Fractal methods and results in cellular morphology--dimensions, lacunarity and multifractals.

This paper discusses the concepts of fractal geometry in a cellular biological context. It defines the concept of the fractal dimension. D, as a measure of complexity and illustrates the two different general ways of quantitatively measuring D by length-related and mass-related methods. Then, these several Ds are compared and contrasted. A goal of the paper is to find methods other than length-related measures that can distinguish between two objects that have the same D but are structurally different. The mass-related D is shown potentially to be such a measure. The concept of lacunarity, L, is defined and methods of measuring L are illustrated. L is also shown to be a potentially distinguishing measure. Finally, the notion of multifracticality is defined and illustrated to exist in certain individual nerve and glial cells.

A parsimonious description of motoneuron dendritic morphology using computer simulation.

Most quantitative descriptions of neuronal dendrite morphology involve tabulations of measurements and correlations among them. The present work is an attempt to extract from such data a parsimonious set of parameters that are sufficient to describe the quantitative features of individual and pooled dendrites, including their statistical variability. A relatively simple stochastic (Monte Carlo) model was devised to simulate branching dendritic trees. The necessary parameters were then derived directly from measurements of 64 completely reconstructed dendrites belonging to six gastrocnemius alpha-motoneurons, labeled by intracellular injection of HRP. Comparison of actual and simulated dendrites was used to guide the process of parameter extraction. The model included only two processes, one to generate individual branches given their starting diameters and the second to select starting diameters for the daughter branches produced at dichotomous branching points. The stochastic process for branch generation was controlled by probability functions for branching (Pbr) and for terminating (Ptrm), together with a constant rate of branch taper. All model parameters were fixed by motoneuron measurements except for branch taper rate, which was allowed to vary within limits consistent with observed taper rates in order to generate the appropriate total number of branches. The simplest model (model 1), in which Pbr and Ptrm depended only on local branch diameter, produced simulated dendrites that fit many, but not all, characteristics of actual motoneuron dendrites. Two additional properties produced significant improvements in the fit: (1) a small but significant dependence of daughter diameters on the normalized starting diameter of the parent branch, and (2) a dependence of Pbr and Ptrm on distance from the soma as well as on local branch diameter. The process of developing this model revealed unsuspected relations in the original data that suggest the existence of fundamental mechanisms for morphological control. The final model succinctly describes a large amount of data and will enable quantitative comparisons between the dendritic structures of different types of neurons, regardless of their relative sizes.

A fractal analysis of cultured rat optic nerve glial growth and differentiation.

Fractal dimension can be used as a quantitative measure of morphological complexity. Separate, enriched populations of oligodendrocytes or type 2 astrocytes derived from neonatal rat optic nerves were allowed to differentiate in vitro. Fractal dimensions of differentiating glial cells were measured over time. The fractal dimension correlated with perceived complexity and increased in value as the glial cells matured. Analysis of the changes in fractal dimension with time revealed unique rates of growth and differentiation for each glial phenotype.

Monosynaptic and dorsal root reflexes during locomotion in normal and thalamic cats.

