Sholl analysis

Last updated June 04, 2024

Sholl analysis is a method of quantitative analysis commonly used in neuronal studies to characterize the morphological characteristics of an imaged neuron, first used to describe the differences in the visual and motor cortices of cats in the early 1950s.^[1] Sholl was interested in comparing the morphology of different types of neurons, such as the star-shaped stellate cells and the cone-shaped pyramidal cells, and of different locations in the dendritic field of the same type of neurons, such as basal and apical processes of the pyramidal neuron. He looked at dendritic length and diameter (Sholl, p. 389, Fig. 1)^[1] and also the number of cells per volume (Sholl, p. 401, The packing density of perikarya).^[1]

While methods for estimating the number of cells have vastly improved since 1953 with the advent of unbiased stereology, the method Sholl used to record the number of intersections at various distances from the cell body is still in use and is actually named after Sholl. "In order to study the way in which the number of branches varies with the distance from the perikaryon, it is convenient to use a series of concentric spherical shells as co-ordinates of reference. ...... these shells have their common centre in the perikaryon" (Sholl, p. 392, The manner of dendritic branching).^[1] What Sholl called the 'Concentric Shell Method' is now known as 'Sholl Analysis'. As well as the number of intersections per concentric shell, Sholl also calculated the mean diameter of the dendrites or axons within each concentric shell (Sholl, p. 396, table 2 and 3).^[1] Sholl appreciated that his method is good for comparing neurons, for instance in figure 8^[1] the differences in the number of dendritic intersections correlated with distance from the cell body is compared between neurons from the motor and visual cortex. Sholl also realized his method is useful to determine where and how big is the region where synapses are possible, something he called the neuron's 'connective zone'.^[1]

In 1953, Sholl was working with projections of 3-D neurons into two-dimensions, but now Sholl analysis can be done on 3-D images (e.g. image stacks or 3-D montages) of neurons, making the concentric circles truly three-dimensional shells. In addition to intersections and diameter: total dendritic length, surface area, and volume of processes per shell; number of nodes, endings, varicosities and spines per shell; and branching order of the dendrites in each shell, can be included in the analysis. For modern examples of the use of Sholl analysis to analyze neurons.^[2]^[3] Curves produced from the 'number of intersections vs. distance from the cell body data' are usually of somewhat irregular shape, and much work has been done to determine appropriate means of analyzing the results. Common methods include Linear Analysis, Semi-log Analysis and Log-Log Analysis

Linear Method

The Linear Method is the analysis of the function N(r), where N is the number of crossings for a circle of radius r.^[1] This direct analysis of the neuron count allows the easy computation of the critical value, the dendrite maximum, and the Schoenen Ramification Index.^[4]

Critical Value: The critical value is the radius r at which there is a maximum number of dendritic crossings, this value is closely related to the dendrite maximum.

Dendrite Maximum: This value is the maximum of the function N(r), as specified by the Critical Value for a given data set.

Schoenen Ramification Index: This index is one measure of the branching of the neuronal cell being studied. It is calculated by dividing the Dendrite Maximum by the number of primary dendrites, that is, the number of dendrites originating at the cell's soma.

Semi-Log Method

Somewhat more complicated than the Linear Method, the Semi-Log Method begins by calculating the function Y(r) = N/S where N is the number of dendrite crossings for a circle of radius r, and S is the area of that same circle. The base 10 logarithm is taken of this function, and a first order linear regression, linear fit, is performed on the resulting data set, that is

\log _{10}\left({\frac {N}{S}}\right)=-k\cdot r+m

.

where k is Sholl's Regression Coefficient.^[1]

Sholl's Regression Coefficient is the measure of the change in density of dendrites as a function of distance from the cell body.^[5] This method has been shown to have good discrimination value between various neuron types, and even similar types in different regions of the body.

Log-Log Method

Closely related to the Semi-Log Method, the Log-Log Method plots the data with the radius plotted in log space. That is the researcher would calculate the value k and m for the relation

\log _{10}\left({\frac {N}{S}}\right)=-k\cdot \log _{10}(r)+m

.

