Measurement of multi-segment foot joint angles during gait using a wearable system

Usually the measurement of multi-segment foot and ankle complex kinematics is done with stationary motion capture devices which are limited to use in a gait laboratory. This study aimed to propose and validate a wearable system to measure the foot and ankle complex joint angles during gait in daily conditions, and then to investigate its suitability for clinical evaluations. The foot and ankle complex consisted of four segments (shank, hindfoot, forefoot, and toes), with an inertial measurement unit (3D gyroscopes and 3D accelerometers) attached to each segment. The angles between the four segments were calculated in the sagittal, coronal, and transverse planes using a new algorithm combining strap-down integration and detection of low-acceleration instants. To validate the joint angles measured by the wearable system, three subjects walked on a treadmill for five minutes at three different speeds. A camera-based stationary system that used a cluster of markers on each segment was used as a reference. To test the suitability of the system for clinical evaluation, the joint angle ranges were compared between a group of 10 healthy subjects and a group of 12 patients with ankle osteoarthritis, during two 50-m walking trials where the wearable system was attached to each subject. On average, over all joints and walking speeds, the RMS differences and correlation coefficients between the angular curves obtained using the wearable system and the stationary system were 1 deg and 0.93, respectively. Moreover, this system was able to detect significant alteration of foot and ankle function between the group of patients with ankle osteoarthritis and the group of healthy subjects. In conclusion, this wearable system was accurate and suitable for clinical evaluation when used to measure the multi-segment foot and ankle complex kinematics during long-distance walks in daily life conditions.     

Predicting timing of foot strike during running,independent of striking technique,using principal component analysis of joint angles

As 3-dimensional (3D) motion-capture for clinical gait analysis continues to evolve, new methods must be developed to improve the detection of gait cycle events based on kinematic data. Recently, the application of principal component analysis (PCA) to gait data has shown promise in detecting important biomechanical features. Therefore, the purpose of this study was to define a new foot strike detection method for a continuum of striking techniques, by applying PCA to joint angle waveforms. In accordance with Newtonian mechanics, it was hypothesized that transient features in the sagittal-plane accelerations of the lower extremity would be linked with the impulsive application of force to the foot at foot strike. Kinematic and kinetic data from treadmill running were selected for 154 subjects, from a database of gait biomechanics. Ankle, knee and hip sagittal plane angular acceleration kinematic curves were chained together to form a row input to a PCA matrix. A linear polynomial was calculated based on PCA scores, and a 10-fold cross-validation was performed to evaluate prediction accuracy against gold-standard foot strike as determined by a 10 N rise in the vertical ground reaction force. Results show 89–94% of all predicted foot strikes were within 4 frames (20 ms) of the gold standard with the largest error being 28 ms. It is concluded that this new foot strike detection is an improvement on existing methods and can be applied regardless of whether the runner exhibits a rearfoot, midfoot, or forefoot strike pattern.     

Comparison of strain-gage and fiber-optic goniometry for measuring knee kinematics during activities of daily living and exercise

There is increasing interest in wearable sensor technology as a tool for rehabilitation applications in community or home environments. Recent studies have focused on evaluating inertial based sensing (accelerometers, gyroscopes, etc.) that provide only indirect measures of joint motion. Measurement of joint kinematics using flexible goniometry is more direct, and still popular in laboratory environments, but has received little attention as a potential tool for wearable systems. The aim of this study was to compare two goniometric devices: a traditional strain-gauge flexible goniometer, and a fiberoptic flexible goniometer, for measuring dynamic knee flexion/extension angles during activity of daily living: chair rise, and gait; and exercise: deep knee bends, against joint angles computed from a "gold standard" Vicon motion tracking system. Six young adults were recruited to perform the above activities in the lab while wearing a goniometer on each knee, and reflective markers for motion tracking. Kinematic data were collected simultaneously from the goniometers (one on each leg) and the motion tracking system (both legs). The results indicate that both goniometers were within 2-5 degrees of the Vicon angles for gait and chair rise. For some deep knee bend trials, disagreement with Vicon angles exceeded ten degrees for both devices. We conclude that both goniometers can record ADL knee movement faithfully and accurately, but should be carefully considered when high (>120?deg) knee flexion angles are required.     

