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NASA NTRS1999

Advanced Techniques for Assessment of Postural and Locomotor Ataxia, Spatial Orientation, and Gaze Stability

In addition to adapting to microgravity, major neurovestibular problems of space flight include postflight difficulties with standing, walking, turning corners, and other activities that require stable upright posture and gaze stability. These difficulties inhibit astronauts' ability to stand or escape from their vehicle during emergencies. The long-ter7n goal of the NSBRI is the development of countermeasures to ameliorate the effects of long duration space flight. These countermeasures must be tested with valid and reliable tools. This project aims to develop quantitative, parametric approaches for assessing gaze stability and spatial orientation during normal gait and when gait is perturbed. Two of this year's most important findings concern head fixation distance and ideal trajectory analysis. During a normal cycle of walking the head moves up and down linearly. A simultaneous angular pitching motion of the head keeps it aligned toward an imaginary point in space at a distance of about one meter in front of a subject and along the line of march. This distance is called the head fixation distance. Head fixation distance provides the fundamental framework necessary for understanding the functional significance of the vestibular reflexes that couple head motion to eye motion. This framework facilitates the intelligent design of counter-measures for the effects of exposure to microgravity upon the vestibular ocular reflexes. Ideal trajectory analysis is a simple candidate countermeasure based upon quantifying body sway during repeated up and down stair stepping. It provides one number that estimates the body sway deviation from an ideal sinusoidal body sway trajectory normalized on the subject's height. This concept has been developed with NSBRI funding in less than one year. These findings are explained in more detail below. Compared to assessments of the vestibuo-ocular reflex, analysis of vestibular effects on locomotor function is relatively less well developed and quantified. We are improving this situation by applying methodologies such as nonlinear orbital stability to quantify responses and by using multivariate statistical approaches to link together the responses across separate tests. In this way we can exploit the information available and increase the ability to discriminate between normal and pathological responses. Measures of stability and orientation are compared to measures such as dynamic visual acuity and with balance function tests. The responses of normal human subjects and of patients having well documented pathophysiologies are being characterized. When these studies are completed, we should have a clearer idea about normal and abnormal patterns of eye, head, and body movements during locomotion and their stability in a wide range of environments. We plan eventually to use this information to validate the efficacy of candidate neurovestibular and neuromuscular rehabilitative techniques. Some representative studies made during this year are summarized.

Wall, Conrad., III↗

NASA NTRS2004

Validation of an Impedance Education Method in Flow

This paper reports results of a research effort to validate a method for educing the normal incidence impedance of a locally reacting liner, located in a grazing incidence, nonprogressive acoustic wave environment with flow. The results presented in this paper test the ability of the method to reproduce the measured normal incidence impedance of a solid steel plate and two soft test liners in a uniform flow. The test liners are known to be locally react- ing and exhibit no measurable amplitude-dependent impedance nonlinearities or flow effects. Baseline impedance spectra for these liners were therefore established from measurements in a conventional normal incidence impedance tube. A key feature of the method is the expansion of the unknown impedance function as a piecewise continuous polynomial with undetermined coefficients. Stewart's adaptation of the Davidon-Fletcher-Powell optimization algorithm is used to educe the normal incidence impedance at each Mach number by optimizing an objective function. The method is shown to reproduce the measured normal incidence impedance spectrum for each of the test liners, thus validating its usefulness for determining the normal incidence impedance of test liners for a broad range of source frequencies and flow Mach numbers. Nomenclature

Watson, Willie R.↗

NASA NTRS2001

Antibody responses to bacteriophage phi X-174 in human subjects exposed to the antarctic winter-over model of spaceflight

