The precision of estimates in stereological analyses

Studying nerve transfers: Searching for a consensus in nerve axons count

Axonal count is the base for efficient nerve transfer; despite its capital importance, few studies have been published on human material, most research approaches being performed on experimental animal models of nerve injury. Thus, standard analysis methods are still lacking. Quantitative data obtained have to be reproducible and comparable with published data by other research groups. To share results with the scientific community, the standardization of quantitative analysis is a fundamental step. For this purpose, the experiences of the Italian, Austrian, German, Greek, and Iberian-Latin American groups have been compared with each other and with the existing literature to reach a consensus in the fiber count and draw up a protocol that can make future studies from different centers comparable. The search for a standardization of the methodology was aimed to reduce all the factors that are associated with an increase in the variability of the results. All the preferential methods to be used have been suggested. On the other hand, alternative methods and different methods have been identified to achieve the same goal, which in our experience are completely comparable; therefore, they can be used indifferently by the different centers according to their experience and availability.

Basic quantitative morphological methods applied to the central nervous system

Generating numbers has become an almost inevitable task associated with studies of the morphology of the nervous system. Numbers serve a desire for clarity and objectivity in the presentation of results and are a prerequisite for the statistical evaluation of experimental outcomes. Clarity, objectivity, and statistics make demands on the quality of the numbers that are not met by many methods. This review provides a refresher of problems associated with generating numbers that describe the nervous system in terms of the volumes, surfaces, lengths, and numbers of its components. An important aim is to provide comprehensible descriptions of the methods that address these problems. Collectively known as design-based stereology, these methods share two features critical to their application. First, they are firmly based in mathematics and its proofs. Second and critically underemphasized, an understanding of their mathematical background is not necessary for their informed and productive application. Understanding and applying estimators of volume, surface, length or number does not require more of an organizational mastermind than an immunohistochemical protocol. And when it comes to calculations, square roots are the gravest challenges to overcome. Sampling strategies that are combined with stereological probes are efficient and allow a rational assessment if the numbers that have been generated are "good enough." Much may be unfamiliar, but very little is difficult. These methods can no longer be scapegoats for discrepant results but faithfully produce numbers on the material that is assessed. They also faithfully reflect problems that associated with the histological material and the anatomically informed decisions needed to generate numbers that are not only valid in theory. It is within reach to generate practically useful numbers that must integrate with qualitative knowledge to understand the function of neural systems.

Design-Based stereology and binary image histomorphometry in nerve assessment

BACKGROUND

Stereology and histomorphometry are widely used by investigators to quantify nerve characteristics in normal and pathological states, including nerve injury and regeneration. While these methods of analysis are complementary, no study to date has systematically compared both approaches in peripheral nerve. This study investigated the reliability of design-based stereology versus semi-automated binary imaging histomorphometry for assessing healthy peripheral nerve characteristics.

NEW METHOD

Stereological analysis was compared to histomorphometry with binary image analysis on uninjured sciatic nerves to determine nerve fiber number, nerve area, neural density, and fiber distribution.

RESULTS

Sciatic nerves were harvested from 6 male Lewis rats, aged 8-12 weeks for comprehensive analysis of 6 nerve specimens. From each animal, sciatic nerve specimens were fixed, stained, and sectioned for analysis by light and electron microscopy. Both histomorphometry and stereological peripheral nerve analyses were performed on all specimens by two blinded and independent investigators who quantified nerve fiber count, fiber width, density, and related distribution parameters.

COMPARISON WITH EXISTING METHODS

Histomorphometry and stereological analysis provided similar outcomes in nerve fiber number and total nerve area. However, the light microscopy, but not electron microscopy, stereological analysis yielded higher nerve fiber area compared to histomorphometry or manual measurement.

CONCLUSION

Both methods measure similar fiber number and overall nerve fiber area; however, stereology with light microscopy quantified higher fiber area. Histomorphometry optimizes throughput and comprehensive analysis but requires user thresholding.

Chlorogenic acid ameliorates memory loss and hippocampal cell death after transient global ischemia