Polymer-supported RNA synthesis and its application to test the nearest-neighbor model for duplex stability

A solid-phase method using a phosphoramidite approach is described for synthesis of oligoribonucleotides. The method was used to synthesize pairs of oligomers with identical nearest neighbors but different sequences. Comparison of thermodynamic parameters for these pairs provides a test of the nearest-neighbor hypothesis for prediction of helix stability. In general, pairs of sequences with identical nearest neighbors have enthalpy and entropy changes for helix formation that differ by 8% on average, delta Go37 that differ by 6% on average, and melting temperatures within 0-5 degrees C of each other. These limits are typical of the accuracy that should be expected from nearest-neighbor predictions of RNA helix stability. UCAUGA and UGAUCA have the same nearest neighbors but melting temperatures that differ by 7 degrees C. This suggests some sequences will not be approximated well by the nearest-neighbor model.     

Pelvic kinematic method for determining vertical jump height

Sacral marker and pelvis reconstruction methods have been proposed to approximate total body center of mass during relatively low intensity gait and hopping tasks, but not during a maximum effort vertical jumping task. In this study, center of mass displacement was calculated using the pelvic kinematic method and compared with center of mass displacement using the ground-reaction force-impulse method, in experienced athletes (n = 13) performing restricted countermovement vertical jumps. Maximal vertical jumps were performed in a biomechanics laboratory, with data collected using an 8-camera motion analysis system and two force platforms. The pelvis center of mass was reconstructed from retro-reflective markers placed on the pelvis. Jump height was determined from the peak height of the pelvis center of mass minus the standing height. Strong linear relationships were observed between the pelvic kinematic and impulse methods (R2 = .86; p < .01). The pelvic kinematic method underestimated jump height versus the impulse method, however, the difference was small (CV = 4.34%). This investigation demonstrates concurrent validity for the pelvic kinematic method to determine vertical jump height.     

A smoothed backbone-dependent rotamer library for proteins derived from adaptive kernel density estimates and regressions

Rotamer libraries are used in protein structure determination, prediction, and design. The backbone-dependent rotamer library consists of rotamer frequencies, mean dihedral angles, and variances as?a function of the backbone dihedral angles. Structure prediction and design methods that employ backbone flexibility would strongly benefit from smoothly varying probabilities and angles. A new version of the?backbone-dependent rotamer library has been developed using adaptive kernel density estimates for the rotamer frequencies and adaptive kernel regression for the mean dihedral angles and variances. This formulation allows for evaluation of the rotamer probabilities, mean angles, and variances as?a smooth and continuous function of phi and psi. Continuous probability density estimates for the nonrotameric degrees of freedom of amides, carboxylates, and aromatic side chains have been modeled as a function of the backbone dihedrals and rotamers of the remaining degrees of freedom. New backbone-dependent rotamer libraries at varying levels of smoothing are available from http://dunbrack.fccc.edu.     

Training multi-parameter gaits to reduce the knee adduction moment with data-driven models and haptic feedback

The purpose of this study was to evaluate gait retraining for reducing the knee adduction moment. Our primary objective was to determine whether subject-specific altered gaits aimed at reducing the knee adduction moment by 30% or more could be identified and adopted in a single session through haptic (touch) feedback training on multiple kinematic gait parameters. Nine healthy subjects performed gait retraining, in which data-driven models specific to each subject were determined through experimental trials and were used to train novel gaits involving a combination of kinematic changes to the tibia angle, foot progression and trunk sway angles. Wearable haptic devices were used on the back, knee and foot for real-time feedback. All subjects were able to adopt altered gaits requiring simultaneous changes to multiple kinematic parameters and reduced their knee adduction moments by 29-48%. Analysis of single parameter gait training showed that moving the knee medially by increasing tibia angle, increasing trunk sway and toeing in all reduced the first peak of the knee adduction moment with tibia angle changes having the most dramatic effect. These results suggest that individualized data-driven gait retraining may be a viable option for reducing the knee adduction moment as a treatment method for early-stage knee osteoarthritis patients with sufficient sensation, endurance and motor learning capabilities.     

