Fractals and the analysis of growth paths

Mapping Extracellular Space Features of Viral Encephalitis to Evaluate the Proficiency of Anti-Viral Drugs

The extracellular space (ECS) is an important barrier against viral attack on brain cells, and dynamic changes in ECS microstructure characteristics are closely related to the progression of viral encephalitis in the brain and the efficacy of antiviral drugs. However, mapping the precise morphological and rheological features of the ECS in viral encephalitis is still challenging so far. Here, a robust approach is developed using single-particle diffusional fingerprinting of quantum dots combined with machine learning to map ECS features in the brain and predict the efficacy of antiviral encephalitis drugs. These results demonstrated that this approach can characterize the microrheology and geometry of the brain ECS at different stages of viral infection and identify subtle changes induced by different drug treatments. This approach provides a potential platform for drug proficiency assessment and is expected to offer a reliable basis for the clinical translation of drugs.

Nonlinear Measures to Evaluate Upright Postural Stability: A Systematic Review

Conventional biomechanical analyses of human movement have been generally derived from linear mathematics. While these methods can be useful in many situations, they fail to describe the behavior of the human body systems that are predominately nonlinear. For this reason, nonlinear analyses have become more prevalent in recent literature. These analytical techniques are typically investigated using concepts related to variability, stability, complexity, and adaptability. This review aims to investigate the application of nonlinear metrics to assess postural stability. A systematic review was conducted of papers published from 2009 to 2019. Databases searched were PubMed, Google Scholar, Science-Direct and EBSCO. The main inclusion consisted of: Sample entropy, fractal dimension, Lyapunov exponent used as nonlinear measures, and assessment of the variability of the center of pressure during standing using force plate. Following screening, 43 articles out of the initial 1100 were reviewed including 33 articles on sample entropy, 10 articles on fractal dimension, and 4 papers on the Lyapunov exponent. This systematic study shows the reductions in postural regularity related to aging and the disease or injures in the adaptive capabilities of the movement system and how the predictability changes with different task constraints.

Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach

Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes occurring in a range of materials including living cells and tissues. However, extracting that information is not a trivial task due to the stochastic nature of the particles' movement and the sampling noise. In this paper, we adopt a deep-learning method known as a convolutional neural network (CNN) to classify modes of diffusion from given trajectories. We compare this fully automated approach working with raw data to classical machine learning techniques that require data preprocessing and extraction of human-engineered features from the trajectories to feed classifiers like random forest or gradient boosting. All methods are tested using simulated trajectories for which the underlying physical model is known. From the results it follows that CNN is usually slightly better than the feature-based methods, but at the cost of much longer processing times. Moreover, there are still some borderline cases in which the classical methods perform better than CNN.

Path Tortuosity in Virtual Reality: A Novel Approach for Quantifying Behavioral Process in a Food Choice Context

There is a pressing need to better understand how parents make feeding decisions for their children, but extant measures focus primarily on outcomes rather than examining the process of food choice as it unfolds. This exploratory study examined parents' translational movement as they moved throughout a virtual reality-based buffet restaurant to select a lunch for their child. Our aim was to explore whether translational movement would be related to cognitive and affective variables that underlie motivation, effort, and ultimate choices within food decision-making contexts (e.g., guilt, self-efficacy). Movement data were quantified in terms of path tortuosity: the degree of straightness of one's path while traveling through a space. Greater path tortuosity predicted a reduction in parents' guilt about their child feeding, above and beyond actual food chosen. Results suggest path tortuosity serves as an implicit measure of effort put forth by parents throughout the food decision-making process. Future work should continue to explore the utility of novel metrics that can be obtained from unique data sources, such as location tracking, for elucidating complicated behavioral processes such as food choice.

Daphnia swimming behaviour as a biomarker in toxicity assessment: A review

Daphnia is a motile common model organism widely used in ecotoxicological testing. Although mortality and immobilisation are the main endpoints used for determination of toxicity, detection of subtle alterations induced by some chemicals particularly at lower levels may require more sensitive biomarkers. As a number of studies indicated that swimming behaviour may be altered by pesticides, nanoparticles, bacterial products or other chemicals, analysis of its various parameters is considered as a novel methodological approach for toxicity assessment and monitoring of water quality. This paper presents the current state of knowledge on the effects induced by various chemical compounds on the parameters of swimming behaviour of Daphnia and systems developed for its analysis. Advantages and limitations of swimming behaviour as a tool in toxicological studies are also discussed.

Tactile Radar: experimenting a computer game with visually disabled

BACKGROUND

Visually disabled people increasingly use computers in everyday life, thanks to novel assistive technologies better tailored to their cognitive functioning. Like sighted people, many are interested in computer games - videogames and audio-games. Tactile-games are beginning to emerge. The Tactile Radar is a device through which a visually disabled person is able to detect distal obstacles. In this study, it is connected to a computer running a tactile-game. The game consists in finding and collecting randomly arranged coins in a virtual room.

METHODS

The study was conducted with nine congenital blind people including both sexes, aged 20-64 years old. Complementary methods of first and third person were used: the debriefing interview and the quasi-experimental design.

RESULTS

The results indicate that the Tactile Radar is suitable for the creation of computer games specifically tailored for visually disabled people.

