Some applications of mathematics in golf.

At its core, like many other sports, golf is a game of integers. The minimization of the number of strokes played is generally what determines the winner, whether each of these are associated with the shortest of putts or the longest of drives. The outcomes of these shots are influenced by very slight changes, but hopefully in a deterministic sense. Understanding the mechanics of golf necessitates the development of models and this is coupled more often than not to the use of statistics. In essence, the individual aspects of the sport can be modelled adequately via fairly simplistic models, but the presence of a human at one end of the kinematic chain has a significant impact on the variability of the entire process. In this paper, we will review some of the ways that mathematics has been used to develop the understanding of the physical processes involved in the sport, including some of the analysis which is exploited within the Equipment Rules. We will also discuss some of the future challenges.

Psychophysical measures from electrical stimulation of the human cochlear nucleus.

Auditory performance on basic psychophysical tasks was measured in ten deaf patients with electrodes positioned near their cochlear nucleus. The device is called the auditory brainstem implant (ABI). Electrodes were placed during surgery to remove an acoustic neuroma, which results in the removal of the VIII nerve and, thus deafness. In patients who received auditory sensation from electrical stimulation we measured auditory performance on standard psychophysical tasks: thresholds, loudness growth, intensity discrimination, temporal integration, temporal modulation detection, gap detection, and forward masking. Plots of threshold as a function of frequency or biphasic pulse duration were markedly different from those of patients with cochlear implants. The difference in threshold functions is probably partly due to the biophysical difference in the neural elements stimulated. Another possibility is that part of the difference is due to the highly abnormal spatial pattern of activation in the cochlear nucleus from electrical stimulation, which prevents normal spatial integration of activity. The usable range of electrical amplitudes above threshold is comparable with that of cochlear implants, typically 10-15 dB. Little temporal integration occurs over a range of stimulus durations from 2-1000 ms. When compared at equivalent loudness levels, gap detection thresholds are similar to, or a bit longer than, gap thresholds in normal-hearing listeners and cochlear implant patients. Forward masking recovery functions are similar to those of normal listeners and cochlear implant patients. Patients' ability to detect amplitude modulation as a function of modulation frequency is similar to that of cochlear implant patients and normal listeners. Thus, direct electrical stimulation of the brainstem produces temporal resolution that does not significantly differ from that of normal listeners when compared in equivalent amplitude units. This implies that the limiting factors for these tasks are more centrally located, and not directly related to threshold mechanisms. Thus, a properly designed speech processor could preserve the important temporal features of speech for these patients.

Iowa cochlear implant clinical project: results with two single-channel cochlear implants and one multi-channel cochlear implant.

Cochlear implants have become a realistic alternative for the management of profoundly deaf patients. A variety of implants with differing electrode designs and coding strategies have been developed by nine major implant centers around the world. Each center has their "star" patient, but objective comparisons between these different implant designs are unavailable. In order to determine the performance characteristics of the present generation of cochlear implants, comparison data are vital. We have developed an independent center where uniform objective comparisons of different cochlear implants can be performed longitudinally. This report will present results of nine patients implanted with three different cochlear implant prostheses. Four patients have been implanted with the Los Angeles (House) single-channel implant, three patients have received the Vienna (Hochmair) single-channel intracochlear device, and two patients have been implanted with the Melbourne (Clark) 21-channel unit. All patients have had 11 months or more of experience with their cochlear prostheses. The results of a comprehensive audiologic battery which includes audiovisual and environmental tasks are presented. All implants provide significant improvement in speechreading and sound awareness. The findings to date suggest that there is strong correlation between top-down cognitive processing (as reflected by lip reading skills) and performance with cochlear implants.

Transient sensorineural hearing loss after overuse of portable headphone cassette radios.

Noise-induced sensorineural hearing loss has been associated with industry for many years. One conservative estimate suggests that 10 million Americans may have industry-related, noise-induced hearing loss. Acoustic trauma from any source, whether associated with work or recreations, is detrimental to hearing. The Occupational Safety and Health Administration has set industrial standards for noise levels, with current standards limiting noise exposure to 95 dBA for 2 hours daily. To date, however, there are no recreational standards. Many portable headphone cassette radios produce peak outputs of more than 100 dBA. Temporary threshold shifts could result from listening levels near the maximum output. Permanent sensorineural loss may result with repeated exposure. A pilot study was conducted in which 16 volunteers listened to headphone sets for 3 hours at their usual maximum level. Six volunteers showed transient shifts of 10 dB, and one volunteer showed a transient shift of approximately 30 dB. These shifts returned to normal within 24 hours. As expected, transient shifts frequently occur with recreational use. Therefore, recreational warnings and standards should be established.