Concurrent musculoskeletal dynamics and finite element analysis predicts altered gait patterns to reduce foot tissue loading

Current computational methods for simulating locomotion have primarily used muscle-driven multibody dynamics, in which neuromuscular control is optimized. Such simulations generally represent joints and soft tissue as simple kinematic or elastic elements for computational efficiency. These assumptions limit application in studies such as ligament injury or osteoarthritis, where local tissue loading must be predicted. Conversely, tissue can be simulated using the finite element method with assumed or measured boundary conditions, but this does not represent the effects of whole body dynamics and neuromuscular control. Coupling the two domains would overcome these limitations and allow prediction of movement strategies guided by tissue stresses. Here we demonstrate this concept in a gait simulation where a musculoskeletal model is coupled to a finite element representation of the foot. Predictive simulations incorporated peak plantar tissue deformation into the objective of the movement optimization, as well as terms to track normative gait data and minimize fatigue. Two optimizations were performed, first without the strain minimization term and second with the term. Convergence to realistic gait patterns was achieved with the second optimization realizing a 44% reduction in peak tissue strain energy density. The study demonstrated that it is possible to alter computationally predicted neuromuscular control to minimize tissue strain while including desired kinematic and muscular behavior. Future work should include experimental validation before application of the methodology to patient care.     

Validation of gait event detection by centre of pressure during target stepping in healthy and paretic gait

BackgroundTarget-stepping paradigms are increasingly used to assess and train gait adaptability. Accurate gait-event detection (GED) is key to locating targets relative to the ongoing step cycle as well as measuring foot-placement error. In the current literature GED is either based on kinematics or centre of pressure (CoP), and both have been previously validated with young healthy individuals. However, CoP based GED has not been validated for stroke survivors who demonstrate altered CoP pattern.MethodsYoung healthy adults and individuals affected by stroke stepped to targets on a treadmill, while gait events were measured using three detection methods; verticies of CoP cyclograms, and two kinematic criteria, (1) vertical velocity and position and of the heel marker, (2) anterior velocity and position of the heel and toe marker, were used. The percentage of unmatched gait events was used to determine the success of the GED method. The difference between CoP and kinematic GED methods were tested with two one sample (two-tailed) t-tests against a reference value of zero. Differences between group and paretic and non-paretic leg were tested with a repeated measures ANOVA.ResultsThe kinematic method based on vertical velocity only detected about 80% of foot contact events on the paretic side in stroke survivors while the method on anterior velocity was more successful in both young healthy adults as stroke survivors (3% young healthy and 7% stroke survivors unmatched). Both kinematic methods detected gait events significantly earlier than CoP GED (p < 0.001) except for foot contact in stroke survivors based on the vertical velocity.ConclusionsCoP GED may be more appropriate for gait analyses of SS than kinematic methods; even when walking and varying steps.     

Online gait event detection using a large force platform embedded in a treadmill

Gait research and clinical gait training may benefit from movement-dependent event control, that is, technical applications in which events such as obstacle appearance or visual/acoustic cueing are (co)determined online on the basis of current gait properties. A prerequisite for successful gait-dependent event control is accurate online detection of gait events such as foot contact (FC) and foot off (FO). The objective of the present study was to assess the feasibility of online FC and FO detection using a single large force platform embedded in a treadmill. Center-of-pressure, total force output and kinematic data were recorded simultaneously in 12 healthy participants. Online FC and FO estimates and spatial and temporal gait parameters estimated from the force platform data-i.e., center-of-pressure profiles-were compared to offline kinematic counterparts, which served as the gold standard. Good correspondence was achieved between online FC detections using center-of-pressure profiles and those derived offline from kinematic data, whereas FO was detected 31ms too late. A good relative and absolute agreement was achieved for both spatial and temporal gait parameters, which was improved further by applying more fine-grained FO estimation procedures using characteristic local minima in the total force output time series. These positive results suggest that the proposed system for gait-dependent event control may be successfully implemented in gait research as well as gait interventions in clinical practice.     

A multi-segment kinematic model of the foot with a novel definition of forefoot motion for use in clinical gait analysis during walking

A multi-segment kinematic model of the foot was developed for use in a gait analysis laboratory. The foot was divided into hindfoot, talus, midfoot and medial and lateral forefoot segments. Six functional joints were defined: ankle and subtalar joints, frontal and transverse plane motions of the hindfoot relative to midfoot, supination/pronation twist of the forefoot relative to midfoot and medial longitudinal arch height-to-length ratio. Twelve asymptomatic subjects were tested during barefoot walking with a six-camera optical stereometric system and auto-reflective markers organized in triads. Repeatability of the joint motions was tested using coefficients of multiple correlation. Ankle and subtalar joint motions and twisting of the forefoot were most repeatable. Hindfoot motions were least repeatable both within-subjects and between-subjects. Hindfoot and forefoot pronation in the frontal plane was found to coincide with dropping of the medial longitudinal arch between early to mid-stance, followed by supination and rising of the arch in late stance and swing phase. This multi-segment foot model addresses an unfortunate shortcoming in current gait analysis practice-the inability to measure motion within the foot. Such measurements are crucial if gait analysis is to remain relevant in the orthopaedic and rehabilitative treatment of the foot and ankle.     