CONCLUSIONS

Furthermore, the device seems capable of eliciting a powerful immersive experience. Methodologically speaking, this research contributes to the consolidation and development of first and third person complementary methods, particularly useful in disabled people research field, including the evaluation by users of the Tactile Radar effectiveness in a virtual reality context. Implications for rehabilitation Despite the growing interest in virtual games for visually disabled people, they still find barriers to access such games. Through the development of assistive technologies such as the Tactile Radar, applied in virtual games, we can create new opportunities for leisure, socialization and education for visually disabled people. The results of our study indicate that the Tactile Radar is adapted to the creation of video games for visually disabled people, providing a playful interaction with the players.

Mobile App to Streamline the Development of Wearable Sensor-Based Exercise Biofeedback Systems: System Development and Evaluation

BACKGROUND

Biofeedback systems that use inertial measurement units (IMUs) have been shown recently to have the ability to objectively assess exercise technique. However, there are a number of challenges in developing such systems; vast amounts of IMU exercise datasets must be collected and manually labeled for each exercise variation, and naturally occurring technique deviations may not be well detected. One method of combatting these issues is through the development of personalized exercise technique classifiers.

OBJECTIVE

We aimed to create a tablet app for physiotherapists and personal trainers that would automate the development of personalized multiple and single IMU-based exercise biofeedback systems for their clients. We also sought to complete a preliminary investigation of the accuracy of such individualized systems in a real-world evaluation.

METHODS

A tablet app was developed that automates the key steps in exercise technique classifier creation through synchronizing video and IMU data collection, automatic signal processing, data segmentation, data labeling of segmented videos by an exercise professional, automatic feature computation, and classifier creation. Using a personalized single IMU-based classification system, 15 volunteers (12 males, 3 females, age: 23.8 [standard deviation, SD 1.8] years, height: 1.79 [SD 0.07] m, body mass: 78.4 [SD 9.6] kg) then completed 4 lower limb compound exercises. The real-world accuracy of the systems was evaluated.

RESULTS

The tablet app successfully automated the process of creating individualized exercise biofeedback systems. The personalized systems achieved 89.50% (1074/1200) accuracy, with 90.00% (540/600) sensitivity and 89.00% (534/600) specificity for assessing aberrant and acceptable technique with a single IMU positioned on the left thigh.

CONCLUSIONS

A tablet app was developed that automates the process required to create a personalized exercise technique classification system. This tool can be applied to any cyclical, repetitive exercise. The personalized classification model displayed excellent system accuracy even when assessing acute deviations in compound exercises with a single IMU.

Technology in Rehabilitation: Comparing Personalised and Global Classification Methodologies in Evaluating the Squat Exercise with Wearable IMUs

BACKGROUND

The barbell squat is a popularly used lower limb rehabilitation exercise. It is also an integral exercise in injury risk screening protocols. To date athlete/patient technique has been assessed using expensive laboratory equipment or subjective clinical judgement; both of which are not without shortcomings. Inertial measurement units (IMUs) may offer a low cost solution for the objective evaluation of athlete/patient technique. However, it is not yet known if global classification techniques are effective in identifying naturally occurring, minor deviations in barbell squat technique.

OBJECTIVES

The aims of this study were to: (a) determine if in combination or in isolation, IMUs positioned on the lumbar spine, thigh and shank are capable of distinguishing between acceptable and aberrant barbell squat technique; (b) determine the capabilities of an IMU system at identifying specific natural deviations from acceptable barbell squat technique; and (c) compare a personalised (N=1) classifier to a global classifier in identifying the above.

METHODS

Fifty-five healthy volunteers (37 males, 18 females, age = 24.21 +/- 5.25 years, height = 1.75 +/- 0.1 m, body mass = 75.09 +/- 13.56 kg) participated in the study. All participants performed a barbell squat 3-repetition maximum max strength test. IMUs were positioned on participants' lumbar spine, both shanks and both thighs; these were utilized to record tri-axial accelerometer, gyroscope and magnetometer data during all repetitions of the barbell squat exercise. Technique was assessed and labelled by a Chartered Physiotherapist using an evaluation framework. Features were extracted from the labelled IMU data. These features were used to train and evaluate both global and personalised random forests classifiers.

RESULTS

Global classification techniques produced poor accuracy (AC), sensitivity (SE) and specificity (SP) scores in binary classification even with a 5 IMU set-up in both binary (AC: 64%, SE: 70%, SP: 28%) and multi-class classification (AC: 59%, SE: 24%, SP: 84%). However, utilising personalised classification techniques even with a single IMU positioned on the left thigh produced good binary classification scores (AC: 81%, SE: 81%, SP: 84%) and moderate-to-good multi-class scores (AC: 69%, SE: 70%, SP: 89%).

CONCLUSIONS

There are a number of challenges in developing global classification exercise technique evaluation systems for rehabilitation exercises such as the barbell squat. Building large, balanced data sets to train such systems is difficult and time intensive. Minor, naturally occurring deviations may not be detected utilising global classification approaches. Personalised classification approaches allow for higher accuracy and greater system efficiency for end-users in detecting naturally occurring barbell squat technique deviations. Applying this approach also allows for a single-IMU set up to achieve similar accuracy to a multi-IMU setup, which reduces total system cost and maximises system usability.