Chlorogenic acid (CGA) is known to have antioxidant potentials, yet the effect of CGA on brain ischemia has not been sufficiently understood. Brain ischemia such as transient global ischemia disrupts many areas of the brain of rats, including the hippocampus. Male Wistar rats were randomly assigned into five groups, that is, sham-operated (SO), bilateral common carotid occlusion (BCCO), and BCCO+ 15, 30, and 60 mg/kg bw CGA groups (CGA15, CGA30, and CGA60, respectively). Brain ischemia was induced in Wistar rats with BCCO for 20 min followed by intraperitoneal injection of CGA. The rats were examined for the spatial memory in a Morris water maze test on the 3rd day and were euthanized on the 10th day after BCCO. The total number of pyramidal cells was estimated, and the mRNA expressions of Bcl2, Bax, caspase-3, SOD2, SOD1, GPx, ET-1, eNOS, CD31, and VEGF-A were measured. The BCCO group spent less time and distance in the target quadrant than any other group in the spatial memory retention test. The CA1 pyramidal cell numbers in the BCCO and CGA15 groups were lower than in the CGA30 and CGA60 groups. The mRNA expressions of Bcl2, SOD2, and CD31 in the BCCO group were lower than in the CGA15, CGA30, and CGA60 groups. The ET-1 expression was higher in the BCCO and CGA15 groups than in the SO, CGA30, and CGA60 groups. CGA improves the spatial memory and prevents the CA1 pyramidal cell death after BCCO by increasing Bcl2, SOD2, and CD31 expressions and decreasing ET-1 expression.

Insights from thrombi retrieved in stroke due to large vessel occlusion

The recent advances of endovascular procedures to treat stroke due to large cerebral vessel occlusion have made it possible to analyze the retrieved thrombus material. Analysis of cerebral thrombi is emerging as a relevant opportunity to complement the diagnostic workup of etiology, to develop new lytic approaches and to optimize the acute treatment of stroke due to large vessel occlusion. Nonetheless, retrieved thrombi are frequently discarded since their informative potential is often neglected and standards are missing. This review provides an overview of the current knowledge and expanding research relating to thrombus composition analysis in large vessel occlusions. We first discuss the heterogeneity of thrombogenic factors that underlie the thrombotic formation in stroke and its implications to identify stroke etiology and thrombus age. Further, we show that understanding structural characteristics of thrombus is pivotal for the development of new-targeted lytic therapies as well as to improve, through thrombus modeling, the development of thrombectomy devices. Finally, we discuss the on-going attempts to identify a signature of thrombus composition indirectly through imaging and peripheral blood biomarkers, which might in future assist treatment decision-making as well as secondary prevention. Thrombus analysis might contribute to the advancement and optimization of personalized stroke treatments.

Microglia Express Insulin-Like Growth Factor-1 in the Hippocampus of Aged APPswe/PS1ΔE9 Transgenic Mice

Insulin-like growth factor-1 (IGF-1) is a pleiotropic molecule with neurotrophic and immunomodulatory functions. Knowing the capacity of chronically activated microglia to produce IGF-1 may therefore show essential to promote beneficial microglial functions in Alzheimer's disease (AD). Here, we investigated the expression of IGF-1 mRNA and IGF-1 along with the expression of tumor necrosis factor (TNF) mRNA, and the amyloid-β (Aβ) plaque load in the hippocampus of 3- to 24-month-old APPswe/PS1ΔE9 transgenic (Tg) and wild-type (WT) mice. As IGF-1, in particular, is implicated in neurogenesis we also monitored the proliferation of cells in the subgranular zone (sgz) of the dentate gyrus. We found that the Aβ plaque load reached its maximum in aged 21- and 24-month-old APPswe/PS1ΔE9 Tg mice, and that microglial reactivity and hippocampal IGF-1 and TNF mRNA levels were significantly elevated in aged APPswe/PS1ΔE9 Tg mice. The sgz cell proliferation decreased with age, regardless of genotype and increased IGF-1/TNF mRNA levels. Interestingly, IGF-1 mRNA was expressed in subsets of sgz cells, likely neuroblasts, and neurons in both genotypes, regardless of age, as well as in glial-like cells. By double in situ hybridization these were shown to be IGF1 mRNA+ CD11b mRNA+ cells, i.e., IGF-1 mRNA-expressing microglia. Quantification showed a 2-fold increase in the number of microglia and IGF-1 mRNA-expressing microglia in the molecular layer of the dentate gyrus in aged APPswe/PS1ΔE9 Tg mice. Double-immunofluorescence showed that IGF-1 was expressed in a subset of Aβ plaque-associated CD11b+ microglia and in several subsets of neurons. Exposure of primary murine microglia and BV2 cells to Aβ42 did not affect IGF-1 mRNA expression. IGF-1 mRNA levels remained constant in WT mice with aging, unlike TNF mRNA levels which increased with aging. In conclusion, our results suggest that the increased IGF-1 mRNA levels can be ascribed to a larger number of IGF-1 mRNA-expressing microglia in the aged APPswe/PS1ΔE9 Tg mice. The finding that subsets of microglia retain the capacity to express IGF-1 mRNA and IGF-1 in the aged APPswe/PS1ΔE9 Tg mice is encouraging, considering the beneficial therapeutic potential of modulating microglial production of IGF-1 in AD.

