 3 to 315 Hz. In order to guarantee the generality of the equal sensation data the four tests were defined to permit checks of the possible influence of three factors: reference signal amplitude, psychophysical test procedure and temporary threshold shift (TTSv) caused by the test exposure. All equal sens ation tests used a reference sinusoid of 63 Hz at either 1.0 or 1.5 m/s2 r.m.s. in amplitude. The four equal sensation curves were similar in shape and suggested a decrease in human sensitivity to hand-arm rotational vibration with increasing frequency. The slopes of the equal sensation curves changed at transition points of approximately 6.3 and 63 Hz. A frequency weighting, called Ws, was developed for the purpose of evaluating steering wheel rotational vibration. The proposed Ws has a slope of 0 dB per octave over the frequency range from 3 to 6.3 Hz, a slope of -6 dB per octave from 6.3 to 50 Hz, a slope of 0 dB per octave from 50 to 160 Hz and a slope of -10 dB per octave from 160 to 315 Hz. Ws provides a possible alternative to the existing Wh frequency weighting defined in International Standards Organisation 5349-1 (2001) and British Standards Institution 6842 (1987)

An integrated approach to whole-body vibration

Obiettivo di questa tesi è la determinazione e quantificazione degli effetti della whole-body vibration al corpo umano, in termini di consumo energetico, tramite un approccio globale e integrato. L’obiettivo è ottenuto considerando il corpo umano come una struttura organica complessa. Allo scopo di comprendere come questo risponda alle vibrazioni verticali, il consumo energetico del corpo umano è stato misurato per mezzo della variazione della temperatura superficiale con tecniche di misurazione a termografia infrarossa. Lo spostamento dei muscoli invece con il sistema di analisi di movimento Vicon MX. Infine, per quanto riguarda il consumo di ossigeno con il sistema telemetrico Cosmed K4. Il primo passo è stato l’istituzione di un protocollo appropriato che soddisfi l’obiettivo di questo studio. Infatti, la mancanza di coerenza nei protocollo di whole-body vibration che si trovano allo stato dell’arte, ha reso essenziale l’istituzione di un apposito protocollo, ed a questo scopo è stata definita la struttura dell’esperimento. Di conseguenza, è stata avviata una serie di prove per esaminare la risposta del corpo umano alle vibrazioni verticali, cambiando la durata e la frequenza della vibrazione, nonché la durata del periodo di riposo. In totale, quattro persone in piedi sono state sottoposte a vibrazioni verticali, in una pedana vibrante, a frequenze da 20 a 50 Hz. Dopo l’instaurazione del protocollo finale, sono stati avviate una serie di prove di laboratorio. In particolare, sono state scelte tre frequenze per le vibrazioni: 20, 30 e 45 Hz. I risultati ottenuti più interessanti di questo studio, riguardano il consumo di ossigeno, la temperatura superficiale e i coefficienti di trasmissibilità dell’accelerazione.The objective of this thesis is to determine and quantify the effects of whole-body vibration to the human body in terms of energy expenditure, by means of a global and integrated approach. This objective is attained by considering the human body as a complex organic structure. In order to understand how it responds to vertical vibrations, the energy expenditure of the human body was measured by means of the variation in superficial temperature with the aid of infrared thermography, the displacement of the muscles with the aid of the Vicon MX motion analysis system and the oxygen uptake with the aid of the Cosmed K4 telemetric system. The establishment of an appropriate protocol which satisfies the aim of this study was the first goal. The lack of consistency in whole-body vibration protocols in the current published studies makes the establishment of an appropriate protocol essential, and in this sense, an experiment setup was implemented. Therefore, a series of experiments was conducted to examine the response of the human body to vertical vibrations, changing the duration and the frequency of vertical vibration, and the duration of rest period. A number of four persons were subjected to vertical vibrations on a vibrating table in a standing position at a frequency ranging from 20 to 50 Hz. After the establishment of the final protocol, a series of laboratory experiments took place. Three different vibration frequencies were chosen: 20, 30 and 45 Hz corresponding to three different tests. The most interesting findings regard the oxygen consumption, the superficial temperature evolution, and the transmissibility coefficients for the acceleration

Hybrid artificial genetic – neural network model to predict the transmission of vibration to the head during whole-body vibration training

In this work, Artificial Neural Network (ANN) modelling has been employed to investigate the effects of various factors on the biodynamic responses to vibration represented by the transmissibility and its phase. These factors include, height, weight, Body Mass Index (BMI), age, frequency and posture. Nine subjects stood on a vibrating plate and were exposed to vertical vibration at nine frequencies in the range 17-46 Hz while adopting four different standing postures; Bent Knee posture (BK), Locked Knee posture (LK), right foot to the Front and left foot to the Back posture (FB) and One Leg posture (OL). The accelerations of the vibrating plate and the head of the subjects were measured during the exposure to vibration in order to calculate the transmissibility between the vibrating plate and the head. Genetic Algorithm (GA) was used to choose ANN’s number of hidden layers and number of neurons in each layer to obtain the best performance for predicting the transmissibility. The GA compared the root mean square errors (RMSE) between the ANN outputs and the experimental outputs, and then choose the best results that could be achieved. The number of hidden layers and number of neurons tested in GA vary from one hidden layer to four hidden layers, and from one neuron per layer to one hundred neurons per layer. Several runs have been conducted to train and validate the ANN model. The results show that double hidden layer with 13 neurons in the first layer and 12 neurons in the second layer give the best candidate. The proposed model can be integrated with whole-body vibration machines in order to choose the suitable exposure based on the user’s characteristics