1. In normal and thalamic walking cats electrical stimulation of muscle nerves via chronically implanted electrodes produced electromyographic (EMG) and neurographic responses that were modulated in amplitude depending on the phase of the step cycle. These responses were examined for possible indications of effects of primary afferent depolarization (PAD) during stepping. 2. Monosynaptic reflexes (MSRs) produced by stimulating the lateral gastrocnemius (LG) and medial gastrocnemius (MG) nerves were recorded as EMGs in MG or LG muscles during treadmill locomotion in normal cats. These heteronymous MSR responses were greatest during the stance (extensor) phase. 3. In the same animals, after decerebration, similar modulation of the heteronymous ankle extensor MSRs occurred during spontaneous locomotion with the use of the same stimulus and recording sites. 4. In both normal and thalamic cats the amplitude of neurogram responses recorded from LG or MG nerve after stimulation of the other muscle nerve varied with phase of stepping but did not parallel the variations of the MSR measured as EMG amplitude in the same muscle. The nerve responses were largest during the flexion phase of the step cycle and had a calculated central latency of 0.6-1.0 ms. These are interpreted as arising from antidromic activity in large-caliber afferent nerve fibers (i.e., dorsal root reflexes). 5. Spontaneous antidromic activity in severed L7 dorsal rootlet fibers to triceps surae was observed in the thalamic cats during episodes of locomotion and was closely correlated with flexion phase EMG activity in semitendinosus, a bifunctional muscle. 6. In decerebrate cats, dorsal root reflexes (DRRs) in severed filaments of L4-L7 dorsal roots were produced by stimulation of saphenous and posterior tibial nerves. These DRRs were always smaller during locomotion than during rest and were smallest during the flexion phase. 7. The short-latency antidromic activity produced in muscle nerves by stimulating heteronymous muscle nerves thus appears to be a DRR produced in Group I terminal arborizations that are depolarized close to threshold during the flexion phase. Such PAD could account for changes in the MSR that do not always parallel the levels of recruitment of the motor pools as manifest by background EMG amplitude.

A fractal analysis of cell images.

Methods of digital image analysis have been adapted to measure the fractal dimension of cellular profiles. The fractal dimension is suggested as a useful measure of the complexity of a contour. Three methods produce similar results when applied to constructed, near-ideal fractal figures. Comparison of the measurements for a variety of image types indicates the measurement accuracy in each case and may help in interpreting the results when applied to real, non-ideal cell images of unknown fractal dimension. Two of the methods are currently adopted as appropriate for use on neuronal contours. A correlation exists between the complexity of these contours and the magnitude of the estimated fractal dimension.

Edge detection in images using Marr-Hildreth filtering techniques.

Details of the morphology of light microscope images of horseradish peroxidase labeled mammalian neurons in cell culture were investigated. A modified Marr-Hildreth edge-detecting algorithm was used in an image processor to obtain a continuous border of the labeled neurons. The interior of the border was filled to obtain isolated binary silhouettes of the neurons. These silhouettes can be used for further quantitative studies.

Cat hindlimb motoneurons during locomotion. I. Destination, axonal conduction velocity, and recruitment threshold.

Fine flexible wire microelectrodes chronically implanted in the fifth lumbar ventral root (L5 VR) of 17 cats rendered stable records of the natural discharge patterns of 164 individual axons during locomotion on a treadmill. Fifty-one out of 164 axons were identified as motoneurons projecting to the anterior thigh muscle group. For these axons, the centrifugal propagation of action potentials was demonstrated by the technique of spike-triggered averaging using signals recorded from cuff electrodes implanted around the femoral nerve. The axonal conduction velocity was measured from the femoral nerve cuff records. For 43/51 motoneurons, the corresponding target muscle was identified by spike-triggered averaging of signals recorded from bipolar EMG electrodes implanted in each of the anterior thigh muscles: vastus intermedius, medialis and lateralis, sartorius anterior and medialis, and rectus femoris. For 32/51 motoneurons, the recruitment threshold during locomotion was determined from the mean value of the rectified digitally smoothed EMG of the target muscle measured at the time when the motoneuron fired its first spike for each step. The recruitment threshold of every motoneuron was relatively constant for a given speed of walking, but for some units there were small systematic variations as a function of treadmill speed (range: 0.1-1.3 m/s). Recruitment thresholds were standardized with respect to the mean value of peak EMG activity of the target muscle during 16 s of walking at 0.5 m/s. For 28/51 motoneurons recorded in nine cats, recruitment thresholds (range: 3-93% of peak target muscle EMG) were linearly correlated (r = 0.51, P less than 0.02) to axonal conduction velocities (range: 57-117 m/s). In addition, for seven recorded pairs of motoneurons that projected to the same muscle in the same cat, the recruitment thresholds were ordered by relative conduction velocities. Taken together, these results are consistent with the notion that, in normal cat locomotion up to a medium trot, anterior thigh motoneurons are progressively recruited in an orderly fashion.