Classification and Segmentation of Nanoparticle Diffusion Trajectories in Cellular Micro Environments

Darkfield and confocal laser scanning microscopy both allow for a simultaneous observation of live cells and single nanoparticles. Accordingly, a characterization of nanoparticle uptake and intracellular mobility appears possible within living cells. Single particle tracking allows to measure the size of a diffusing particle close to a cell. However, within the more complex system of a cell’s cytoplasm normal, confined or anomalous diffusion together with directed motion may occur. In this work we present a method to automatically classify and segment single trajectories into their respective motion types. Single trajectories were found to contain more than one motion type. We have trained a random forest with 9 different features. The average error over all motion types for synthetic trajectories was 7.2%. The software was successfully applied to trajectories of positive controls for normal- and constrained diffusion. Trajectories captured by nanoparticle tracking analysis served as positive control for normal diffusion. Nanoparticles inserted into a diblock copolymer membrane was used to generate constrained diffusion. Finally we segmented trajectories of diffusing (nano-)particles in V79 cells captured with both darkfield- and confocal laser scanning microscopy. The software called “TraJClassifier” is freely available as ImageJ/Fiji plugin via https://git.io/v6uz2.

Fabrication of Microfiber Patterns with Ivy Shoot-Like Geometries Using Improved Electrospinning

Fibers and fibrous structures are used extensively in various fields due to their many advantages. Microfibers, as well as nanofibers, are considered to be some of the most valuable forms of advanced materials. Accordingly, various methods for fabricating microfibers have been developed. Electrospinning is a useful fabrication method for continuous polymeric nano- and microfibers with attractive merits. However, this technique has limitations in its ability to control the geometry of fibrous structures. Herein, advanced electrospinning with direct-writing functionality was used to fabricate microfiber patterns with ivy shoot-like geometries after experimentally investigating the effects of the process conditions on the fiber formation. The surface properties of the fibers were also modified by introducing nanoscale pores through the use of higher levels of humidity during the fabrication process.

Dynamic balance deficits in individuals with chronic ankle instability compared to ankle sprain copers 1 year after a first-time lateral ankle sprain injury

PURPOSE

To quantify the dynamic balance deficits that characterise a group with chronic ankle instability compared to lateral ankle sprain copers and non-injured controls using kinematic and kinetic outcomes.

METHODS

Forty-two participants with chronic ankle instability and twenty-eight lateral ankle sprain copers were initially recruited within 2 weeks of sustaining a first-time, acute lateral ankle sprain and required to attend our laboratory 1 year later to complete the current study protocol. An additional group of non-injured individuals were also recruited to act as a control group. All participants completed the anterior, posterior-lateral and posterior-medial reach directions of the star excursion balance test. Sagittal plane kinematics of the lower extremity and associated fractal dimension of the centre of pressure path were also acquired.

RESULTS

Participants with chronic ankle instability displayed poorer performance in the anterior, posterior-medial and posterior-lateral reach directions compared with controls bilaterally, and in the posterior-lateral direction compared with lateral ankle sprain copers on their 'involved' limb only. These performance deficits in the posterior-lateral and posterior-medial directions were associated with reduced flexion and dorsiflexion displacements at the hip, knee and ankle at the point of maximum reach, and coincided with reduced complexity of the centre of pressure path.

CONCLUSION

In comparison with lateral ankle sprain copers and controls, participants with chronic ankle instability were characterised by dynamic balance deficits as measured using the SEBT. This was attested to reduced sagittal plane motions at the hip, knee and ankle joints, and reduced capacity of the stance limb to avail of its supporting base.

LEVEL OF EVIDENCE

III.

The future of computer-aided sperm analysis

Computer-aided sperm analysis (CASA) technology was developed in the late 1980s for analyzing sperm movement characteristics or kinematics and has been highly successful in enabling this field of research. CASA has also been used with great success for measuring semen characteristics such as sperm concentration and proportions of progressive motility in many animal species, including wide application in domesticated animal production laboratories and reproductive toxicology. However, attempts to use CASA for human clinical semen analysis have largely met with poor success due to the inherent difficulties presented by many human semen samples caused by sperm clumping and heavy background debris that, until now, have precluded accurate digital image analysis. The authors review the improved capabilities of two modern CASA platforms (Hamilton Thorne CASA-II and Microptic SCA6) and consider their current and future applications with particular reference to directing our focus towards using this technology to assess functional rather than simple descriptive characteristics of spermatozoa. Specific requirements for validating CASA technology as a semi-automated system for human semen analysis are also provided, with particular reference to the accuracy and uncertainty of measurement expected of a robust medical laboratory test for implementation in clinical laboratories operating according to modern accreditation standards.

Dynamic Balance Deficits 6 Months Following First-Time Acute Lateral Ankle Sprain: A Laboratory Analysis

STUDY DESIGN

Controlled laboratory study.

OBJECTIVE

To utilize kinematic and stabilometric measures to compare dynamic balance during performance of the Star Excursion Balance Test between persons 6 months following first-time lateral ankle sprain (LAS) and a noninjured control group.

BACKGROUND

Biomechanical evaluation of dynamic balance in persons following first-time LAS during performance of the Star Excursion Balance Test could provide insight into the mechanisms by which individuals proceed to recover fully or develop chronic ankle instability.

METHODS

Sagittal plane kinematics of the lower extremity and the center-of-pressure path during the performance of the anterior, posterolateral, and posteromedial reach directions of the Star Excursion Balance Test were obtained from 69 participants 6 months following first-time acute LAS and from a control group of 20 noninjured participants.

RESULTS

Compared to the control group, the LAS group displayed lower normalized reach distances in all 3 reach directions on the injured and noninjured limbs, with the largest observed effect size in the posterolateral direction (P = .001, ηp(2) = 0.07). The performance impairment was associated with less hip and knee flexion and ankle dorsiflexion at the point of maximum reach (P<.02), and coincided with less complexity of the center-of-pressure path (P<.05).