Artificial neural network model for the generation of muscle activation patterns for human locomotion.

Skilled locomotor behaviour requires information from various levels within the central nervous system (CNS). Mathematical models have permitted researchers to simulate various mechanisms in order to understand the organization of the locomotor control system. While it is difficult to adequately characterize the numerous inputs to the locomotor control system, an alternative strategy may be to use a kinematic movement plan to represent the complex inputs to the locomotor control system based on the possibility that the CNS may plan movements at a kinematic level. We propose the use of artificial neural network (ANN) models to represent the transformation of a kinematic plan into the necessary motor patterns. Essentially, kinematic representation of the actual limb movement was used as the input to an ANN model which generated the EMG activity of 8 muscles of the lower limb and trunk. Data from a wide variety of gait conditions was necessary to develop a robust model that could accommodate various environmental conditions encountered during everyday activity. A total of 120 walking strides representing normal walking and ten conditions where the normal gait was modified in terms of cadence, stride length, stance width or required foot clearance. The final network was assessed on its ability to predict the EMG activity on individual walking trials as well as its ability to represent the general activation pattern of a particular gait condition. The predicted EMG patterns closely matched those recorded experimentally, exhibiting the appropriate magnitude and temporal phasing required for each modification. Only 2 of the 96 muscle/gait conditions had RMS errors above 0.10, only 5 muscle/gait conditions exhibited correlations below 0.80 (most were above 0.90) and only 25 muscle/gait conditions deviated outside the normal range of muscle activity for more than 25% of the gait cycle. These results indicate the ability of single network ANNs to represent the transformation between a kinematic movement plan and the necessary muscle activations for normal steady state locomotion but they were also able to generate muscle activation patterns for conditions requiring changes in walking speed, foot placement and foot clearance. The abilities of this type of network have implications towards both the fundamental understanding of the control of locomotion and practical realizations of artificial control systems for use in rehabilitation medicine.     

Influence of the posterior tibial tendon on the medial arch of the foot: an in vitro kinetic and kinematic study]

INTRODUCTION: The respective contributions of the active and passive structures of the foot to the stability of the medical arch were investigated using an in vitro kinetic and kinematic model. The effect of the tibialis posterior tendon on foot and ankle movements, and plantar pressure distribution of the foot were tested in a cadaveric human foot. METHOD: The stance phase from heel-contact to toe-off of normal walking gait and after tibialis posterior tendon rupture was simulated in eight roentenographically normal human feet (age 66 +/- 19 years, males). Ground reaction force and tibial inclination was simulated by means of a tilting angle and force-controlled translation stage. Plantar pressure was measured using a pressure-measuring platform. The force developed by the flexors and extensor muscles of the foot were simulated via cables attached to 7 force-controlled hydraulic cylinders. Tibial rotation was produced by an electric servo-motor, and foot movements measured with an ultrasonic analysis system. RESULTS: The model was verified against the plantar distribution and kinematics of healthy subjects measured during normal gait. Tibialis posterior deficit did not result in any detectable changes in pressure or force-time integral in the medial regions of the foot--a common sign of flat foot (pressure: midfoot 0.2 < or = 0.9; medial forefoot 0.5 < or = p < or = 0.9; hallux 0.5 < or = p < or = 0.9; force-time integral: midfoot p = 0-871; medial forefoot p = 0.632; hallux p = 0.068). Only small tendential changes in the kinematics of the talus and calcaneus were observed in dorsiflexion (0-58 sec; talus 0.1 < or = p < or = 0.6; calcaneus 0.4 < or = p < or = 0.06) and eversion (talus: 0-60 sec. 0.1 < or = p < or = 0.6; calcaneus: 37-60 sec. 0.2 < or = p < or = 0.7). CONCLUSION: The results of this in vitro study show that defective tibialis posterior alone does not produce significant changes in the kinetics or kinematics of the stance phase of normal gait. This suggests that the development of flat foot observed in degeneration of the tibialis posterior tendon occurs only after fatigue of the passive structures of the foot.     