BACKGROUND: It has been proposed that exposure to long-term spaceflight conditions (stress, isolation, sleep disruption, containment, microbial contamination, and solar radiation) or to ground-based models of spaceflight will alter human immune responses, but specific antibody responses have not been fully evaluated. OBJECTIVE: We sought to determine whether exposure to the 8-month Antarctic winter-over model of spaceflight would alter human antibody responses. METHODS: During the 1999 Australian National Antarctic Research Expeditions, 11 adult study subjects at Casey, Antarctica, and 7 control subjects at Macquarie Island, sub-Antarctica, received primary and secondary immunizations with the T cell-dependent neoantigen bacteriophage phi X-174. Periodic plasma samples were analyzed for specific antibody function. RESULTS: All of the subjects from Casey, Antarctica, cleared bacteriophage phi X-174 normally by 1 week after primary immunization, and all had normal primary and secondary antibody responses, including immunologic memory amplification and switch from IgM to IgG antibody production. One subject showed a high normal pattern, and one subject had a low normal pattern. The control subjects from Macquarie Island also had normal immune responses to bacteriophage phi X-174. CONCLUSIONS: These data do not support the hypothesis that de novo specific antibody responses of subjects become defective during the conditions of the Antarctic winter-over. Because the Antarctic winter-over model of spaceflight lacks the important factors of microgravity and solar radiation, caution must be used in interpreting these data to anticipate normal antibody responses in long-term spaceflight.

Non-NASA Center↗

NASA NTRS2000

Outcome analysis of individualized vestibular rehabilitation protocols

OBJECTIVE: To determine the outcome of vestibular rehabilitation protocols in subjects with peripheral vestibular disorders compared with normal and abnormal control subjects. STUDY DESIGN: Prospective study using repeated measure, matched control design. Subjects were solicited consecutively according to these criteria: vestibular disorder subjects who had abnormal results of computerized dynamic posturography (CDP) sensory organization tests (SOTs) 5 and 6 and underwent rehabilitation; vestibular disorder subjects who had abnormal results of SOTs 5 and 6 and did not undergo rehabilitation; and normal subjects (normal SOTs). SETTING: Tertiary neurotology clinic. SUBJECTS: Men and women over age 18 with chronic vestibular disorders and chief complaints of unsteadiness, imbalance, and/or motion intolerance, and normal subjects. INTERVENTIONS: Pre- and post-rehabilitation assessment included CDP, vestibular disability, and activities of daily living questionnaires. Individualized rehabilitation plans were designed and implemented to address the subject's specific complaints and functional deficits. Supervised sessions were held at weekly intervals, and self-administered programs were devised for daily home use. MAIN OUTCOME MEASURES: CDP composite and SOT scores, number of falls on CDP, and self-assessment questionnaire results. RESULTS: Subjects who underwent rehabilitation (Group A) showed statistically significant improvements in SOTs, overall composite score, and reduction in falls compared with abnormal (Group B) control groups. Group A's performances after rehabilitation were not significantly different from those of normal subjects (Group C) in SOTs 3 through 6, and close to normal on SOTs 1 and 2. Subjects in Group A also reported statistically significant symptomatic improvement. CONCLUSIONS: Outcome measures of vestibular protocol physical therapy confirmed objective and subjective improvement in subjects with chronic peripheral vestibular disorders. These findings support results reported by other investigators.

NASA Discipline Neuroscience↗

NASA NTRS1996

Effects of vestibular loss on head stabilization in response to head and body perturbations

Control of head position during postural responses is important to facilitate both the interpretation of vestibular signals and the stabilization of gaze. In these experiments, we compared head stabilization for two different postural tasks: 1) in response to perturbations at the head, and 2) in response to perturbations induced at the support surface, which perturb both body and head position. To determine whether normal vestibular function is necessary for head stabilization in these two tasks, responses to forward and backward mechanical perturbations of the head and body were compared for 13 normal subjects and 4 patients with profound bilateral vestibular loss (two with vestibular loss in adulthood and two in infancy). Normal subjects showed little neck muscle activity for body perturbations, but large, early activations in both neck extensors and flexors for head perturbations. In contrast, vestibular patients showed excessive neck muscle activation for body perturbations and reduced or absent neck muscle activity for head perturbations. Patients with vestibular loss in adulthood also showed increased head acceleration in response to both head and body perturbations, but patients with vestibular loss in infancy showed more normal head accelerations. For body perturbations, the differences in head acceleration between patients and normals were greater for later head acceleration peaks, indicating poor head control during the execution of the postural response. Trunk angle changes were also higher in the patients for forward body perturbations, indicating that poorer control of trunk position could have contributed to their poorer head stabilization. These results indicate that the vestibular system plays an important role in head and trunk stabilization for both head and body perturbations. However, the more normal head accelerations of the patients with infant vestibular loss also indicate that other mechanisms, possibly involving neck reflexes, can at least partially substitute for the vestibular system to provide head and trunk stabilization.