Cat hindlimb motoneurons during locomotion. II. Normal activity patterns.

Activity patterns were recorded from 51 motoneurons in the fifth lumbar ventral root of cats walking on a motorized treadmill at a range of speeds between 0.1 and 1.3 m/s. The muscle of destination of recorded motoneurons was identified by spike-triggered averaging of EMG recordings from each of the anterior thigh muscles. Forty-three motoneurons projected to one of the quadriceps (vastus medialis, vastus lateralis, vastus intermedius, or rectus femoris) or sartorius (anterior or medial) muscles of the anterior thigh. Anterior thigh motoneurons always discharged a single burst of action potentials per step cycle, even in multifunctional muscles (e.g., sartorius anterior) that exhibited more than one burst of EMG activity per step cycle. The instantaneous firing rates of most motoneurons were lowest upon recruitment and increased progressively during a burst, as long as the EMG was still increasing. Firing rates peaked midway through each burst and tended to decline toward the end of the burst. The initial, mean, and peak firing rates of single motoneurons typically increased for faster walking speeds. At any given walking speed, early recruited motoneurons typically reached higher firing rates than late recruited motoneurons. In contrast to decerebrated cats, initial doublets at the beginning of bursts were seen only rarely. In the 4/51 motoneurons that showed initial doublets, both the instantaneous frequency of the doublet and the probability of starting a burst with a doublet decreased for faster walking speeds. The modulations in firing rate of every motoneuron were found to be closely correlated to the smoothed electromyogram of its target muscle. For 32 identified motoneurons, the unit's instantaneous frequencygram was scaled linearly by computer to the rectified smoothed EMG recorded from each of the anterior thigh muscles. The covariance between unitary frequencygram and muscle EMG was computed for each muscle. Typically, the EMG profile of the target muscle accounted for 0.88-0.96 of the variance in unitary firing rate. The EMG profiles of the other anterior thigh muscles, when tested in the same way, usually accounted only for a significantly smaller fraction of the variance. Brief amplitude fluctuations observed in the EMG envelopes were usually also reflected in the individual motoneuron frequencygrams. To further demonstrate the relationship between unitary frequencygrams and EMG, EMG envelopes recorded during walking were used as templates to generate depolarizing currents that were applied intracellularly to lumbar motoneurons in an acute spinal preparation.(ABSTRACT TRUNCATED AT 400 WORDS)

Cat hindlimb motoneurons during locomotion. III. Functional segregation in sartorius.

Cat sartorius has two distinct anatomical portions, anterior (SA-a) and medial (SA-m). SA-a acts to extend the knee and also to flex the hip. SA-m acts to flex both the knee and the hip. The objective of this study was to investigate how a "single motoneuron pool" is used to control at least three separate functions mediated by the two anatomical portions of one muscle. Discharge patterns of single motoneurons projecting to the sartorius muscle were recorded using floating microelectrodes implanted in the L5 ventral root of cats. The electromyographic activity generated by the anterior and medial portions of sartorius was recorded with chronically implanted electrodes. The muscle portion innervated by each motoneuron was determined by spike-triggered averaging of the EMGs during walking on a motorized treadmill. During normal locomotion, SA-a exhibited two bursts of EMG activity per step cycle, one during the stance phase and one during the late swing phase. In contrast, every recorded motoneuron projecting to SA-a discharged a single burst of action potentials per step cycle. Some SA-a motoneurons discharged only during the stance phase, whereas other motoneurons discharged only during the late swing phase. In all cases, the instantaneous frequencygram of the motoneuron was well fit by the rectified smoothed EMG envelope generated by SA-a during the appropriate phase of the step cycle. During normal locomotion, SA-m exhibited a single burst of EMG activity per step cycle, during the swing phase. The temporal characteristics of the EMG bursts recorded from SA-m differed from the swing-phase EMG bursts generated by SA-a.(ABSTRACT TRUNCATED AT 250 WORDS)

Cat hindlimb motoneurons during locomotion. IV. Participation in cutaneous reflexes.