Repeatability of gait data using a functional hip joint centre and a mean helical knee axis

Repeatability of traditional kinematic and kinetic models is affected by the ability to accurately locate anatomical landmarks (ALs) to define joint centres and anatomical coordinate systems. Numerical methods that define joint centres and axes of rotation independent of ALs may also improve the repeatability of kinematic and kinetic data. The purpose of this paper was to compare the repeatability of gait data obtained from two models, one based on ALs (AL model), and the other incorporating a functional method to define hip joint centres and a mean helical axis to define knee joint flexion/extension axes (FUN model). A foot calibration rig was also developed to define the foot segment independent of ALs. The FUN model produced slightly more repeatable hip and knee joint kinematic and kinetic data than the AL model, with the advantage of not having to accurately locate ALs. Repeatability of the models was similar comparing within-tester sessions to between-tester sessions. The FUN model may also produce more repeatable data than the AL model in subject populations where location of ALs is difficult. The foot calibration rig employed in both the AL and FUN model provided an easy alternative to define the foot segment and obtain repeatable data, without accurately locating ALs on the foot.     

Validity and reliability of a shoe-embedded sensor module for measuring foot progression angle during over-ground walking

Wearable systems are becoming increasingly popular for gait assessment outside of laboratory settings. A single shoe-embedded sensor module can measure the foot progression angle (FPA) during walking. The FPA has important clinical utility, particularly in populations with knee osteoarthritis, as it is a target for biomechanical treatments. However, the validity and the day-to-day reliability of FPA measurement using wearable systems during over-ground walking has yet to be established. Two gait analysis sessions on 20 healthy adults were conducted. During both sessions, participants performed natural over-ground walking in a motion capture laboratory and on a 100 m linear section of outdoor athletics track. FPA was measured in the laboratory via marker trajectory data, while the sensor module measured FPA during the outdoor track walking. Validity was examined by comparing the laboratory- and sensor-measured average FPA. Day-to-day reliability was examined by comparing the sensor-measured FPA between the first and second gait analysis sessions. Average absolute error between motion capture and sensor measured FPA were 1.7° and 2.1° at session 1 and 2, respectively. A Bland and Altman plot indicated no systematic bias, with 95% limit of agreement widths of 4.2° – 5.1°. Intraclass correlation coefficient (ICC_2k) analysis resulted in good to excellent validity (ICC = 0.89 – 0.91) and reliability (ICC = 0.95). Overall, the shoe-embedded sensor module is a valid and reliable method of measuring FPA during over-ground walking without the need for laboratory equipment.     

Slip-induced fall-risk assessment based on regular gait pattern in older adults

Aging-associated fall-risk assessment is crucial for fall prevention. Thus, this study aimed to develop a prognostic model to predict fall-risk following an unexpected over-ground slip perturbation based on normal gait pattern in healthy older adults. 112 healthy older adults who experienced a novel slip in a safe laboratory environment were included. Their slip trial and natural walking trial immediately prior to it were analyzed. To identify the best fall-risk predictive model, gait related variables including step length, segment angles, center of mass state, and ground reaction force (GRF) were determined and inputted into a stepwise logistic regression. The optimal slip-induced fall prediction model was based on the right thigh angle at slipping foot touchdown (TD), the maximum GRF of the slipping limb after TD, and the momentum change from TD to recovery foot liftoff (LO), with an overall prediction accuracy of 75.9%, predicting 74.5% of falls (sensitivity) and 77.2% of recoveries (specificity). Conversely, a model based on clinical and demographic measures predicted 78.2% of falls and 47.4% of recoveries, resulting in a much lower overall accuracy of 62.5%. The fall-risk model based on normal gait pattern which was developed for slip-induced perturbations in healthy older adults was able to provide a high predictive accuracy. This information could provide insight about the ideal normal gait measures which could be used to contribute towards development of therapeutic strategies related to dynamic balance and fall prevention to enhance preventive interventions in populations with high-risk for slip-induced falls.     

