Total Trajectory Length Research Articles

Gaze stabilization exercises derive sensory reweighting of vestibular for postural control

[Purpose] The aim of this study was to investigate whether gaze stabilization exercise derives sensory reweighting of vestibular for upright postural control. [Subjects and Methods] Twenty-three healthy volunteers participated in this study. The center of pressure of the total trajectory length was measured before (pre), immediately after (post), and 10 min after (post10) gaze stabilization exercise, in the static standing position, with the eyes open or closed, on the floor or on foam rubber. The sensory contribution values of the visual, somatosensory, and vestibular systems were calculated using center of pressure of the total trajectory length value in these measuring conditions. [Results] The center of pressure of the total trajectory length on foam rubber in post and post10 were significantly lower than that in the pre. The sensory contribution values of vestibular in post10 stages were significantly higher than that in pre-stage. [Conclusion] Gaze stabilization exercise can improve the static body balance in a condition that particularly requires vestibular function. The possible mechanism involves increasing sensory contribution of the vestibular system for postural control by the gaze stabilization exercise, which may be useful to derive sensory reweighting of the vestibular system for rehabilitation.

A Study of the Reliability of a New Dynamic Trunk Balance Measuring Device

Objective: A new method of evaluating sitting balance that improved on a previous device was developed. However, the reliability of body trunk balance measured by this device is unknown. The purpose of this study was to verify its reliability within and between examiners. Methods: This was a cross-sectional study involving healthy adult males (age 20 to 45 years) who were able to walk. The seating surface could be vibrated at a constant cycle (0.2 Hz, 0.4 Hz, 0.6 Hz), the pressure of the seating surface under vibration was detected by three small force sensors installed under the seating surface, and the center of pressure (COP) could be calculated. Measurements were performed by two examiners, and each participant was measured three times in a sitting position. The platform was tilted to the left and right at a front face inclination angle ± 7°, with two cycles in 10 s (0.2 Hz), while the participant’s gaze was fixed to a mark 2 m in front of the participant at eye height, and the participant was asked to maintain the position of the head constant. Measurement was then performed for 30 s. The fluctuation of the center of gravity on the seat surface over time was measured, and the total trajectory length of the COP was used as the evaluation item. To examine the reliability of the measuring instrument, ICC (1.3) was obtained as the intra-class correlation coefficient for intra-examiner reliability, and ICC (2.1) was obtained for inter-examiner reliability. Results: The ICC for intra-examiner reliability was 0.815, and that for inter-examiner reliability was 0.789. No adverse events occurred during balance evaluation. Conclusion: This device could be used to evaluate dynamic trunk balance with relatively high reliability. Thus, the present device appears to be useful for quantitatively evaluating dynamic trunk balance conveniently and safely.

Multi-objective sidetracking horizontal well trajectory optimization in cluster wells based on DS algorithm

To optimize sidetracking horizontal well trajectory in cluster wells, a new multi-objective optimization model has been established. The new model synthetically considers the total trajectory length, the well profile energy and the accuracy of target hitting as the objective functions and takes the anti-collision with adjacent well as constraint. A novel heuristic algorithm based on DS is presented to solve the established optimization model, and the constraint is handled by a penalty method using an S-type penalty function. The comparisons between multi-objective optimization and single-objective optimization indicate that multi-objective optimization is more superior in sidetracking well trajectory optimization which can obtain a relatively short total trajectory length, a low well profile energy and an extremely high accuracy of target hitting. Furthermore, the optimization model considering anti-collision can ensure the minimum distance with adjacent well no less than the safety distance which can avoid collision in cluster wells. At last, the convergence and stability of the proposed algorithm have been discussed, and the results indicate that d-DS has good convergence and numerical stability, thus the d-DS algorithm is excellent for solving trajectory optimization problem.

Multi-objective optimization design and control of deviation-correction trajectory with undetermined target

In the horizontal drilling process, when the actual trajectory deviates from the planned trajectory, it is necessary to take corrective action. The target point is difficult to determine explicitly; however, it is assumed to be in a certain interval of the planned trajectory. This paper presents a mathematical formulation for deviation-correction trajectory design in the case of an undetermined target point, and an optimum design model is established that considers two cases of planned trajectory. The criteria to evaluate the deviation-correction trajectory are summarized as the total trajectory length, the coincidence rate and the well profile energy. The optimum trajectory based on multi-objective optimization is discussed in terms of comprehensive criteria and different weight factors, and a novel heuristic algorithm to solve the established optimization model is presented. The results demonstrate that the maximum value of curvature results in a trajectory with a minimum total length and maximum coincidence rate yet a maximum well profile energy, whereas the maximum horizontal displacement leads to a trajectory with minimum well profile energy. Additionally, the multi-objective optimization model can guarantee a smaller trajectory length, high coincidence rate and low well profile energy. Finally, the multi-objective control method is proposed to obtain an optimization trajectory in different situations.