The multichannel auditory brain stem implant: performance in twenty patients.

The auditory brain stem implant has been used effectively to provide hearing sensations to individuals deafened by bilateral auditory nerve tumors (neurofibromatosis type 2). During tumor removal, the auditory brain stem implant is implanted into the lateral recess of the fourth ventricle by a translabyrinthine approach and is intended to stimulate auditory neurons of the cochlear nucleus complex. A new eight-electrode multichannel auditory brain stem implant was developed and evaluated in 20 patients who had at least 3 months' experience with the device. Mild nonauditory sensations (primarily tingling in the head or torso) were encountered in some instances but could be managed by changing the stimulus characteristics or excluding electrodes. Testing of perceptual performance indicated significant benefit from the device for communication purposes, including sound-only sentence recognition scores in three patients ranging from 49% to 58% and ability to converse on the telephone. These results indicate that significant auditory benefit can be derived from direct multichannel electrical stimulation of the auditory portion of the human brain stem.

Cochlear implants: histopathologic findings related to performance in 16 human temporal bones.

This paper presents results of a histologic study of 16 temporal bones with cochlear implants from 13 subjects. Damage caused by electrode insertion in the basal turn of the cochlea was evaluated. Dendrite and spiral ganglion cell populations were compared to clinical performance scores to determine structures necessary for stimulation and the minimum number needed for electrical stimulation. Results show that damage from insertion of long electrodes was located mainly at the most anterior part of the basal turn; that despite total degeneration of dendrites in the area near the electrode, some spiral ganglion cells remained; and that spiral ganglion cells or possibly axons are the stimulated structures and that fewer of them than previously thought are necessary to achieve a hearing sensation from electrical stimulation.

Auditory brain stem implant: effect of tumor size and preoperative hearing level on function.

The auditory brain stem implant is an investigational device designed to provide hearing sensations to patients without functioning auditory nerves. We analyzed results from 17 implants in 15 patients to determine if tumor size or preoperative hearing level might be related to proper device function. We found no significant correlation between preoperative hearing level or tumor size and device function. We also found no significant correlation between preoperative hearing level and tumor size in these 15 patients.

Audiological results with two single channel cochlear implants.

We tested six patients with single channel cochlear implants on several tests from the Minimal Auditory Capabilities battery and the Iowa Cochlear Implant Tests. All patients were able to discriminate some everyday sounds and to identify the number of syllables in the words presented. Five patients were able to identify speaker sex reliably. Surprisingly, some patients had difficulty discriminating between a modulated noise and a voice or between a question and a statement or identifying the accented word in a sentence. On several audiovisual tests, an improvement was observed for the sound plus vision condition compared to the vision only condition. This was particularly true for sentence tests, but was not uniform across patients or across tests.

Brainstem electronic implants for bilateral anacusis following surgical removal of cerebello pontine angle lesions.

The multichannel auditory brainstem implant (ABI) has been used successfully to treat deafness in individuals with neurofibromatosis type II. The device has been implanted in nearly 150 recipients worldwide, and clinical trials with the device are approaching completion. The implantation and fitting of the multichannel ABI differ significantly from cochlear implantation, and the processes are illustrated in a series of case studies. Performance data also are included from recipients with up to 7 years experience.

Obstetric clavicular fractures. A three-year analysis.

A three-year retrospective study of al deliveries in a military residency program revealed 24 cases of fractured clavicles. Fifteen of these 24 cases were thoroughly reviewed. The incidence of clavicular fractures was 7.2 per 1,000 term deliveries. Fractured clavicle seemed to be best correlated with birth weight, level of obstetric experience of the delivering physician and midforceps deliveries. It was not well correlated with type of anesthesia, length of labor, length of second stage, Apgar scores, parity and judged difficulty of delivery. Only 1 infant of 15 suffered neurologic injury. A review of the literature and suggestions for possible prevention are presented.

Effects of electrical brainstem stimulation on tinnitus.