NASA Discipline Neuroscience↗

NASA NTRS1993

Alkali absorption and citrate excretion in calcium nephrolithiasis

The role of net gastrointestinal (GI) alkali absorption in the development of hypocitraturia was investigated. The net GI absorption of alkali was estimated from the difference between simple urinary cations (Ca, Mg, Na, and K) and anions (Cl and P). In 131 normal subjects, the 24 h urinary citrate was positively correlated with the net GI absorption of alkali (r = 0.49, p < 0.001). In 11 patients with distal renal tubular acidosis (RTA), urinary citrate excretion was subnormal relative to net GI alkali absorption, with data from most patients residing outside the 95% confidence ellipse described for normal subjects. However, the normal relationship between urinary citrate and net absorbed alkali was maintained in 11 patients with chronic diarrheal syndrome (CDS) and in 124 stone-forming patients devoid of RTA or CDS, half of whom had "idiopathic" hypocitraturia. The 18 stone-forming patients without RTA or CDS received potassium citrate (30-60 mEq/day). Both urinary citrate and net GI alkali absorption increased, yielding a significantly positive correlation (r = 0.62, p < 0.0001), with the slope indistinguishable from that of normal subjects. Thus, urinary citrate was normally dependent on the net GI absorption of alkali. This dependence was less marked in RTA, confirming the renal origin of hypocitraturia. However, the normal dependence was maintained in CDS and in idiopathic hypocitraturia, suggesting that reduced citrate excretion was largely dietary in origin as a result of low net alkali absorption (from a probable relative deficiency of vegetables and fruits or a relative excess of animal proteins).

Non-NASA Center↗

NASA NTRS2005

Surface Collisions Involving Particles and Moisture (SCIP'M)

Experiments were performed on the collision of a solid sphere with a nearly horizontal flat surface covered with a thin layer of viscous liquid. High-speed collisions were obtained by dropping the ball onto the surface from various heights, using gravitational acceleration. Low-speed collisions were obtained using pendulums with long strings or by launching the balls at low velocities in the reduced-gravity environment of parabolic flight. The sphere bounces only when the impact velocity exceeds a critical value. The coefficient of restitution (ratio of rebound velocity to impact velocity) increases with increasing impact velocity above the critical value, indicating the increasing relative importance of elastic deformation to viscous dissipation. The critical impact velocity increases, and the coefficient of restitution decreases, with increasing viscosity or thickness of the liquid layer and with decreasing density or size of the sphere. The ratio of the wet and dry coefficients is expressed as a function of the Stokes number (ratio of particle inertia and viscous forces), showing good agreement between theory and experiment. Similar experiments were performed with the flat surface inclined at various angles to the approaching sphere. A modified Stokes number, which is a measure of the ratio of inertia of the sphere in the normal direction to the viscous forces exerted by the fluid layer, was used for the analysis of oblique collisions. Even for these oblique collisions, it was found that no rebound of the ball was observed below a certain critical Stokes number. The coefficient of normal restitution, defined as a ratio of normal rebound velocity to normal approach velocity, was found to increase beyond the critical Stokes number and even out as it approaches the value for dry restitution at high Stokes numbers. It was also found that, for smooth spheres like steel, the normal restitution at the same modified Stokes number is independent of the angle of impact. The tangential coefficient of restitution, defined as the ratio of tangential rebound velocity to tangential approach velocity, is found to be nearly unity, except for very low approach velocities. Thus, as a first approximation, the theories that predict the coefficient of restitution for head-on wet collisions can be extended to predict the coefficient of normal restitution for oblique wet collisions. Additional experiments were performed with soft surfaces in which a porous cloth or sponge layer was placed over the hard, flat surface. In these experiments, the coefficient of restitution was found to decrease with increasing impact velocity, due to inelastic losses in the soft material. A model combining inelastic deformation and flow through porous media was developed to describe these findings.