Relationships between gait and standing balance in hemiplegia

Objective To study the relationships between the standing balance and walking ability of hemiplegic stroke survivors. Methods Eighty-eight post-stroke hemiplegic patients who could walk independently for more than 10 metres were selected into a patient group, while 88 healthy counterparts were recruited into a control group. Descriptors of the gait and balance function of both groups were collected using a gait and balance training and evaluation apparatus (Model: AL-600). The gait parameters were step width, walking speed, step length asymmetry (SLA), swing time asymmetry (SWTA) and stand time asymmetry (STA). The balance parameters studied were total trajectory length of the center of plantar pressure (COPD), the average left and right deviation of the center of plantar pressure (COPD-X) and the average anterio-posterior deviation of the center of plantar pressure (COPD-Y). Differences in indexes of gait and balance function between the two groups were analyzed using t-tests, and the relationships between the gait and balance indicators were analyzed using Pearson correlation coefficients. Results The walking speed, step width, COPD, COPD-X, COPD-Y, SLA, SWTA and STA of the patient group[(37.64±18.29)cm/s, (14.45±4.17)cm, (66.75±29.04)cm, (2.04±1.41)cm, (2.48±1.28)cm, (1.30±0.46), (1.65±0.67) and (1.18±0.16), respectively]all increased significantly more compared to the control group[(90.76±14.72)cm/s, (8.70±2.62)cm, (27.84±6.54)cm, (1.30±0.53)cm, (1.68±0.40)cm, (1.07±0.06), (1.07±0.08) and (1.05±0.06), respectively], though the walking speed was significantly slower than that in the control group (P<0.05). The patient group's average COPD-X showed slightly and moderately negative correlation with their walking speed, step width, SLA and SWTA (P<0.05). COPD-Y was weakly related with step width (P<0.05). Conclusion The standing balance of hemiplegic patients after stroke is related to their walking speed, step width and gait asymmetry. Especially significant correlation is observed between standing balance parameters such as COPD-X and gait parameters. Key words: Stroke; Balance control; Step width; Walking speed; Center of plantar pressure

Reproducibility of Dynamic Body Balance Measurement by Center of Foot Pressure Analysis Immediately after Single-Leg Hop Landing.

Dynamic balance was evaluated using the trajectory length of the center of foot pressure (COP) in the early phase from immediately after landing to the time of pastoral maintenance. Ten young volunteers with an average age of 23.8 years were asked to stand on one foot on a horizontal floor, hop forward half a step and land on one foot 10 times on each of 3 non-consecutive days. The peak of the vertical component of the floor reaction force (Fz), and the initiation time of the maximum value (tz) and COP trajectory length were measured by a force plate (AMTI, Ltd.). None of the subjects complained of any feeling of fear or loss of balance during the 3 days.The interclass correlation coefficient values of Fz and tz over the three days were 0.75 or higher. Single-leg hop for half a step as a motor task enabled safe measurement of COP trajectory length with high reproducibility. Fz reached its peak within 200 ms after landing and the COP trajectory length within 200 ms after landing accounted for approximately 50% of the total COP trajectory length at one second. Although the length differed in each subject, the interclass correlation coefficients for COP up to 100 ms and 200 ms were 0.68 and 0.80, respectively.The COP trajectory length within 200 ms after landing was considered to be useful as an objective criteria for the evaluation of dynamic balance in the early phase after landing.