This method is used in a manner similar to the Semi-Log Method, but primarily to treat neurons with long dendrites that do not branch much along their length.^[5]

Modified Sholl Method

The Modified Sholl Method is the calculation of a polynomial fit of the N and r pairs from the Linear Method.^[6] That is, it attempts to calculate a polynomial such that:

\ N(r)\ =a_{0}+a_{1}*r+a_{2}*r^{2}+...+a_{t}*r^{t}.

where t is the order of the polynomial fit to the data. The data must be fit to each of these polynomials individually, and the correlation calculated in order to determine the best fit. The maximum value of the polynomial is calculated and used in place of the Dendrite Maximum. Additionally, the average of the resulting polynomial can be determined by taking its integral for all positive values represented in the data set (most data sets contain some zero values).

Drawbacks

Sholl analysis is used to measure the number of crossings processes make at different distances from the centroid, and is a type of morphometric analysis. It is primarily used to measure arbour complexity. Certain morphologies cannot however be indexed using Sholl alone. For instance it may not make sense to compare neurons with arbors that take up small volumes to those that take up large volumes, and instead an analysis like 'complexity index' could be used.^[7] Also, dendrite thickness of a whole dendrite cannot be measured, only the mean thickness of the dendrites within a shell. Dendrite length of a given dendrite also cannot be determined, since dendrites do not necessarily emanate radially from the soma; dendrites can curve, cross the same circles multiple times, or extend tangentially and not cross at a circle at all. Additionally, Sholl analysis can be time consuming, and automated analysis software is limited.

Neurite ramification and Sholl analysis

Using the Sholl analysis, a mathematical algorithm named the branching index (BI) has been described to analyze neuronal morphology.^[8] The BI compares the difference in the number of intersections made in pairs of consecutive circles of the Sholl analysis relative to the distance from the neuronal soma. The BI distinguishes neurons with different types of neurite ramification.

Software

Several software packages perform Sholl analysis, namely those dedicated to neuronal tracing. An open-source implementation for the image processing package Fiji can be used to perform the analysis directly from microscope imagery of neurons or their traced reconstructions.^[9]

In modern implementations, analysis is performed in three dimensions: concentric shells are nested around a centre, and a surrogate of neurite mass^[5] (e.g., number of intersections, or total neurite length) contained within each shell is reported. Such software is amenable to high-throughput studies^[10]^[11] .

Related Research Articles

A dendrite or dendron is a branched protoplasmic extension of a nerve cell that propagates the electrochemical stimulation received from other neural cells to the cell body, or soma, of the neuron from which the dendrites project. Electrical stimulation is transmitted onto dendrites by upstream neurons via synapses which are located at various points throughout the dendritic tree.

Within a nervous system, a neuron, neurone, or nerve cell is an electrically excitable cell that fires electric signals called action potentials across a neural network. Neurons communicate with other cells via synapses, which are specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap.

<span class="mw-page-title-main">Dendritic spine</span> Small protrusion on a dendrite that receives input from a single axon

A dendritic spine is a small membranous protrusion from a neuron's dendrite that typically receives input from a single axon at the synapse. Dendritic spines serve as a storage site for synaptic strength and help transmit electrical signals to the neuron's cell body. Most spines have a bulbous head, and a thin neck that connects the head of the spine to the shaft of the dendrite. The dendrites of a single neuron can contain hundreds to thousands of spines. In addition to spines providing an anatomical substrate for memory storage and synaptic transmission, they may also serve to increase the number of possible contacts between neurons. It has also been suggested that changes in the activity of neurons have a positive effect on spine morphology.

An artificial neuron is a mathematical function conceived as a model of biological neurons in a neural network. Artificial neurons are the elementary units of artificial neural networks. The artificial neuron is a function that receives one or more inputs, applies weights to these inputs, and sums them to produce an output.

<span class="mw-page-title-main">Pyramidal cell</span> Projection neurons in the cerebral cortex and hippocampus

Pyramidal cells, or pyramidal neurons, are a type of multipolar neuron found in areas of the brain including the cerebral cortex, the hippocampus, and the amygdala. Pyramidal cells are the primary excitation units of the mammalian prefrontal cortex and the corticospinal tract. One of the main structural features of the pyramidal neuron is the conic shaped soma, or cell body, after which the neuron is named. Other key structural features of the pyramidal cell are a single axon, a large apical dendrite, multiple basal dendrites, and the presence of dendritic spines.