The primary aim of the auditory brainstem implant (ABI), an investigational device, is to restore auditory sensations in neurofibromatosis-2 patients deafened by bilateral acoustic neuroma surgery. An electrode is placed on the dorsal cochlear nucleus after the tumor is removed through the translabyrinthine approach. This procedure was performed on 18 patients: 13 were completely deafferentated after bilateral tumor removal and had received the ABI during surgery on the second-sided tumor; 5 were implanted at first-sided tumor removal. Three of these 5 patients had usable hearing remaining on the side of the second acoustic neuroma and were stimulated only during laboratory sessions. All patients had tinnitus. We used a questionnaire to assess the effects of brainstem stimulation on this symptom. Of the 18 patients, one early patient deceased, and one patient with no follow-up was not included in this study. Six patients who were unable to use the ABI because of temporary hardware problems or side effects from electrical stimulation were also excluded. Thus, we studied 10 patients. Of 7 patients who used their implant daily, 6 reported noticeable tinnitus reduction; the ABI had no effect in the remaining case. Of 3 recently implanted patients who used this implant only during laboratory testing, one patient reported complete suppression of tinnitus, one described worse tinnitus, and one reported no effect.

Ball launch conditions for skilled golfers using drivers of different lengths in an indoor testing facility.

The displacement of the golf ball struck by a driving club is affected by several player characteristics and equipment parameters and their interrelationships. Some modelling and simulation studies have shown a relationship between shaft length and clubhead speed, supported by a few experimental studies. The aim of the present study was to examine the relationship between driver length and ball launch conditions in an indoor test facility using a ball launch monitor. Nine males considered to be skilled golfers participated in the study. Four driving clubs of total length 117, 119, 124, and 132 cm were assembled from commercially available components and were used to strike golf shots while initial ball velocity, backspin rate, and launch angles were measured. Statistical analysis identified a significant difference in initial launch speed due to club length, a significant difference between participants, but no difference between the trials for a given golfer. A positive trend was noted between backspin and launch angle for all four clubs, and significant inverse associations between initial launch speed and backspin rate and launch angle. However, the combined launch conditions associated with increasing length were not considered optimal, with uncontrolled swingweight and moment of inertia effects considered to be limiting factors.

Enhanced efficiency of feeding and mixing due to chaotic flow patterns around choanoflagellates.

The motion of particles and feeding currents created by micro-organisms due to a flagellum are considered. The calculations are pertinent to a range of sessile organisms, but we concentrate on a particular organism, namely Salpingoeca amphoridium (SA) (a choanoflagellate), due to the availability of experimental data (Pettitt, 2000). These flow fields are characterized as having very small Reynolds numbers, which implies that viscous forces dominate over inertial ones consistent with using the Stokes flow equations. The flow generated by the flagellum is modelled via the consideration of a point force known as a stokeslet. The interaction between the boundary, to which the organism is attached, and its flagellum leads to toroidal eddies, which serve to transport particles towards the micro-organism, promoting filtering of nutrients by the microvilli which constitute the cell's collar (the filtering mechanism in SA). It is our conjecture that the interaction of multiple toroidal eddies will lead to chaotic advection and hence enhance the domain of feeding for these organisms. The degree of mixing in the region around SA is investigated using chaotic and statistical measures to study the influence the flagellum has on the surrounding fluid. The three-dimensional particle paths around such organisms are also considered with the aim of showing that the plane within which they are situated is an attractor.

The recognition of vowels differing by a single formant by cochlear-implant subjects.

The ability to recognize synthetic, two-formant vowels with equal duration and similar loudness was measured in five subjects with the Cochlear and five subjects with the Symbion cochlear implants. In one set of test stimuli, vowel pairs differed only in the first-formant frequency (F1). In another set, vowel pairs differed only in the second-formant frequency (F2). When F1 differed, four of five Cochlear subjects and four of five Symbion subjects recognized the vowels significantly above chance. When F2 differed, two of five Cochlear subjects and three of five Symbion subjects scored above chance. These results suggest that implanted subjects can utilize both "place" information across different electrodes and "rate" information on a single electrode to derive information about the spectral content of the stimulus.

Cochlear implant histopathology.