Trajectory length of pitch vs. roll: Technique for assessment of postural stability

Background: Patients with disorders of nervous or musculoskeletal system often show instability of the body segments during the stance tasks. Traditionally, stabilometric platforms are used to measure body sway. However, these devices are expensive and do not allow the evaluation of the individual movements of body segments. At present, accelerometers or gyroscopes are used to measure the movements of the body segments. For these new motion capture (MoCap) systems, methods for quantitative evaluation of a body segment movement are being developed. Objective: The main objective of this paper is to describe a new method which would be suitable for quantifying postural stability and identifying differences in balance control using data recorded by an inexpensive 2-DoF gyroscope. Methods: Method based on total length of trajectory (TL) in a 2-D plot of angles was proposed for quantitative evaluation of the trunk and feet sway. The sway was measured during quiet stance of ten middle-aged patients (Pts) with degenerative cerebellar disorder and eleven young healthy subjects (HS) standing with eyes open (EO) on a firm surface (FiS) and eyes closed (EC) on a foam surface (FoS). Data were obtained using three gyroscopes (Xsens) to measure roll and pitch angular movements of the trunk, and left and right foot. The pitch versus roll plots of the trunk and feet were created and the trajectory lengths of the pitch vs. roll angle were calculated. Results: Although the results vary while measuring different segments of the body, the method showed significant differences between the two different groups. Significant differences between the HS and Pts were found in EO standing on a FiS for TLs of the trunk (p = .02) and TLs of the feet (p < .01). Similarly in EC standing on a FoS significant differences (p < .01) between groups were found for TLs of both the trunk and the feet (p < .01). Conclusions: It was found that the TL of pitch vs. roll is suitable for quantifying postural sway and identifying differences in balance control. The technique, based on the length of the pitch angle vs. roll angle trajectory can be used even where MoCap systems can only measure two sway angles which could extend the clinical information of the body sway.

The varying effects of warm-water bathing therapies: partial bathing decreases exercise tolerance to levels similar to full-body bathing.

[Purpose] The purpose of this study was to determine differences in postural sway and tolerance to exercise before and after full-body, forearm, and lower leg bathing in warm-water. [Subjects and Methods] Thirteen healthy, young adult males were subjected to full-body, forearm, and lower leg bathing at 41 °C for 10 minutes. [Results] The 2-point discrimination sense value and total trajectory length significantly decreased after bathing. [Conclusion] In summary, we found that warm-water bathing sharpens plantar sensation, and thus may help to prevent falls in the elderly. Even partial forearm and lower leg bathing increased exercise tolerance to levels similar to full-body bathing.

Center-of-pressure total trajectory length is a complementary measure to maximum excursion to better differentiate multidirectional standing limits of stability between individuals with incomplete spinal cord injury and able-bodied individuals

BackgroundSensorimotor impairments secondary to a spinal cord injury affect standing postural balance. While quasi-static postural balance impairments have been documented, little information is known about dynamic postural balance in this population. The aim of this study was to quantify and characterize dynamic postural balance while standing among individuals with a spinal cord injury using the comfortable multidirectional limits of stability test and to explore its association with the quasi-static standing postural balance test.MethodsSixteen individuals with an incomplete spinal cord injury and sixteen able-bodied individuals participated in this study. For the comfortable multidirectional limits of stability test, participants were instructed to lean as far as possible in 8 directions, separated by 45° while standing with each foot on a forceplate and real-time COP visual feedback provided. Measures computed using the center of pressure (COP), such as the absolute maximal distance reached (COPmax) and the total length travelled by the COP to reach the maximal distance (COPlength), were used to characterize performance in each direction. Quasi-static standing postural balance with eyes open was evaluated using time-domain measures of the COP. The difference between the groups and the association between the dynamic and quasi-static test were analyzed.ResultsThe COPlength of individuals with SCI was significantly greater (p ≤ 0.001) than that of able-bodied individuals in all tested directions except in the anterior and posterior directions (p ≤ 0.039), indicating an increased COP trajectory while progressing towards their maximal distance. The COPmax in the anterior direction was significantly smaller for individuals with SCI. Little association was found between the comfortable multidirectional limits of stability test and the quasi-static postural balance test (r ≥ −0.658).ConclusionStanding dynamic postural balance performance in individuals with an incomplete spinal cord injury can be differentiated from that of able-bodied individuals with the comfortable limits of stability test. Performance among individuals with an incomplete spinal cord injury is characterized by lack of precision when reaching. The comfortable limits of stability test provides supplementary information and could serve as an adjunct to the quasi-static test when evaluating postural balance in an incomplete spinal cord injury population.