Davis, Robert H.↗

NASA NTRS2007

Monitoring by Use of Clusters of Sensor-Data Vectors

The inductive monitoring system (IMS) is a system of computer hardware and software for automated monitoring of the performance, operational condition, physical integrity, and other aspects of the health of a complex engineering system (e.g., an industrial process line or a spacecraft). The input to the IMS consists of streams of digitized readings from sensors in the monitored system. The IMS determines the type and amount of any deviation of the monitored system from a nominal or normal ( healthy ) condition on the basis of a comparison between (1) vectors constructed from the incoming sensor data and (2) corresponding vectors in a database of nominal or normal behavior. The term inductive reflects the use of a process reminiscent of traditional mathematical induction to learn about normal operation and build the nominal-condition database. The IMS offers two major advantages over prior computational monitoring systems: The computational burden of the IMS is significantly smaller, and there is no need for abnormal-condition sensor data for training the IMS to recognize abnormal conditions. The figure schematically depicts the relationships among the computational processes effected by the IMS. Training sensor data are gathered during normal operation of the monitored system, detailed computational simulation of operation of the monitored system, or both. The training data are formed into vectors that are used to generate the database. The vectors in the database are clustered into regions that represent normal or nominal operation. Once the database has been generated, the IMS compares the vectors of incoming sensor data with vectors representative of the clusters. The monitored system is deemed to be operating normally or abnormally, depending on whether the vector of incoming sensor data is or is not, respectively, sufficiently close to one of the clusters. For this purpose, a distance between two vectors is calculated by a suitable metric (e.g., Euclidean distance) and "sufficiently close" signifies lying at a distance less than a specified threshold value. It must be emphasized that although the IMS is intended to detect off-nominal or abnormal performance or health, it is not necessarily capable of performing a thorough or detailed diagnosis. Limited diagnostic information may be available under some circumstances. For example, the distance of a vector of incoming sensor data from the nearest cluster could serve as an indication of the severity of a malfunction. The identity of the nearest cluster may be a clue as to the identity of the malfunctioning component or subsystem. It is possible to decrease the IMS computation time by use of a combination of cluster-indexing and -retrieval methods. For example, in one method, the distances between each cluster and two or more reference vectors can be used for the purpose of indexing and retrieval. The clusters are sorted into a list according to these distance values, typically in ascending order of distance. When a set of input data arrives and is to be tested, the data are first arranged as an ordered set (that is, a vector). The distances from the input vector to the reference points are computed. The search of clusters from the list can then be limited to those clusters lying within a certain distance range from the input vector; the computation time is reduced by not searching the clusters at a greater distance.

Iverson, David L.↗

NASA NTRS2017

Quantifying Pilot Contribution to Flight Safety during Drive Shaft Failure

Accident statistics cite the flight crew as a causal factor in over 60% of large transport aircraft fatal accidents. Yet, a well-trained and well-qualified pilot is acknowledged as the critical center point of aircraft systems safety and an integral safety component of the entire commercial aviation system. The latter statement, while generally accepted, cannot be verified because little or no quantitative data exists on how and how many accidents/incidents are averted by crew actions. A joint NASA/FAA high-fidelity motion-base simulation experiment specifically addressed this void by collecting data to quantify the human (pilot) contribution to safety-of-flight and the methods they use in today's National Airspace System. A human-in-the-loop test was conducted using the FAA's Oklahoma City Flight Simulation Branch Level D-certified B-737-800 simulator to evaluate the pilot's contribution to safety-of-flight during routine air carrier flight operations and in response to aircraft system failures. These data are fundamental to and critical for the design and development of future increasingly autonomous systems that can better support the human in the cockpit. Eighteen U.S. airline crews flew various normal and non-normal procedures over a two-day period and their actions were recorded in response to failures. To quantify the human's contribution to safety of flight, crew complement was used as the experiment independent variable in a between-subjects design. Pilot actions and performance during single pilot and reduced crew operations were measured for comparison against the normal two-crew complement during normal and non-normal situations. This paper details the crew's actions, including decision-making, and responses while dealing with a drive shaft failure - one of 6 non-normal events that were simulated in this experiment.

Kramer, Lynda J.↗

NASA NTRSDate not supplied

A Gene Expression and Histologic Approach to Study Production and Outflow of Cerebrospinal Fluid in Hindlimb Suspended Rats