Foot structure and knee joint kinetics during walking with and without wedged footwear insoles

The relationship between static foot structure characteristics and knee joint biomechanics during walking, or the biomechanical response to wedged insoles are currently unknown. In this study, 3D foot scanning, dual X-ray absorptiometry and gait analysis methods were used to determine structural parameters of the foot and assess their relation to knee joint loading and biomechanical response to wedged insoles in 30 patients with knee osteoarthritis. In multiple linear regression models, foot fat content, height of the medial longitudinal arch and static hind foot angle were not associated with the magnitude of the knee adduction moment (R² = 0.24, p = 0.060), knee adduction angular impulse (R² = 0.21, p = 0.099) or 3D resultant knee moment (R² = 0.23, p = 0.073) during gait. Furthermore, these foot structure parameters were not associated with the patients’ biomechanical response to medial or lateral wedge footwear insoles (all p < 0.01). These findings suggest that static foot structure is not associated with gait mechanics at the knee, and that static foot structure alone cannot be utilized to predict an individual’s biomechanical response to wedged footwear insoles in patients with knee osteoarthritis.     

Support vector machines for detecting age-related changes in running kinematics

Age-related changes in running kinematics have been reported in the literature using classical inferential statistics. However, this approach has been hampered by the increased number of biomechanical gait variables reported and subsequently the lack of differences presented in these studies. Data mining techniques have been applied in recent biomedical studies to solve this problem using a more general approach. In the present work, we re-analyzed lower extremity running kinematic data of 17 young and 17 elderly male runners using the Support Vector Machine (SVM) classification approach. In total, 31 kinematic variables were extracted to train the classification algorithm and test the generalized performance. The results revealed different accuracy rates across three different kernel methods adopted in the classifier, with the linear kernel performing the best. A subsequent forward feature selection algorithm demonstrated that with only six features, the linear kernel SVM achieved 100% classification performance rate, showing that these features provided powerful combined information to distinguish age groups. The results of the present work demonstrate potential in applying this approach to improve knowledge about the age-related differences in running gait biomechanics and encourages the use of the SVM in other clinical contexts.     

When Is Visual Information Used to Control Locomotion When Descending a Kerb?

Background

Descending kerbs during locomotion involves the regulation of appropriate foot placement before the kerb-edge and foot clearance over it. It also involves the modulation of gait output to ensure the body-mass is safely and smoothly lowered to the new level. Previous research has shown that vision is used in such adaptive gait tasks for feedforward planning, with vision from the lower visual field (lvf) used for online updating. The present study determined when lvf information is used to control/update locomotion when stepping from a kerb.

Methodology/Principal Findings

12 young adults stepped down a kerb during ongoing gait. Force sensitive resistors (attached to participants'' feet) interfaced with an high-speed PDLC ‘smart glass’ sheet, allowed the lvf to be unpredictably occluded at either heel-contact of the penultimate or final step before the kerb-edge up to contact with the lower level. Analysis focussed on determining changes in foot placement distance before the kerb-edge, clearance over it, and in kinematic measures of the step down. Lvf occlusion from the instant of final step contact had no significant effect on any dependant variable (p>0.09). Occlusion of the lvf from the instant of penultimate step contact had a significant effect on foot clearance and on several kinematic measures, with findings consistent with participants becoming uncertain regarding relative horizontal location of the kerb-edge.

Conclusion/Significance

These findings suggest concurrent feedback of the lower limb, kerb-edge, and/or floor area immediately in front/below the kerb is not used when stepping from a kerb during ongoing gait. Instead heel-clearance and pre-landing-kinematic parameters are determined/planned using lvf information acquired in the penultimate step during the approach to the kerb-edge, with information related to foot placement before the kerb-edge being the most salient.     

A local nearest-neighbor convex-hull construction of home ranges and utilization distributions

We describe a new method for estimating the area of home ranges and constructing utilization distributions (UDs) from spatial data. We compare our method with bivariate kernel and α-hull methods, using both randomly distributed and highly aggregated data to test the accuracy of area estimates and UD isopleth construction. The data variously contain holes, corners, and corridors linking high use areas. Our method is based on taking the union of the minimum convex polygons (MCP) associated with the k−1 nearest neighbors of each point in the data and, as such, has one free parameter k. We propose a "minimum spurious hole covering" (MSHC) rule for selecting k and interpret its application in terms of type I and type II statistical errors. Our MSHC rule provides estimates within 12% of true area values for all 5 data sets, while kernel methods are worse in all cases: in one case overestimating area by a factor of 10 and in another case underestimating area by a factor of 50. Our method also constructs much better estimates for the density isopleths of the UDs than kernel methods. The α-hull method does not lead directly to the construction of isopleths and also does not always include all points in the constructed home range. Finally we demonstrate that kernel methods, unlike our method and the α-hull method, does not converges to the true area represented by the data as the number of data points increase.