In cellular neuroscience, the soma, perikaryon, neurocyton, or cell body is the bulbous, non-process portion of a neuron or other brain cell type, containing the cell nucleus. Although it is often used to refer to neurons, it can also refer to other cell types as well, including astrocytes, oligodendrocytes, and microglia. There are many different specialized types of neurons, and their sizes vary from as small as about 5 micrometres to over 10 millimetres for some of the smallest and largest neurons of invertebrates, respectively.

An apical dendrite is a dendrite that emerges from the apex of a pyramidal cell. Apical dendrites are one of two primary categories of dendrites, and they distinguish the pyramidal cells from spiny stellate cells in the cortices. Pyramidal cells are found in the prefrontal cortex, the hippocampus, the entorhinal cortex, the olfactory cortex, and other areas. Dendrite arbors formed by apical dendrites are the means by which synaptic inputs into a cell are integrated. The apical dendrites in these regions contribute significantly to memory, learning, and sensory associations by modulating the excitatory and inhibitory signals received by the pyramidal cells.

In neuroscience, Golgi cells are the most abundant inhibitory interneurons found within the granular layer of the cerebellum. Golgi cells can be found in the granular layer at various layers. The Golgi cell is essential for controlling the activity of the granular layer. They were first identified as inhibitory in 1964. It was also the first example of an inhibitory feedback network in which the inhibitory interneuron was identified anatomically. Golgi cells produce a wide lateral inhibition that reaches beyond the afferent synaptic field and inhibit granule cells via feedforward and feedback inhibitory loops. These cells synapse onto the dendrite of granule cells and unipolar brush cells. They receive excitatory input from mossy fibres, also synapsing on granule cells, and parallel fibers, which are long granule cell axons. Thereby this circuitry allows for feed-forward and feed-back inhibition of granule cells.

<span class="mw-page-title-main">NeuronStudio</span>

NeuronStudio was a non-commercial program created at Icahn School of Medicine at Mount Sinai by the Computational Neurobiology and Imaging Center. This program performed automatic tracing and reconstruction of neuron structures from confocal image stacks. The resulting models were then exported to file using standard formats for further processing, modeling, or for statistical analyses. NeuronStudio handled morphologic details on scales spanning local Dendritic spine geometry through complex tree topology to the gross spatial arrangement of multi-neuron networks. Its capability for automated digitization avoided the subjective errors inherent in manual tracing. The program ceased to be supported in 2012 and the project pages were eventually removed from the ISMMS Website. Its documentation and the Windows source code however are still available via the Internet Archive.

A neurite or neuronal process refers to any projection from the cell body of a neuron. This projection can be either an axon or a dendrite. The term is frequently used when speaking of immature or developing neurons, especially of cells in culture, because it can be difficult to tell axons from dendrites before differentiation is complete.

In neuroscience, classical cable theory uses mathematical models to calculate the electric current along passive neurites, particularly the dendrites that receive synaptic inputs at different sites and times. Estimates are made by modeling dendrites and axons as cylinders composed of segments with capacitances $and resistances combined in parallel. The capacitance of a neuronal fiber comes about because electrostatic forces are acting through the very thin lipid bilayer. The resistance in series along the fiber is due to the axoplasm's significant resistance to movement of electric charge.$

Neuromorphology is the study of nervous system form, shape, and structure. The study involves looking at a particular part of the nervous system from a molecular and cellular level and connecting it to a physiological and anatomical point of view. The field also explores the communications and interactions within and between each specialized section of the nervous system. Morphology is distinct from morphogenesis. Morphology is the study of the shape and structure of biological organisms, while morphogenesis is the study of the biological development of the shape and structure of organisms. Therefore, neuromorphology focuses on the specifics of the structure of the nervous system and not the process by which the structure was developed. Neuromorphology and morphogenesis, while two different entities, are nonetheless closely linked.

The synaptotropic hypothesis, also called the synaptotrophic hypothesis, is a neurobiological hypothesis of neuronal growth and synapse formation. The hypothesis was first formulated by J.E. Vaughn in 1988, and remains a focus of current research efforts. The synaptotropic hypothesis proposes that input from a presynaptic to a postsynaptic cell eventually can change the course of synapse formation at dendritic and axonal arbors. This synapse formation is required for the development of neuronal structure in the functioning brain.