CONCLUSION

Participants with a 6-month history of LAS exhibit a persistence of deficits previously established in the acute phase of injury.

Laboratory Measures of Postural Control During the Star Excursion Balance Test After Acute First-Time Lateral Ankle Sprain

CONTEXT

No researchers, to our knowledge, have investigated the immediate postinjury-movement strategies associated with acute first-time lateral ankle sprain (LAS) as quantified by center of pressure (COP) and kinematic analyses during performance of the Star Excursion Balance Test (SEBT).

OBJECTIVE

To analyze the kinematic and COP patterns of a group with acute first-time LAS and a noninjured control group during performance of the SEBT.

DESIGN

Case-control study.

SETTING

University biomechanics laboratory.

PATIENTS OR OTHER PARTICIPANTS

A total of 81 participants with acute first-time LAS (53 men, 28 women; age = 23.22 ± 4.93 years, height = 1.73 ± 0.09 m, mass = 75.72 ± 13.86 kg) and 19 noninjured controls (15 men, 4 women; age = 22.53 ± 1.68 years, height = 1.74 ± 0.08 m, mass = 71.55 ± 11.31 kg).

INTERVENTION

Participants performed the anterior (ANT), posterolateral (PL), and posteromedial (PM) reach directions of the SEBT.

MAIN OUTCOME MEASURE(S)

We assessed 3-dimensional kinematics of the lower extremity joints and associated fractal dimension (FD) of the COP path during performance of the SEBT.

RESULTS

The LAS group had decreased normalized reach distances in the ANT, PL, and PM directions when compared with the control group on their injured (ANT: 58.16% ± 6.86% versus 64.86% ± 5.99%; PL: 85.64% ± 10.62% versus 101.14% ± 8.39%; PM: 94.89% ± 9.26% versus 107.29 ± 6.02%) and noninjured (ANT: 60.98% ± 6.74% versus 64.76% ± 5.02%; PL: 88.95% ± 11.45% versus 102.36% ± 8.53%; PM: 97.13% ± 8.76% versus 106.62% ± 5.78%) limbs (P < .01). This observation was associated with altered temporal sagittal-plane kinematic profiles throughout each reach attempt and at the point of maximum reach (P < .05). This result was associated with a reduced FD of the COP path for each reach direction on the injured limb only (P < .05).

CONCLUSIONS

Acute first-time LAS was associated with bilateral deficits in postural control, as evidenced by the bilateral reduction in angular displacement of the lower extremity joints and reduced reach distances and FD of the COP path on the injured limb during performance of the SEBT.

Inter-joint coordination strategies during unilateral stance 6-months following first-time lateral ankle sprain

BACKGROUND

Longitudinal analyses of participants with a history of lateral ankle sprain are lacking. This investigation combined measures of inter-joint coordination and stabilometry to evaluate eyes-open (condition 1) and eyes-closed (condition 2) static unilateral stance performance in a group of participants, 6-months after they sustained an acute, first-time lateral ankle sprain in comparison to a control group.

METHODS

Sixty-nine participants with a 6-month history of first-time lateral ankle sprain and 20 non-injured controls completed three 20-second unilateral stance task trials in conditions 1 and 2. An adjusted coefficient of multiple determination statistic was used to compare stance limb 3-dimensional kinematic data for similarity in the aim of establishing patterns of lower-limb inter-joint coordination. The fractal dimension of the stance limb centre of pressure path was also calculated.

FINDINGS

Between-group analyses revealed significant differences in stance limb inter-joint coordination strategies for conditions 1 and 2, and in the fractal dimension of the centre-of-pressure path for condition 2 only. Injured participants displayed increases in ankle-hip linked coordination compared to controls in condition 1 (sagittal/frontal plane: 0.15 [0.14] vs 0.06 [0.04]; η(2)=.19; sagittal/transverse plane: 0.14 [0.11] vs 0.09 [0.05]; η(2)=0.14) and condition 2 (sagittal/frontal plane: 0.15 [0.12] vs 0.08 [0.06]; η(2)=0.23), with an associated decrease in the fractal dimension of the centre-of-pressure path (injured limb: 1.23 [0.13] vs 1.36 [0.13]; η(2)=0.20).

INTERPRETATION

Participants with a 6-month history of first-time lateral ankle sprain exhibit a hip-dominant coordination strategy for static unilateral stance compared to non-injured controls.

Postural control strategies during single limb stance following acute lateral ankle sprain

BACKGROUND

Single-limb stance is maintained via the integration of visual, vestibular and somatosensory afferents. Musculoskeletal injury challenges the somatosensory system to reweight distorted sensory afferents. This investigation supplements kinetic analysis of eyes-open and eyes-closed single-limb stance tasks with a kinematic profile of lower limb postural orientation in an acute lateral ankle sprain group to assess the adaptive capacity of the sensorimotor system to injury.

METHODS

Sixty-six participants with first-time acute lateral ankle sprain completed a 20-second eyes-open single-limb stance task on their injured and non-injured limbs (task 1). Twenty-three of these participants successfully completed the same 20-second single-limb stance task with their eyes closed (task 2). A non-injured control group of 19 participants completed task 1, with 16 completing task 2. 3-dimensional kinematics of the hip, knee and ankle joints, as well as associated fractal dimension of the center-of-pressure path were determined for each limb during these tasks.