Abstract 1801: Lyn and Fyn inhibition as a potential novel treatment for glioblastoma multiforme

Abstract Background: Glioblastoma multiforme (GBM) is the most malignant and most aggressive of the adult brain tumors. The current therapies including surgical resection, radiation therapy and chemotherapy remain palliative with median survival of 14 months. Two of the Src family kinases, Lyn and Fyn, have been reported to be involved in the pathogenesis and aggressiveness of GBM in clinical and laboratory research studies. Specific Aims: We evaluated the effect of Lyn and Fyn kinase inhibition on GBM cell motility and survival by utilizing a clinically relevant Lyn and Fyn kinase inhibitor, bafetinib or formerly INNO-406 (CytRx Corporation, Los Angeles, CA). Bafetinib, a dual Bcr-Abl and Lyn tyrosine kinase inhibitor has been shown to inhibit 4 of the 79 tyrosine kinases, namely Abl, Abl-related gene (Arg), and two of the Src family kinases Lyn and Fyn but not Src. Methodology: We used Lyn- expressing T98G and Fyn-expressing U87MG human GBM cell lines. The effect of bafetinib on the motile activity was evaluated by the wound healing, single cell trajectory, and the trans-well assays. The cell survival and mitochondrial membrane potential were evaluated by Guava Easycyte *HT flowcytometer (Millipore) in cells treated with bafetinib for 24 h. Further, we examined the effect of bafetinib on cell survival in combination with temozolomide (TMZ), a widely used chemotherapy agent for the management of GBM, in U87MG cells using microplate MTT assay. Results: At 16 h post-wounding, bafetinib at 5 µM concentration inhibited the motility of T98G and U87MG cells by 33% (P &amp;lt; 0.01) and 24% (P &amp;lt; 0.01), respectively. This significant inhibition in the wound healing was accompanied by the inhibition of total length of cell trajectory, total length of the final cell displacement and average speed of cell locomotion. Bafetinib induced 62% mitochondrial membrane depolarization in U87MG cells and 20% depolarization in T98G cells. Higher depolarization levels in U87MG cells correlated with higher apoptosis (49.4%). Treatment of U87MG cells for 4 days with a combination of bafetinib and TMZ reduced the IC50 values as much as 60% and 80%, respectively, compared to the values obtained with each of the drugs, suggesting that bafetinib has the potential to improve the therapeutic effect of TMZ in GBM cells. Conclusion: Our preliminary findings suggest that targeting Lyn and Fyn kinase pathways with bafetinib may have a therapeutic potential for GBM. Our in vivo studies in mouse models with bafetinib will further establish the feasibility of targeting Lyn and Fyn kinases as possible therapeutic targets in GBM. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 103rd Annual Meeting of the American Association for Cancer Research; 2012 Mar 31-Apr 4; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2012;72(8 Suppl):Abstract nr 1801. doi:1538-7445.AM2012-1801

Impact of Perceptual Ability and Mental Imagery Training on Simulated Laparoscopic Knot-Tying in Surgical Novices Using a Nissen Fundoplication Model

Performing minimally invasive surgery requires training and visual-spatial intelligence. The aim of our study was to examine the impact of visual-spatial perception and additional mental training on the simulated laparoscopic knot-tying task performed by surgical novices. A total of 40 medical students randomly assigned to two groups underwent two sessions of laparoscopic basic training on a VR simulator (SimSurgery®, Oslo, Norway). The variables time and tip trajectory (total path length of the instrument tip trajectory) were used to assess the performance of the intracorporeal knot-tying task using a laparoscopic Nissen fundoplication model. The experimental group completed additional mental practice during the interval between the two training sessions. All performed a cube subtest of a standard intelligence test (I-S-T 2000 R) to evaluate visual-spatial ability. All participants achieved an improvement in time (t = 9.861; p < 0.001) and tip trajectory (t = 6.833; p < 0.001) in the second training session. High scores on the visual-spatial test correlated with a faster performance (r = -0.557; p < 0.001) and more precise movements (r = -0.377; p = 0.016). Comparison of the two groups did not show any statistical significant differences in the parameters time and tip trajectory. Visual-spatial intelligence tested by a cube test correlated with simulated laparoscopic knot-tying skills in surgical novices. Additional mental practice did not improve the overall knot-tying performance. Further studies are therefore required to determine whether mental practice might be beneficial for experienced laparoscopic surgeons or for more complex tasks.