The responses of 11 individual motoneurons, the muscle to which each projected, plus all other muscles in the anterior thigh of the cat, were recorded following single non-noxious electrical stimuli to cutaneous nerves while the intact animal walked on a treadmill. The various excitatory and/or inhibitory responses were qualitatively similar for stimuli within the range 1.1-10 times threshold for group I fibers in the stimulated nerve (usually saphenous). Monarticular knee extensor muscles in the vastus group and their motoneurons were usually inhibited in the period 10- to 25-ms poststimulus. The faster contracting vastus medialis and lateralis muscles tended to have an excitatory rebound at approximately 25- to 40-ms poststimulus that was confined to the stance phase of the step cycle when these muscles were normally active. Biarticular hip flexor muscles rectus femoris and both the anterior and medial parts of sartorius and their motoneurons all had similar bimodal excitatory responses, including an early period 3- to 18-ms poststimulus and a later period 20- to 35-ms poststimulus. The short-latency excitatory responses appeared to be proportional to the normal recruitment of the muscles in the step cycle, whereas the long-latency responses tended to be phase advanced with respect to normal recruitment. Motoneurons projecting to muscles with two excitatory peaks tended to have similar excitatory responses at both latencies and occasionally responded at both latencies to a single stimulus.

Activity of spindle afferents from cat anterior thigh muscles. III. Effects of external stimuli.

Chronically implanted electrodes were used to record the activity of identified single muscle spindle afferents in awake cats during responses to various types of manual and electrical stimulation. During vigorous cyclical responses such as shaking and scratching, spindle afferents generally maintained at least some activity during both lengthening and shortening of the parent muscle, indicating that the programs for these movements include both extra- and intrafusal recruitment. During noncyclical responses such as ipsilateral limb withdrawal and crossed-extension, spindle activity was modest and poorly correlated with extrafusal activity. Weak cutaneous nerve shocks during walking elicited complex excitatory and inhibitory phase-dependent reflexes in the various muscles studied but caused relatively little change in spindle afferent activity, indicating a lack of correlation between alpha and gamma motoneuron activity. A primary and a secondary afferent from sartorius muscle were recorded simultaneously during walking cycles that were perturbed by electrically induced twitches of the antagonist hamstring muscles; both demonstrated highly sensitive, short latency responses to the resulting skeletal motion, consistent with their previously suggested roles in detecting small brief mechanical perturbations. The degree to which fusimotor responses were correlated with extrafusal responses to somatosensory perturbations was highly dependent on the specific nature of the stimulus and the response. Fusimotor reprogramming of the spindle sensitivity appears to be a feature of cyclical movements that are presumably under proprioceptive control, whereas brief perturbations within the context of a particular motor program may be ignored by the fusimotor system.

The responses of cat motor cortical units to electrical cutaneous stimulation during locomotion and during lifting, falling and landing.