FINDINGS

Between trial analyses revealed significant differences in stance limb kinematics and fractal dimension of the center-of-pressure path for task 2 only. The control group bilaterally assumed a position of greater hip flexion compared to injured participants on their side-matched "involved"(7.41 [6.1°] vs 1.44 [4.8]°; η(2)=.34) and "uninvolved" (9.59 [8.5°] vs 2.16 [5.6°]; η(2)=.31) limbs, with a greater fractal dimension of the center-of-pressure path (involved limb=1.39 [0.16°] vs 1.25 [0.14°]; uninvolved limb=1.37 [0.21°] vs 1.23 [0.14°]).

INTERPRETATION

Bilateral impairment in postural control strategies present following a first time acute lateral ankle sprain.

Balance failure in single limb stance due to ankle sprain injury: an analysis of center of pressure using the fractal dimension method

Instrumented postural control analysis plays an important role in evaluating the effects of injury on dynamic stability during balance tasks, and is often conveyed with measures based on the displacement of the center-of-pressure (COP) assessed with a force platform. However, the desired outcome of the task is frequently characterized by a loss of dynamic stability, secondary to injury. Typically, these failed trials are discarded during research investigations, with the potential loss of informative data pertaining to task success. The novelty of the present study is that COP characteristics of failed trials in injured participants are compared to successful trial data in another injured group, and a control group of participants, using the fractal dimension (FD) method. Three groups of participants attempted a task of eyes closed single limb stance (SLS): twenty-nine participants with acute ankle sprain successfully completed the task on their non-injured limb (successful injury group); twenty eight participants with acute ankle sprain failed their attempt on their injured limb (failed injury group); sixteen participants with no current injury successfully completed the task on their non-dominant limb (successful non-injured group). Between trial analyses of these groups revealed significant differences in COP trajectory FD (successful injury group: 1.58±0.06; failed injury group: 1.54±0.07; successful non-injured group: 1.64±0.06) with a large effect size (0.27). These findings demonstrate that successful eyes-closed SLS is characterized by a larger FD of the COP path when compared to failed trials, and that injury causes a decrease in COP path FD.

Nonlinear indices of circadian changes in individuals with dementia and aggression

Nonlinear analyses of actigraphy data were utilized to investigate circadian rest-activity system motor control in nursing-home residents with dementia and with/without aggressive behavior (AB). Significant differences observed between groups in measures of approximate entropy (ApEn) and fractal dimension (FD). ApEn and FD are sensitive to detecting and characterizing discrete changes in central motoric control and temporality of behaviors in dementia. Findings may inform understanding of clinical heterogeneity and possible physiologic sub-classifications of Alzheimer's dementia.

Effects of plant gross morphology on predator searching behaviour

Plant morphology influences insect predators' abilities to capture prey and control pest populations. Several mechanisms for this effect of plants on predator foraging have been proposed. In particular, it is often claimed that increased complexity of plant structures may increase search time and reduce foraging success. Using time-lapse photography we recorded search paths, and compared the total path lengths, percentages of plants searched, and path tortuosity of adult multicolored Asian lady beetles (Harmonia axyridis Pallas) and green lacewing larvae (Chrysoperla carnea Stephens) foraging for pea aphids (Acyrthosiphon pisum Harris) on pea near-isolines (Pisum sativum L.) that differed in shape. We found that H. axyridis searched leafy morphologies less thoroughly than those with more branches, while C. carnea larvae search paths did not differ on any of the pea morphologies. In addition, the ability of H. axyridis to attach to plants and maneuver was increased on morphologies with many branches and edges, while C. carnea was able to attach to all morphologies. Both species, however, had significantly reduced predation success on inverted leaf surfaces. We conclude that undersides of leaves, far from the leaf margin, may serve as partial prey refugia. In addition, we find increased plant branching or an increase in other morphological features which provide predator attachment points may promote foraging success.

Comparison of fractal dimension estimation algorithms for epileptic seizure onset detection

Fractal dimension (FD) is a natural measure of the irregularity of a curve. In this study the performances of three waveform FD estimation algorithms (i.e. Katz's, Higuchi's and the k-nearest neighbour (k-NN) algorithm) were compared in terms of their ability to detect the onset of epileptic seizures in scalp electroencephalogram (EEG). The selection of parameters involved in FD estimation, evaluation of the accuracy of the different algorithms and assessment of their robustness in the presence of noise were performed based on synthetic signals of known FD. When applied to scalp EEG data, Katz's and Higuchi's algorithms were found to be incapable of producing consistent changes of a single type (either a drop or an increase) during seizures. On the other hand, the k-NN algorithm produced a drop, starting close to the seizure onset, in most seizures of all patients. The k-NN algorithm outperformed both Katz's and Higuchi's algorithms in terms of robustness in the presence of noise and seizure onset detection ability. The seizure detection methodology, based on the k-NN algorithm, yielded in the training data set a sensitivity of 100% with 10.10 s mean detection delay and a false positive rate of 0.27 h(-1), while the corresponding values in the testing data set were 100%, 8.82 s and 0.42 h(-1), respectively. The above detection results compare favourably to those of other seizure onset detection methodologies applied to scalp EEG in the literature. The methodology described, based on the k-NN algorithm, appears to be promising for the detection of the onset of epileptic seizures based on scalp EEG.