Neural backpropagation is the phenomenon in which, after the action potential of a neuron creates a voltage spike down the axon, another impulse is generated from the soma and propagates towards the apical portions of the dendritic arbor or dendrites. In addition to active backpropagation of the action potential, there is also passive electrotonic spread. While there is ample evidence to prove the existence of backpropagating action potentials, the function of such action potentials and the extent to which they invade the most distal dendrites remain highly controversial.

<span class="mw-page-title-main">Biological neuron model</span> Mathematical descriptions of the properties of certain cells in the nervous system

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In neurophysiology, a dendritic spike refers to an action potential generated in the dendrite of a neuron. Dendrites are branched extensions of a neuron. They receive electrical signals emitted from projecting neurons and transfer these signals to the cell body, or soma. Dendritic signaling has traditionally been viewed as a passive mode of electrical signaling. Unlike its axon counterpart which can generate signals through action potentials, dendrites were believed to only have the ability to propagate electrical signals by physical means: changes in conductance, length, cross sectional area, etc. However, the existence of dendritic spikes was proposed and demonstrated by W. Alden Spencer, Eric Kandel, Rodolfo Llinás and coworkers in the 1960s and a large body of evidence now makes it clear that dendrites are active neuronal structures. Dendrites contain voltage-gated ion channels giving them the ability to generate action potentials. Dendritic spikes have been recorded in numerous types of neurons in the brain and are thought to have great implications in neuronal communication, memory, and learning. They are one of the major factors in long-term potentiation.

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Neuronal tracing, or neuron reconstruction is a technique used in neuroscience to determine the pathway of the neurites or neuronal processes, the axons and dendrites, of a neuron. From a sample preparation point of view, it may refer to some of the following as well as other genetic neuron labeling techniques,

Neuronal self-avoidance, or isoneural avoidance, is an important property of neurons which consists in the tendency of branches arising from a single soma to turn away from one another. The arrangements of branches within neuronal arbors are established during development and result in minimal crossing or overlap as they spread over a territory, resulting in the typical fasciculated morphology of neurons.

Patch-sequencing (patch-seq) is a modification of patch-clamp technique that combines electrophysiological, transcriptomic and morphological characterization of individual neurons. In this approach, the neuron's cytoplasm is collected and processed for RNAseq after electrophysiological recordings are performed on it. The cell is simultaneously filled with a dye that allows for subsequent morphological reconstruction.

References

1 2 3 4 5 6 7 8 9 Sholl, D.A., 1953. Dendritic organization in the neurons of the visual and motor cortices of the cat. J. Anat. 87, 387–406
↑ O'Neill KM1, Akum BF2, Dhawan ST2, Kwon M2, Langhammer CG2, Firestein BL2. (2015) Assessing effects on dendritic arborization using novel Sholl analyses. Front Cell Neurosci. Jul 30;9:285. doi: 10.3389/fncel.2015.00285. eCollection 2015.
↑ Chowdhury, T., Barbarich-Marsteller, N., Chan, T., & Aoki, C. (2013). Activity-based anorexia has differential effects on apical dendritic branching in dorsal and ventral hippocampal CA1. Brain Structure and Function, 1-11.
↑ Schoenen, J (1982). "The dendritic organization of the human spinal cord: the dorsal horn". Neuroscience. 7 (9): 2057–2087. doi:10.1016/0306-4522(82)90120-8. PMID 7145088. S2CID 12824120.
1 2 3 Nebojsa T. Milosevic, Dusan Ristanovic, 20 September 2006, Journal of Theoretical Biology 245 (2007) 130–140
↑ Dusan Ristanovic, Nebojsa T. Milosivic, Vesna Stulic, 29 May 2006, Journal of Neuroscience Methods 158 (2006) 212–218
↑ Pillai; de Jong, Kanatsu (2012). "Dendritic Morphology of Hippocampal and Amygdalar Neurons in Adolescent Mice Is Resilient to Genetic Differences in Stress Reactivity". PLOS ONE. 7 (6): e38971. Bibcode:2012PLoSO...738971P. doi: 10.1371/journal.pone.0038971 . PMC 3373517 . PMID 22701737.
↑ Garcia-Segura, LM; Perez-Marquez J (Apr 15, 2014). "A new mathematical function to evaluate neuronal morphology using the Sholl analysis". Journal of Neuroscience Methods. 226: 103–9. doi:10.1016/j.jneumeth.2014.01.016. PMID 24503022. S2CID 22359521.
↑ "ImageJ.net/Sholl" . Retrieved 10 February 2017.
↑ Wu, Chi-Cheng; Reilly, John F.; Young, Warren G.; Morrison, John H.; Bloom, Floyd E. (2004-05-01). "High-throughput Morphometric Analysis of Individual Neurons". Cerebral Cortex. 14 (5): 543–554. doi: 10.1093/cercor/bhh016 . ISSN 1047-3211. PMID 15054070.
↑ Ferreira, T; Blackman, A; Oyrer, J; Jayabal, A; Chung, A; Watt, A; Sjöström, J; van Meyel, D (2004). "Neuronal morphometry directly from bitmap images". Nat Methods. 11 (10): 982–984. doi:10.1038/nmeth.3125. PMC 5271921 . PMID 25264773.