INTRODUCTION: The Spaceflight Associated Neuro-ocular Syndrome (SANS) is thought to be associated with weightlessness-induced cephalad fluid shift, possibly associated with a chronic elevation of intracranial pressure (ICP) during long-duration ISS missions. Changes in cerebrospinal fluid (CSF) dynamics and cranial compliance might be involved in the ICP increase. It is not known whether CSF production and/or outflow are altered in microgravity, but changes at the molecular and cellular level in the structures that produce and regulate the transcellular and paracellular secretion and reabsorption of CSF may be relevant. In this study, we used the rat hindlimb suspension (HS) model to examine the relationship between intracranial pressure (ICP) and the cellular responses to the prolonged change in body posture elicited specifically in the choroid plexus (CP). This was evaluated by transcriptomics, histopathology and ultrastructure of the CP and arachnoid villi (AV). METHODS: ICP was measured by telemetry. The morphology, ultrastructure, and gene expression profile of the CP was examined using male 9-month-old Long Evans rats subjected to HS for 14 and 90 days. A subset of animals completing 90-day HS returned to normal posture for 14 and 90 additional days of recovery. All HS rats had age-matched cage controls maintained in normal posture. A group of animals was maintained in conditions of 1% CO2 throughout the entire protocol. The rat brains were carefully removed and preserved for various analyses, including transmission electron microscopy (TEM), immunohistochemical analysis of specific targets involved in CSF regulation, and RNA sequencing analysis of laser capture micro-dissected CP tissue from the lateral ventricles. SUMMARY OF RESULTS: The ICP record was limited, which impacted any conclusions derived from the results. However, the ICP of rats in the CO2-enriched atmosphere appeared increased compared to those in a normal air composition. HS of rats resulted in an altered transcriptomics profile in the choroid plexus compared to animals maintained at normal posture. This was observed during both the HS period and during normal posture recovery period following 90 days of suspension. The greatest number of differentially expressed genes was observed at 90 days HS. Elevated CO2 also led to a different transcriptomics profile in the CP. The histology and ultrastructure results should be considered preliminary due to the limited number of samples. Examination of the CP by TEM showed blood vessel congestion and microvilli swelling in the CP, as well as some subpial and periventricular gliosis, but no associations were observed with treatment. There was no evidence of a reduced clearance of b-amyloid in the periventricular, perivascular and subpial regions of the brain in HS animals versus those in normal posture. Immunohistochemical staining of aquaporin 4, showed the localization to the subpial region and ependyma with increased immunoreactivity in the brains of CO2 exposed rats. This work was supported by awards NNX15AW48G to S.Z. Animal tissue and live data was provided under a tissue/data sharing agreement with Dr. Charles Fuller, UC Davis.

S B Zanello↗

NASA NTRSDate not supplied

A Gene Expression and Histologic Approach to Study Production and Outflow of Cerebrospinal Fluid in Hindlimb Suspended RATS

S B Zanello↗

NASA NTRS1973

Magnetopause structure and dynamics of the magnetosphere

It is shown how satellite magnetometer data at a magnetopause penetration can be used to determine the vector normal to the magnetopause current layer and the magnetic field component along this normal. Results from 22 Explorer 12 boundary penetrations indicate normal field components of less than 5 gamma in two-thirds of the cases. Measured field variations within the current layer demonstrate the existence of two fundamentally different types of boundary structure, the rotational and the tangential discontinuity. The rotational discontinuity seems to occur predominantly during magnetic storms. Finally, the calculated normal vector is compared with the normal to the surface of the Mead-Beard magnetosphere model.

Sonnerup, B. U. O.↗

NASA NTRS1973

Ultraviolet photometry from the Orbiting Astronomical Observatory. VIII

A comprehensive ultraviolet photometric survey of the blue Ap stars was conducted in order to determine whether the close similarity, deduced from ground observations, between the blue Ap stars and normal B stars with similar UBV colors is maintained at wavelengths shortward of 3000 A. Data are presented for 24 Ap stars and 31 normal comparison standard dwarfs and giants observed by the Wisconsin Experiment Package on OAO 2. Both normal and peculiar stars were chosen, with a few exceptions, for their minimal interstellar reddening and for the absence of known bright companions. The similarity between blue Ap stars and normal B stars of similar UBV colors is not maintained in the ultraviolet. The blue Ap stars emit less ultraviolet flux than normal stars of like UBV colors. They are underluminous and cool in effective temperature for their colors.