Measurement of the visual contribution to postural steadiness from the COP movement: methodology and reliability

We studied the reliability of different measures of the visual contribution to postural steadiness by recording the postural sway during standing with eyes open (EO) or eyes closed (EC). The COP trajectory was recorded in 21 subjects aged 42-61 standing on a firm or foam support. The improvement of postural steadiness due to vision was measured with a higher reliability (i.e. lower intra- and inter-subject variabilities) with the sway velocity V, than with the position RMS. Due to the increase of the variability of V and RMS with their own mean values, we quantified the visual contribution to posture by the stabilization ratio (SR), based on a logarithm transform of V or RMS. As compared to the Romberg quotient (EC/EO), SR improved the reliability of the measurement of the visual contribution to posture within individuals, across subjects, and even across different studies in the literature. Our method led to decrease the inter-subject coefficient of variation of this measurement to about 25%, using a foam support. It leads to a similar accuracy in binocular and monocular vision, and it also applies to the quantification of other non-visual sensory contributions to posture.

Fractal analysis of Daphnia motion for acute toxicity bioassay

To quantify individual behavioral responses to toxic chemicals, the swimming motion of individual Daphnia magna was continuously monitored using a motion analysis system. The fractal dimension was introduced to compare the straightness or complexity of the swimming trajectory before and after exposure to toxic chemicals. Analysis indicated that the swimming trajectory of individual Daphnia has a fractal structure. The basal fractal dimension in the control medium was 1.35+/-0.01 (n = 50 Daphnia). Exposure to CuSO(4) (10 microg/L), organophosphorus (Dichlorvos; 10 microg/L), and carbamate (Propoxur; 500 microg/L) pesticide caused a significant increase in the fractal dimension with a latency of 60 min, reaching a maximal level of 2.26+/-0.34, 2.43+/-0.19, and 2.51+/-0.21, respectively, after a 120-min exposure. The magnitude of the change in the fractal dimension was related to the toxic chemical concentration and the exposure time. Threshold concentrations determined at 60 min of exposure were 10 microg/L for CuSO(4), 5 microg/L for Dichlorvos, and 500 microg/L for Propoxur. The toxicity index (EC(50)) values after 120 min of exposure were 6.31 microg/L, 7.64 microg/L, and 466 microg/L for CuSO(4), Dichlorvos, and Propoxur, respectively. Thus, the fractal dimension seems useful for analyzing and comparing complex trails, such as swimming trajectories, which could be used as the endpoint for an acute bioassay.

Postnatal dendritic development of Y-like geniculocortical relay neurons

We describe the dendritic development of neurons in the dorsal lateral geniculate nucleus (LGNd) projecting to cortical area 18 in the postnatal cat. LGN neurons were identified by retrograde labeling from area 18 with fluorescent latex microspheres and injected in the fixed slice with Lucifer yellow (LY) and horseradish peroxidase (HRP) to visualize their dendritic arborizations. Both topological (measures of the patterns of dendritic branching and their territorial coverage) and metric parameters (measures of the quantitative parameters describing the size, length, extent and diameter of the dendritic arbors) were measured in three-dimensions for 25 LGN neurons in cats between 1 and 18 postnatal weeks. In addition, dendritic growth was compared to the changing dimensions of the LGNd. At all ages, neurons projecting to area 18 have large somata and radiate dendrites. From 1 to 18 weeks neurons increase in size--both soma area and the length of all dendritic segments double during this period. Intermediate and terminal dendritic segments show comparable growth until 5 weeks. However, only terminal segments continue to grow significantly from 5 until 18 weeks. Dendrites become straighter during development, the angle between daughter branches decreases and dendritic segment diameter increases, with terminal segments showing a greater increase relative to intermediate segments. The density of dendritic appendages increases transiently at 5 weeks and a differential redistribution occurs, so that by 18 weeks dendrites further from the soma have a greater density of appendages than those near the soma. Some dendritic relationships remain invariant during development--intermediate segments are always shorter, thicker and straighter than terminal segments. During these changes however, area 18 projecting neurons maintain a constant number of primary dendrites and have, on average, a constant branching pattern. The relative volume of the LGNd occupied by an area 18 projecting neuron increases 2.4-fold between 1 and 18 weeks as the dendrites grow with the result that the coverage of a given point of the LGNd by dendrites of area 18 projecting nearly doubles from 24 to 45 neurons per unit volume. This increased net dendritic overlap provides a substrate for enhanced numerical synaptic divergence of the Y-cell pathway from a point source in the retina to the visual cortex.

An improved technique for the extraction of stochastic parameters from stabilograms

An improved characterization of the dynamics of postural sway can provide a better understanding about the functional organization of the postural control system as well as a more robust tool for postural pattern recognition. To this aim, a novel parameterization was applied to the stabilogram diffusion analysis formerly proposed by Collins and De Luca [Collins JJ, De Luca CJ. Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Exp Brain Res 1993;95:308-18] that considered the act of maintaining posture as a stochastic process. The main purpose of the present technique was to overcome some drawbacks of the model presented by Collins and De Luca that may restrain its potential application in clinical practice. The approach uses a unique non-linear model to describe the center of pressure (COP) dynamics that reduces the number of parameters and decreases their intra-subject variability; consequently, fewer trials are required to perform reliable estimates of stochastic parameters and this is of particular importance for subjects that cannot afford many repeated measurements because of age or pathology. Four new statistical mechanics parameters (NSMP) were computed on the log-log stabilogram diffusion plots and their estimates were compared in terms of reliability and sensitivity to the visual conditions with: (1) a minimal set of four summary statistic scores (SSS); and (2) the six statistical mechanics parameters (SMP) proposed by Collins and De Luca. All four NSMP showed at least a fair-to-good reliability (intraclass correlation coefficient, ICC>0.49) while SMP (ICC>0.20) showed some poor reliability. A better overall reliability was also observed with respect to SSS. Moreover, only NSMP had a similar score for eyes open and eyes closed conditions. Three out of four NSMP were also significantly sensitive to eyes open or closed conditions (P<0.001) while only three out of six SMP were sensitive to operating conditions (P<0.01).