Postural adaptations to long-term training in Prader-Willi patients

BackgroundImproving balance and reducing risk of falls is a relevant issue in Prader-Willi Syndrome (PWS). The present study aims to quantify the effect of a mixed training program on balance in patients with PWS.MethodsEleven adult PWS patients (mean age: 33.8 ± 4.3 years; mean BMI: 43.3 ± 5.9 Kg/m2) attended a 2-week training program including balance exercises during their hospital stay. At discharge, Group 1 (6 patients) continued the same exercises at home for 6 months, while Group 2 (5 patients) quitted the program. In both groups, a low-calorie, well-balanced diet of 1.200 kcal/day was advised. They were assessed at admission (PRE), after 2 weeks (POST1) and at 6-month (POST2). The assessment consisted of a clinical examination, video recording and 60-second postural evaluation on a force platform. Range of center of pressure (CoP) displacement in the antero-posterior direction (RANGEAP index) and the medio-lateral direction (RANGEML index) and its total trajectory length were computed.ResultsAt POST1, no significant changes in all of the postural parameters were observed. At completion of the home program (POST2), the postural assessment did not reveal significant modifications. No changes in BMI were observed in PWS at POST2.ConclusionsOur results showed that a long-term mixed, but predominantly home-based training on PWS individuals was not effective in improving balance capacity. Possible causes of the lack of effectiveness of our intervention include lack of training specificity, an inadequate dose of exercise, an underestimation of the neural and sensory component in planning rehabilitation exercise and failed body weight reduction during the training. Also, the physiology of balance instability in these patients may possibly compose a complex puzzle not affected by our exercise training, mainly targeting muscle weakness.

Postural strategies in Prader–Willi and Down syndrome patients

Patients affected by Down (DS) and Prader–Willi syndrome (PWS) are characterised by some common clinical and functional features including gait disorders and reduced postural control. The aim of our study was to quantitatively compare postural control in adult PWS and DS.We studied 12 PWS and 19 DS adult patients matched for age, height, weight and body mass index.They were instructed to maintain an upright standing position on a force platform for 30s with open eyes (OE) and we calculated the range of center of pressure (CoP) displacement in the A/P direction (RANGEAP) and in the M/L direction (RANGEML) and the total CoP trajectory length during quiet stance (Sway Path, SP).The range of oscillations in PWS and DS in both AP and ML direction were higher than in controls. PWS and DS were statistically different for RANGEAP, with PWS showing higher mean values.Our results confirm a reduced capacity of both PWS and DS in maintaining postural stability. This appears to be in some respect different in PWS and DS, with PWS showing poorer control in AP. DS and, particularly, PWS should be encouraged to undergo specific balance training and strengthening of the ankle muscles as part of a comprehensive rehabilitation program to enhance daily functioning and quality of life.

Olfactory stimuli and enhanced postural stability in older adults

Ameliorating postural instability is an important component of geriatric health care. The effect of olfactory stimuli (lavender and black pepper oils) on postural control in 17 older adults (78 ± 6 years old) who had no apparent neurological deficits was studied. Measurements of center of pressure (CoP) trajectories were done with subjects standing quietly on a force plate. Control measurements were compared with olfactory interventions: brief exposure to sham (distilled water), lavender oil, and black pepper oil; experiments were repeated with eyes open and eyes closed. From the CoP data, the root mean square (RMS) displacement and velocity in mediolateral (ML) and antero-posterior (AP) directions, and the total trajectory length were computed. This study found that with eyes closed, olfactory stimulation with either lavender or black pepper oil significantly decreased both ML and AP RMS velocities and trajectory lengths compared with baseline. In contrast, little effect was observed under the eyes-open condition. Decreases in RMS displacements were small and mostly insignificant. The study suggests that olfactory stimulation may improve posture stability in older adults through decreasing the velocities of postural adjustments during normal sway.

Examination of the Relationship Between Mandibular Position and Body Posture

The purpose of this study was to evaluate the effect of changing mandibular position on body posture and reciprocally, body posture on mandibular position. Forty-five (45) asymptomatic subjects (24 males and 21 females, ages 21-53 years, mean age 30.7 years) were included in this study and randomly assigned to one of two groups, based on the table of random numbers. The only difference between group I and group II was the sequence of the testing. The MatScan (Tekscan, Inc., South Boston, MA) system was used to measure the result of changes in body posture (center of foot pressure: COP) while subjects maintained the following 5 mandibular positions: 1) rest position, 2) centric occlusion, 3) clinically midlined jaw position with the labial frena aligned, 4) a placebo wax appliance, worn around the labial surfaces of the teeth and 5) right eccentric mandibular position. The T-Scan II (Tekscan, Inc., South Boston, MA) system was used to analyze occlusal force distribution in two postural positions, with and without a heel lift under the right foot. Total trajectory length of COP in centric occlusion was shorter than in the rest position (p<0.05). COP area in right eccentric mandibular position was larger than in centric occlusion (p<0.05). When subjects used a heel lift under the right foot, occlusal forces shifted to the right side compared to no heel lift (p<0.01). Based on these findings, it was concluded that changing mandibular position affected body posture. Conversely, changing body posture affected mandibular position.