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[Sholl_1953-1] 1 2 3 4 5 6 7 8 9 Sholl, D.A., 1953. Dendritic organization in the neurons of the visual and motor cortices of the cat. J. Anat. 87, 387–406

[2] O'Neill KM1, Akum BF2, Dhawan ST2, Kwon M2, Langhammer CG2, Firestein BL2. (2015) Assessing effects on dendritic arborization using novel Sholl analyses. Front Cell Neurosci. Jul 30;9:285. doi: 10.3389/fncel.2015.00285. eCollection 2015.

[3] Chowdhury, T., Barbarich-Marsteller, N., Chan, T., & Aoki, C. (2013). Activity-based anorexia has differential effects on apical dendritic branching in dorsal and ventral hippocampal CA1. Brain Structure and Function, 1-11.

[4] Schoenen, J (1982). "The dendritic organization of the human spinal cord: the dorsal horn". Neuroscience. 7 (9): 2057–2087. doi:10.1016/0306-4522(82)90120-8. PMID 7145088. S2CID 12824120.

[Milosivic-5] 1 2 3 Nebojsa T. Milosevic, Dusan Ristanovic, 20 September 2006, Journal of Theoretical Biology 245 (2007) 130–140

[6] Dusan Ristanovic, Nebojsa T. Milosivic, Vesna Stulic, 29 May 2006, Journal of Neuroscience Methods 158 (2006) 212–218

[7] Pillai; de Jong, Kanatsu (2012). "Dendritic Morphology of Hippocampal and Amygdalar Neurons in Adolescent Mice Is Resilient to Genetic Differences in Stress Reactivity". PLOS ONE. 7 (6): e38971. Bibcode:2012PLoSO...738971P. doi: 10.1371/journal.pone.0038971 . PMC 3373517 . PMID 22701737.

[8] Garcia-Segura, LM; Perez-Marquez J (Apr 15, 2014). "A new mathematical function to evaluate neuronal morphology using the Sholl analysis". Journal of Neuroscience Methods. 226: 103–9. doi:10.1016/j.jneumeth.2014.01.016. PMID 24503022. S2CID 22359521.

[9] "ImageJ.net/Sholl" . Retrieved 10 February 2017.

[10] Wu, Chi-Cheng; Reilly, John F.; Young, Warren G.; Morrison, John H.; Bloom, Floyd E. (2004-05-01). "High-throughput Morphometric Analysis of Individual Neurons". Cerebral Cortex. 14 (5): 543–554. doi: 10.1093/cercor/bhh016 . ISSN 1047-3211. PMID 15054070.

[11] Ferreira, T; Blackman, A; Oyrer, J; Jayabal, A; Chung, A; Watt, A; Sjöström, J; van Meyel, D (2004). "Neuronal morphometry directly from bitmap images". Nat Methods. 11 (10): 982–984. doi:10.1038/nmeth.3125. PMC 5271921 . PMID 25264773.

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