High-Altitude Cognitive Impairment Is Prevented by Enriched Environment Including Exercise via VEGF Signaling

Exposure to hypobaric hypoxia at high altitude (above 2500 m asl) causes cognitive impairment, mostly attributed to changes in brain perfusion and consequently neuronal death. Enriched environment and voluntary exercise has been shown to improve cognitive function, to enhance brain microvasculature and neurogenesis, and to be neuroprotective. Here we show that high-altitude exposure (3540 m asl) of Long Evans rats during early adulthood (P48-P59) increases brain microvasculature and neurogenesis but impairs spatial and visual memory along with an increase in neuronal apoptosis. We tested whether enriched environment including a running wheel for voluntary exercise (EE) can prevent cognitive impairment at high-altitude and whether apoptosis is prevented. We found that EE retained spatial and visual memory at high altitude, and prevented neuronal apoptosis. Further, we tested whether vascular endothelial growth factor (VEGF) signaling is required for the EE-mediated recovery of spatial and visual memory and the reduction in apoptosis. Pharmacological inhibition of VEGF signaling by oral application of a tyrosine kinase inhibitor (Vandetanib) prevented the recovery of spatial and visual memory in animals housed in EE, along with an increase in apoptosis and a reduction in neurogenesis. Surprisingly, inhibition of VEGF signaling also caused impairment in spatial memory in EE-housed animals reared at low altitude, affecting mainly dentate gyrus microvasculature but not neurogenesis. We conclude that EE-mediated VEGF signaling is neuroprotective and essential for the maintenance of cognition and neurogenesis during high-altitude exposure, and for the maintenance of spatial memory at low altitude. Finally, our data also underlines the potential risk of cognitive impairment and disturbed high altitude adaption from the use of VEGF-signaling inhibitors for therapeutic purposes.

Diverse Protein Profiles in CNS Myeloid Cells and CNS Tissue From Lipopolysaccharide- and Vehicle-Injected APPSWE/PS1ΔE9 Transgenic Mice Implicate Cathepsin Z in Alzheimer's Disease

Neuroinflammation, characterized by chronic activation of the myeloid-derived microglia, is a hallmark of Alzheimer’s disease (AD). Systemic inflammation, typically resulting from infection, has been linked to the progression of AD due to exacerbation of the chronic microglial reaction. However, the mechanism and the consequences of this exacerbation are largely unknown. Here, we mimicked systemic inflammation in AD with weekly intraperitoneal (i.p.) injections of APP_SWE/PS1_ΔE9 transgenic mice with E. coli lipopolysaccharide (LPS) from 9 to 12 months of age, corresponding to the period with the steepest increase in amyloid pathology. We found that the repeated LPS injections ameliorated amyloid pathology in the neocortex while increasing the neuroinflammatory reaction. To elucidate mechanisms, we analyzed the proteome of the hippocampus from the same mice as well as in unique samples of CNS myeloid cells. The repeated LPS injections stimulated protein pathways of the complement system, retinoid receptor activation and oxidative stress. CNS myeloid cells from transgenic mice showed enrichment in pathways of amyloid-beta clearance and elevated levels of the lysosomal protease cathepsin Z, as well as amyloid precursor protein, apolipoprotein E and clusterin. These proteins were found elevated in the proteome of both LPS and vehicle injected transgenics, and co-localized to CD11b⁺ microglia in transgenic mice and in primary murine microglia. Additionally, cathepsin Z, amyloid precursor protein, and apolipoprotein E appeared associated with amyloid plaques in neocortex of AD cases. Interestingly, cathepsin Z was expressed in microglial-like cells and co-localized to CD68⁺ microglial lysosomes in AD cases, and it was expressed in perivascular cells in AD and control cases. Taken together, our results implicate systemic LPS administration in ameliorating amyloid pathology in early-to-mid stage disease in the APP_SWE/PS1_ΔE9 mouse and attract attention to the potential disease involvement of cathepsin Z expressed in CNS myeloid cells in AD.

Hemispheric differences in the number of parvalbumin-positive neurons in subdivisions of the rat basolateral amygdala complex

The amygdala is a bilateral temporal lobe brain region which plays an important role in emotional processing. Past studies on the amygdala have shown hemispheric differences in amygdalar processes and responses associated with specific pain and fear behaviors. Despite the functional differences in the amygdala, few studies have been performed to characterize whether anatomical differences exist between the left and right amygdala. Parvalbumin (PV) is a phenotypic marker for an inhibitory interneuronal population in cortical brain structures such as the basolateral amygdala complex (BLC). This study examined the number of PV-positive neurons in the left and right BLC of adult, male Long-Evans rats using unbiased stereology. Coronal sections through the rostral-caudal extent of the BLC were immunohistochemically-stained for PV and the optical fractionator method was used to obtain an unbiased estimate of the number of PV-positive neurons in subdivisions through the BLC. The lateral and basolateral amygdala divisions of the BLC were analyzed, were subdivided into the dorsolateral, ventrolateral and ventromedial and the posterior, anterior and ventral subdivisions, respectively. The results indicate that there are significantly more PV-positive neurons in the left basolateral amygdala compared to the right, with a significant difference specifically in the posterior subdivision. This difference in PV neuronal number could help explain the distinct hemispheric roles of the BLC in the behavioral processing following exposure to painful and fearful stimuli.