Influence of Muscle Fatigue on Balance Disturbance in a Stable Upright Position

In order to identify the group of muscles related to deterioration of balance function in the elderly, an exploratory experiment was conducted to analyze and study the influence of lower limb muscular fatigue on balance disturbance in the stable upright position. A stabilometer and a multipurpose muscle function testing and training system were used to assess 12 normal healthy subjects. Evaluations were made using the total trajectory length and the trajectory length per unit area with the eyes-open for 30 seconds. All statistical analyses were performed using SPSS Ver. 13.0 with analysis of variance (repeated measures) at a significance level of below 5%. In the gluteus maximus muscles, the total trajectory length showed a significant downward trend while the trajectory length per unit area showed a significant upward trend.

Some Difficulties in Research into Cell Motile Activity under Isotropic Conditions

Movement of Dictyostelium discoideum amoebae under isotropic and anisotropic conditions was recorded and analysed with computer-aided methods and the results are presented in various manners as described in the subject literature. Cell movement under isotropic conditions showed great diversity. Some cells moved almost in a straight path whereas others in close proximity turned around with little net translocation. When cell movement under isotropic conditions was observed, no direct correlation was found between the total length of cell trajectories and the length of final displacements of the cells. It was necessary to present the results in the form of histograms, circular diagrams of cell trajectories or in scatter correlation diagrams showing the motile behaviour of many individual cells. These methods of presentation are more informative than methods which present only average values, the "representative" behaviour of single cells, or start and end points of cell tracks. The latter methods can only illustrate but do not document the results of experiments. The use of statistical methods appears necessary in cases when it is difficult to monitor the same cells before and during experimental treatment. However, when cell movement under anisotropic conditions becomes oriented and ordered as during tactic cell movements, then the diversity in cell behaviour decreases and methods based on estimation of starting and end points of cell positions appear more credible.

Statistical Properties of Trajectories of Friendly Walkers on Spatio-Temporal Plane

Friendly walkers are the non-crossing random walkers on a lattice with attractive interactions. We characterize each trajectory of friendly walkers by the number of walkers m , the time interval of observation t and the total length of trajectory r . A new algorithm to generate trajectories on a spatio-temporal plane is proposed and the distribution function of number of distinct trajectories characterized by ( m , t , r ), f m , t ( r ), is estimated by a random sampling method. The variance, the skewness and the kurtosis of f m , t ( r ) converge to finite values without scaling as t →∞ for each m . The distribution is asymmetric and its tails are expressed by stretched exponential functions. We consider the canonical distribution of m friendly walkers by introducing a parameter p which plays the same role of the Boltzmann factor e -β in the usual equilibrium systems. We calculate the mean and variance of r in the canonical distribution as a function of p for each m at t . It is observed that the varian...

Mechanism of unassisted ion transport across membrane bilayers.

To establish how charged species move from water to the nonpolar membrane interior and to determine the energetic and structural effects accompanying this process, we performed molecular dynamics simulations of the transport of Na+ and Cl- across a lipid bilayer located between two water lamellae. The total length of molecular dynamics trajectories generated for each ion was 10 ns. Our simulations demonstrate that permeation of ions into the membrane is accompanied by the formation of deep, asymmetric thinning defects in the bilayer, whereby polar lipid head groups and water penetrate the nonpolar membrane interior. Once the ion crosses the midplane of the bilayer the deformation "switches sides"; the initial defect slowly relaxes, and a defect forms in the outgoing side of the bilayer. As a result, the ion remains well solvated during the process; the total number of oxygen atoms from water and lipid head groups in the first solvation shell remains constant. A similar membrane deformation is formed when the ion is instantaneously inserted into the interior of the bilayer. The formation of defects considerably lowers the free energy barrier to transfer of the ion across the bilayer and, consequently, increases the permeabilities of the membrane to ions, compared to the rigid, planar structure, by approximately 14 orders of magnitude. Our results have implications for drug delivery using liposomes and peptide insertion into membranes.