Twenty-two temporal bones and one brain stem from 13 cochlear implant patients were examined histologically. Sixteen temporal bones had undergone one or more implant procedure. Results of analysis suggested that the ganglion cells were the responding elements to the implant and that useful auditory sensation could result from as few as 10 percent of the normal number of ganglion cells. All implanted bones exhibited varying amounts of fibrosis (some ossified) in the basal turn of the cochlea and beyond in some cases. Usually there was damage to the surviving elements of the organ of Corti and the dendrites throughout the extent of the electrode insertion. However, the ganglion cell population was not affected. Prolonged electrical stimulation (up to 14 years) did not affect ganglion cell survival in three cases, and had no effect on the cochlear nerves in two cases or on cochlear nuclei in one case.

Initial Iowa results with the multichannel cochlear implant from Melbourne.

Two subjects who use the Melbourne multichannel cochlear implant were studied. Live-voice word, consonant, and vowel recognition tests, and a speech-tracking task were administered at regular intervals during the first 90 days after implantation. Results indicated 30-50% correct recognition of vowels (given 9 alternatives) and about 30-60% correct recognition of consonants (given 12 alternatives). Speech tracking showed from two to three times faster rates with the implant and vision compared to a vision-alone condition. After 3-4 months of implant experience, a number of recorded tests from the Minimal Auditory Capabilities battery and the Iowa Cochlear-Implant tests were then administered. These results indicated about 80% recognition of everyday sounds in a five-choice closed-set condition and about 50% recognition of everyday sounds in an open-set condition. The subjects were 50% correct at identifying the accented words in a sentence and about 50% correct at determining the number of syllables in a word. One subject was unable to recognize a sentence as a statement or a question. Background noise (+10 dB S/N) reduced their performance on a four-choice spondee test to chance. Both subjects were able to identify a sound as either a voice or a modulated noise at 95% correct, and both could recognize speaker sex at 95% correct. Neither could discriminate whether two (successive) sentences were spoken by the same speaker or by two different speakers. Remarkably, one subject identified 45% and the other 85% of the words in sentences that were preceded by a contextual picture using sound alone. One subject identified 13% of the words in sentences in sound alone even without contextual information.

Preliminary assessment of the Los Angeles, Vienna and Melbourne cochlear implants.

We tested four patients using the single-channel cochlear implant from Los Angeles, three patients using the single-channel cochlear implant from Vienna, and two patients using the multichannel cochlear implant from Melbourne. Tests from the MAC battery and the Iowa Cochlear Implant Battery were used. Most patients were able to identify some environmental sounds. Three of the patients had difficulty distinguishing between male and female voices, and three could not distinguish between a noise and a voice. All patients had difficulty discriminating between unknown speakers of the same sex. A four-choice spondee test in noise showed that all patients suffered drastically from background noise. In all cases there was an improvement in lipreading ability with the implant. On a sentence test with a contextual cue seven patients got some words with sound alone. Results obtained with the multichannel implant are superior on several tasks, but we have tested too few patients to allow us any firm conclusions.

Previous experience as a confounding factor in comparing cochlear-implant processing schemes.

It is of great importance to compare the relative merits of different cochlear-implant speech-processing strategies. Some groups have compared different strategies within single subjects, but usually the subject has prior experience with one strategy, and no allowance is made for this prior experience. We show in the present study that this is inappropriate. We tested one subject using the Melbourne (Cochlear Corp.) multichannel implant with the device set to process sounds in two different ways. In the first processing scheme, the device functioned normally, extracting information about voicing frequency, amplitude and second-formant frequency. This information activated the 21-channel device, determining pulse rate, pulse amplitude and electrode position (respectively). In the second processing scheme, a single electrode (with the largest dynamic range) was activated. This electrode coded overall amplitude and voicing frequency. The subject was tested on an audiovisual test of a 14-choice consonant recognition in the form /iCi/ over a period of over 4 months. During this time the subject used the 21-channel processor outside of the laboratory. Upon initial connection, there was little difference between the results obtained with the two schemes when tested in sound alone or in sound plus vision. However, after about 4 months, scores obtained with the 21-channel processor in sound plus vision were superior to the scores obtained with the one channel. This advantage came from a superiority in the features of voicing and nasality, but not place. Scores for sound-alone conditions between the two processing schemes remained similar for the 4-month period.(ABSTRACT TRUNCATED AT 250 WORDS)