Leckrone, D. S.↗

NASA NTRS1977

Analysis of vector wind change with respect to time for Cape Kennedy, Florida: Wind aloft profile change vs. time, phase 1

Wind vector change with respect to time at Cape Kennedy, Florida, is examined according to the theory of multivariate normality. The joint distribution of the four variables represented by the components of the wind vector at an initial time and after a specified elapsed time is hypothesized to be quadravariate normal; the fourteen statistics of this distribution, calculated from fifteen years of twice daily Rawinsonde data are presented by monthly reference periods for each month from 0 to 27 km. The hypotheses that the wind component changes with respect to time is univariate normal, the joint distribution of wind component changes is bivariate normal, and the modulus of vector wind change is Rayleigh, has been tested by comparison with observed distributions. Statistics of the conditional bivariate normal distributions of vector wind at a future time given the vector wind at an initial time are derived. Wind changes over time periods from one to five hours, calculated from Jimsphere data, are presented.

Adelfang, S. I.↗

NASA NTRS1978

Analysis of vector wind change with respect to time for Cape Kennedy, Florida

Multivariate analysis was used to determine the joint distribution of the four variables represented by the components of the wind vector at an initial time and after a specified elapsed time is hypothesized to be quadravariate normal; the fourteen statistics of this distribution, calculated from 15 years of twice-daily rawinsonde data are presented by monthly reference periods for each month from 0 to 27 km. The hypotheses that the wind component changes with respect to time is univariate normal, that the joint distribution of wind component change with respect to time is univariate normal, that the joint distribution of wind component changes is bivariate normal, and that the modulus of vector wind change is Rayleigh are tested by comparison with observed distributions. Statistics of the conditional bivariate normal distributions of vector wind at a future time given the vector wind at an initial time are derived. Wind changes over time periods from 1 to 5 hours, calculated from Jimsphere data, are presented. Extension of the theoretical prediction (based on rawinsonde data) of wind component change standard deviation to time periods of 1 to 5 hours falls (with a few exceptions) within the 95 percentile confidence band of the population estimate obtained from the Jimsphere sample data. The joint distributions of wind change components, conditional wind components, and 1 km vector wind shear change components are illustrated by probability ellipses at the 95 percentile level.

Adelfang, S. I.↗

NASA NTRS1980

Plants and weightlessness

The growth of two plants, wall cress and short-day red goosefoot, was traced for their entire lifetime in weightlessness. In the beginning both plants grew normally: the seeds sprouted in the normal periods, and the shoots did not differ in any way from the control plants. It is true that certain roots lost their normal orientation and did not go deeper into the nutrient medium, but rather crept over its surface. But then both the wall cress and the goosefoot slowed down their normal rate of growth, which became noticeable from the rate of formation of new leaves in the wall cress and stem development in the goosefoot. Although no disorders were successfully found in the morphology of the two plants, almost half of the experimental cress and goosefoot plants ceased growth completely, yellowed and died. The other part continued to develop normally and by the end of vegetation, differed from the control plants only in a lower height. Not all were fertile since certain experimental plants, after losing spatial orientation, became twisted and produced sterile flowers.

Karminskiy, V.↗

NASA NTRS1980

Oblique-incidence secondary emission from charged dielectrics

Secondary electron emission coefficients were measured on FEP-Teflon for normal and oblique incidence in the presence of a normal electric field. Such measurements require knowledge of the electrostatic environment surrounding the specimen, and they require calculation of particle trajectories such that particle impact parameters can be known. A simulation using a conformal mapping, a Green's integral, and a trajectory generator provides the necessary mathematical support for the measurements, which were made with normal fields of 1.5 and 2.7 kV/mm. When incidence is normal and energy exceeds the critical energy, the coefficient is given by (V sub 0/V) to the .58 power, and for oblique incidence this expression may be divided by the cosine of the angle. The parameter V sub 0 is a function of normal field.

Robinson, J. W.↗

NASA NTRS1980

Reversed-polarity regions

The 58 RPRS studied have a lifespan comparable to normal active regions and have no tendency to rotate toward a more normal alignment. They seem to have stable configurations with no apparent evidence suggesting stress due to their anomalous magnetic alignment. Magnetic complexity in RPRs is the key to flare productivity just as it is in normal regions - weak field RPRs produced no flares and regions with complex spots produced more flares than regions with noncomplex spots by a factor of 5. The RPRs however, differ from normal regions in the frequency of having complex spots, particularly the long lived complex spots, in them. Less than 17 percent of normal ARs have complex spots; less than 1.8 percent have long lived complex spots. In contrast, 41 percent of RPRs have complex spots and 24 percent have long lived complex spots.

Tang, F.↗