The dose-response effects of terbutaline on the variability, approximate entropy and fractal dimension of heart rate and blood pressure

AIMS

To study the dose-response effects of intravenous terbutaline on the cardiovascular and respiratory autonomic nervous regulation.

METHODS

The study followed a randomized, placebo-controlled crossover design in six healthy adult volunteers. The terbutaline dose ranged from 10 to 30 microg min(-1) We continuously measured electrocardiogram, finger systolic arterial pressure (SAP) and flow-volume spirometry in supine and upright positions at baseline and during 3 h drug infusion. The periodic variability components of R-R intervals (time between successive heart beats) and SAP in relation to respiration were assessed using spectral analysis techniques. The regularity of the time series was assessed by approximate entropy (ApEn) and the convolutedness by fractal dimension (FD).

RESULTS

Terbutaline dose-dependently decreased total variability of R-R intervals, low frequency (LF) variability of R-R intervals (10 s waves), high frequency (HF) variability of R-R intervals (respiratory variability), total variability of SAP, HF variability of SAP, baroreflex sensitivity, plasma potassium concentration, approximate entropy of R-R interval and of SAP as well as fractal dimension of R-R interval. Terbutaline dose-dependently increased heart rate, LF/HF ratios of R-R intervals and of SAP, LF variability of SAP, minute ventilation and plasma terbutaline concentration.

CONCLUSIONS

Terbutaline infusion decreases parasympathetic cardiovascular reactivity, baroreflex sensitivity, dimensionality of heart rate and plasma potassium concentration; it increases sympathetic dominance in cardiovascular autonomic balance, minute ventilation, and the regularity of heart rate and blood pressure time series.

Effect of age on long-term heart rate variability

OBJECTIVE

Previous studies on short-term time series of heart rage suggest an inverse relationship between age and spectral powers of heart rate variability in various frequency bands. In this study, we examined the relationship between age (6-61 years) and long-term heart rate variability.

METHODS

We obtained 24-h Holter ECG in 33 healthy human subjects (11 children and 22 adults). The heart rate data were analyzed by using spectral analysis and fractal dimensions of the time series.

RESULTS

We found a significant negative correlation between age and very low frequency (VLF, 0.0033-0.04 Hz), low frequency (LF, 0.04-0.15 Hz) and high frequency (HF, 0.15-0.5 Hz) powers and fractal dimensions during awake as well as sleep periods, and a positive correlation between age and LF/HF ratios. Age and ultra-low frequency (ULF, < 0.0033 Hz) were modestly and negatively correlated only during the awake period.

CONCLUSIONS

Sleep ULF power is not significantly affected by age, whereas VLF, LF and HF powers and fractal dimensions of heart rate significantly decrease with age during awake as well as sleep periods.

Computer simulation of nerve growth cone filopodial dynamics for visualization and analysis

The neuronal growth cone plays a fundamental role in nerve development and regeneration. A sensory-motile structure, it determines the path of axonal extension through its interactions with the extracellular environment, ultimately directing the formation of functional connections in the nervous system. Though several mechanisms of interaction have been proposed, these have been difficult to describe quantitatively due to the complexity of growth cone behavior, as manifested in the randomly and rapidly changing shape of the growth cone. The application of mathematical techniques to model growth cone shape and motility in terms of underlying processes represents a promising approach with untapped potential for helping to unravel this complexity while revealing new insights into axonal pathfinding events. This paper presents a simulation model for filopodial dynamics, a primary feature of the motile growth cone. The model produces realizations of dynamic filopodial structure on representative growth cones for a given set of model parameters, which include the rates of filopodial initiation, extension, and retraction, filopodial length at maximum extension, and angular orientation. These parameters are based on recent experimental characterization of filopodial dynamics [Buettner et al., 1994: Dev. Biol. 163:407-422]. The mathematical relationship between the model parameters and average filopodial number and length per growth cone is described, and the contribution of individual parameters to overall filopodial morphology is illustrated both visually and numerically. In addition, the model is used to simulate filopodial encounter with a target for various conditions of filopodial dynamics. The result is characterized in terms of a mean encounter time for a population of growth cones and provides an indication of the effect of individual parameters of filopodial dynamics on the encounter process. Future experimental testing will be required to develop the model further. However, in its current form, the model enables a first approximation analysis of many hypothesis of growth cone migration and pathfinding and offers insight into the the underlying mechanisms of nerve growth and regeneration.