Experiments were performed to examine the influence of cutaneous information on motor cortical cells during movement in intact, awake cats. The movements investigated were locomotion and a sequence in which the animal was repeatedly lifted and dropped. Electrical stimuli to distal skin areas were delivered periodically during the movements and responses of motor cortical cells were examined. The animals used in these experiments were chronically implanted with cortical microelectrodes, a pyramidal tract stimulating electrode, cutaneous stimulating electrodes in the forepaw, and a recording cuff electrode around the median nerve. EMG electrodes were implanted in several forelimb muscles and a length gauge was implanted across the elbow joint. Results included in this report were obtained from three cats. The twenty-two cortical units analysed in this study (seven were PT units) were selected from a larger sample by the following criteria: cutaneous receptive fields which included the distal part of the limb, consistent short latency responses to electrical cutaneous stimulation and spontaneous activity modulated in consistent patterns during the movement investigated. Sixteen units were recorded during locomotion, 12 during the lifting and dropping cycle and 6 of these during both conditions. Most of the cells were influenced by the cutaneous input during locomotion. Three units had no response to peripheral stimulation during locomotion though they were responsive to this stimulus when the animal was sitting quietly. All the cells were responsive to the cutaneous input during the lifting and dropping cycle. The responses to cutaneous stimuli were found to be modulated in relation to phases of the step cycle and the lifting and dropping cycle. In 13 units this modulation did not parallel the modulation of the unit's spontaneous firing during these activities. For these units a common finding during locomotion was that the response to cutaneous stimuli increased throughout stance, reached maximum during the flexion part of the swing, and then declined to a minimum during the beginning of the next stance. During the lifting and dropping cycle, the responses were greatest when the animal was held in the air and when starting to fall, and minimal just prior to and after landing. In both movements, cutaneous responses were reduced when the limb was used to support the animal's weight. There is apparently a movement phase-related modulation of cutaneous input to some motor cortical cells. This modulation of cutaneous input resembled the modulation of cutaneous reflexes during locomotion.(ABSTRACT TRUNCATED AT 400 WORDS)

The distal hindlimb musculature of the cat. Cutaneous reflexes during locomotion.

In order to better understand the organization of the locomotor control system, we examined the temporal patterns of distal hindlimb muscle responses to brief electrical stimulation of cutaneous nerves during walking on a treadmill. Electromyographic recordings were made from twelve muscles; stimuli were applied individually to three nerves at random times throughout the step cycle. A new graphical technique was developed to assist detailed examination of the time course and gating of complex reflex patterns. The short latency reflexes were of two primary types: inhibition of extensors and excitation of flexors; these responses were only evident during locomotor phases in which the respective motoneuron pools were active. Longer-latency response components were gated in a similar but not identical manner, suggesting some independence from the basic locomotory influence on the motoneuronal pool. The phase-dependent gating of reflexes appeared to be consistent with a functional role for reflex responses during locomotion. The reflex responses of muscles with complex anatomical actions were often correspondingly complex.

Unit responses in the frog's caudal thalamus.

Single unit microelectrode recordings were made in the caudal thalamic region of the frog, Rana pipiens, from a sample of multimodal sensory units which included monocular, binocular, tactile, and spontaneous types, and which showed a wide variety of receptive field sizes, response rates, preferred stimulus sizes habituation rates, and velocity and tactile sensitivities. A number of special response properties were occasionally observed, including directional sensitivity, stationary object sensitivity, afterdischarges, and visual and tactile inhibitory fields. Computer analysis of spontaneously active units revealed four types: regular, exponential, bursting, and multimodal.

Action currents, internodal potentials, and extracellular records of myelinated mammalian nerve fibers derived from node potentials.

The potential distribution within the internodal axon of mammalian nerve fibers is derived by applying known node potential waveforms to the ends of an equivalent circuit model of the internode. The complete spatial/temporal profile of action potentials synthesized from the internodal profiles is used to compute the node current waveforn, and the extracellular action potential around fibers captured within a tubular electrode. For amphibia, the results agreed with empirical values. For mammals, the amplitude of the node currents plotted against conduction velocity was fitted by a straight line. The extracellular potential waveform depended on the location of the nodes within the tube. For tubes of length from 2 to 8 internodes, extracellular wave amplitude (mammals) was about one-third of the product of peak node current and tube resistance (center to ends). The extracellular potentials developed by longitudinal and radial currents in an anisotropic medium (fiber bundle) are compared.

Visual pigment density in single primate foveal cones.

The feasibility is demonstrated of microspectrophotometric studies on primate photoreceptors aligned at right angles to the test beam, rather than axially illuminated. Pigment densities, and hence absorption per unit thickness, are approximately equal in primate rods and foveal cones. These pigment densities are similar to those reported for frog rods and fish cones.