A comparative fractal analysis of various mammalian astroglial cell types

Camera-lucida drawings of Golgi-impregnated astroglial cells and their processes are described by the fractal dimension of their borders, which is an objective, quantitative measure of morphological complexity. Protoplasmic astrocytes from human neocortex have fractal dimensions (D) that are larger than those of fibrous astrocytes from the cat optic nerve. Marginal astrocytes from monkey cerebropontile angle have two kinds of processes: (1) short, thick processes with endfeet abutting the pial surface, with relatively high D's, and (2) very long, thin processes extending into the neuronal tissue, with very low D's. These data indicate that short astrocytic processes may have a complex surface (and have a high D), whereas long processes are rather smooth (and have a low D). A comparison between transmission electron microscopy morphometry and measures of D at the light microscopic level, performed on different parts of rabbit retinal Müller glial cells, suggests that D is strongly correlated to the surface-to-volume ratio which, in part, determines the length constant of a cable for core-conductance of currents. We provide data supporting the hypothesis that astroglial cell geometry is adjusted to allow for sufficient spatial buffering K+ currents, even through very long processes.

Quantitative effects of laminin concentration on neurite outgrowth in vitro

Recent studies indicate that mediation of neurite outgrowth by the glycoprotein laminin may be a significant factor in the outgrowth of neurites to their targets during embryogenesis. To further characterize the possible role of this extracellular matrix molecule during development, we have systematically measured several features of outgrowth by neonatal rat sympathetic neurons on different concentrations of laminin. Individual neurons, obtained by mechanical dissociation of superior cervical ganglia (SCG), were cultured at low density on laminin substrates ranging from 0.01 to 1.0 microgram/cm2. Outgrowth characteristics were subsequently analyzed for noninteracting cells in both fixed and live cultures. Data obtained from neurons fixed after 11 hr of culture showed approximately twofold increases in neurite initiation and outgrowth, and a twofold decrease in branching for a corresponding 100-fold increase in adsorbed laminin concentration. In time-lapse videomicroscopy observations, the root-mean square speed of growth cone movement increased from 60 to 90 microns/hr over the same range in concentration, while the persistence time remained constant at 0.10 hr. In general, neurite outgrowth parameters were relatively insensitive to changes in laminin concentration, supporting the idea that laminin is a permissive rather than an "instructive" substrate during development. Data obtained from fixed cultures were examined in terms of probability models to suggest possible mechanisms contributing to the dose-dependent effects observed.

Axonal shortening and the mechanisms of axonal motility

Axons in tissue culture retract and shorten if their tips are detached from the substrate. The shortening reaction of the axon involves contractile forces that also arise during normal axonal motility, elongation, and retraction. We studied shortening in axonal segments isolated from their parent axons by transecting the axon between the growth cone and the most distal point of adhesion to the substrate. Within 15-20 minutes after transection, an isolated axonal segment shortened and pulled its tail end toward the growth cone. During the shortening process, long sinusoidal bends arose along the axon. The identical shortening reaction occurs without transection, when the axon tip is detached from the substrate. Pharmacological studies with inhibitors of glycolysis indicate that the shortening mechanisms utilize metabolic energy, presumably ATP. The rate of sinusoidal shortening is similar to both the rate of polymer translocation in the axon by slow axonal transport and the rate of normal axonal elongation. Taxol inhibits the shortening reaction with a similar dose dependence to its inhibition of axonal growth. Together, all these observations suggest that the same basic intracellular motility mechanisms are involved in normal axonal growth, in slow axonal transport, and in the shortening reaction: the intracellular dynamic system that utilizes ATP to generate longitudinal movements of polymers within the axon may be the same mechanism underlying both the retraction and the elongation of the axon.

Fractals and the analysis of waveforms

Waveforms are planar curves--ordered collections of (x, y) point pairs--where the x values increase monotonically. One technique for numerically classifying waveforms assesses their fractal dimensionality, D. For waveforms: D = log(n)/(log(n) + log(d/L], with n = number of steps in the waveform (one less than the number of (x, y) point pairs), d = planar extent (diameter) of the waveform, and L = total length of the waveform. Under this formulation, fractal dimensions range from D = 1.0, for straight lines through approximately D = 1.15 for random-walk waveforms, to D approaching 1.5 for the most convoluted waveforms. The fractal characterization may be especially useful for analyzing and comparing complex waveforms such as electroencephalograms (EEGs).

Quantitative effects of NGF on the growth of embryonic frog axons

Sparse, dissociated cultures of embryonic Xenopus CNS neurons were grown with and without NGF. Under both conditions the same number of neurons survived and extended neurites, and under both conditions the neurites moved at approximately the same overall rates and with the same degree of straightness. On the other hand, neurons in the NGF-supplemented cultures had more neurites and these neurites branched 64% more often. Detailed measurements showed that the axons elongated 44% faster in NGF and that this increase could be ascribed to a selective increase in the stepping rate of axonal elongation. These observations raise the possibility that NGF may selectively modulate the rate of movement of the core cytoskeleton of the axon.

Early axon patterns of the spinal cord: experiments with a computer

In the vertebrate central nervous system, most axons appear in one of two elemental patterns--sheets or bundles. Many developmental mechanisms are involved in the formation of the elemental axon patterns, and these mechanisms often act simultaneously. The major axon-patterning mechanisms include differential adhesivity, internal growth constraints on axons, and initial orientation of axonal outgrowth. To evaluate the effects of these mechanisms on the formation of axon patterns, a computer was used to model axonal growth. Experiments with the computer model suggest that axon sheets are produced by the cooperative action of more than one mechanism. Furthermore, in the appropriate combination, these mechanisms produce orderly axon sheets even on patternless substrates. On the other hand, to transform the sheets into axon bundles, the substrate must be patterned.