Sampling the Mouse Hippocampal Dentate Gyrus

Sampling is a critical step in procedures that generate quantitative morphological data in the neurosciences. Samples need to be representative to allow statistical evaluations, and samples need to deliver a precision that makes statistical evaluations not only possible but also meaningful. Sampling generated variability should, e.g., not be able to hide significant group differences from statistical detection if they are present. Estimators of the coefficient of error (CE) have been developed to provide tentative answers to the question if sampling has been “good enough” to provide meaningful statistical outcomes. We tested the performance of the commonly used Gundersen-Jensen CE estimator, using the layers of the mouse hippocampal dentate gyrus as an example (molecular layer, granule cell layer and hilus). We found that this estimator provided useful estimates of the precision that can be expected from samples of different sizes. For all layers, we found that a smoothness factor (m) of 0 generally provided better estimates than an m of 1. Only for the combined layers, i.e., the entire dentate gyrus, better CE estimates could be obtained using an m of 1. The orientation of the sections impacted on CE sizes. Frontal (coronal) sections are typically most efficient by providing the smallest CEs for a given amount of work. Applying the estimator to 3D-reconstructed layers and using very intense sampling, we observed CE size plots with m = 0 to m = 1 transitions that should also be expected but are not often observed in real section series. The data we present also allows the reader to approximate the sampling intervals in frontal, horizontal or sagittal sections that provide CEs of specified sizes for the layers of the mouse dentate gyrus.

Turmeric (Curcuma longa L.) extract may prevent the deterioration of spatial memory and the deficit of estimated total number of hippocampal pyramidal cells of trimethyltin-exposed rats

CONTEXT

Protection of neurons from degeneration is an important preventive strategy for dementia. Much of the dementia pathology implicates oxidative stress pathways. Turmeric (Curcuma longa L.) contains curcuminoids which has anti-oxidative and neuro-protective effects. These effects are considered to be similar to those of citicoline which has been regularly used as one of standard medications for dementia.

OBJECTIVE

This study aimed at investigating the effects of turmeric rhizome extract on the hippocampus of trimethyltin (TMT)-treated Sprague-Dawley rats.

MATERIALS AND METHODS

The rats were divided randomly into six groups, i.e., a normal control group (N); Sn group, which was given TMT chloride; Sn-Cit group, which was treated with citicoline and TMT chloride; and three Sn-TE groups, which were treated with three different dosages of turmeric rhizome extract and TMT chloride. Morris water maze test was carried out to examine the spatial memory. The estimated total number of CA1 and CA2-CA3 pyramidal cells was calculated using a stereological method.

RESULTS

The administration of turmeric extract at a dose of 200 mg/kg bw has been shown to prevent the deficits in the spatial memory performance and partially inhibit the reduction of the number of CA2-CA3 regions pyramidal neurons.

DISCUSSION

TMT-induced neurotoxic damage seemed to be mediated by the generation of reactive oxygen species and reactive nitrogen species. Turmeric extract might act as anti inflammatory as well as anti-oxidant agent.

CONCLUSIONS

The effects of turmeric extract at a dose of 200 mg/kg bw seem to be comparable to those of citicoline.

Primary olfactory cortex in autism and epilepsy: increased glial cells in autism

Autism Spectrum Disorder is characterized by sensory anomalies including impaired olfactory identification. Between 5 and 46 percent of individuals with autism have a clinical diagnosis of epilepsy. Primary olfactory cortex (piriform cortex) is central to olfactory identification and is an epileptogenic structure. Cytoarchitectural changes in olfactory cortex may underlie olfactory differences seen in autism. Primary olfactory cortex was sampled from 17 post-mortem autism cases with and without epilepsy, 11 epilepsy cases without autism and 11 typically developed cases. Stereological and neuropathological methods were used to quantify glial, pyramidal and non-pyramidal cell densities in layers of the piriform as well as identify pathological differences in this area and its neighbouring region, the olfactory tubercle. We found increased layer II glial cell densities in autism with and without epilepsy, which were negatively correlated with age and positively correlated with levels of corpora amylacea in layer I. These changes were also associated with greater symptom severity and did not extend to the olfactory tubercle. Glial cell organization may follow an altered trajectory of development with age in autism. The findings are consistent with other studies implicating increased glial cells in the autism brain. Altered cytoarchitecture may contribute to sensory deficits observed in affected individuals. This study provides evidence that autism is linked to alterations in the cytoarchitectural structure that underlies primary sensory processes and is not restricted to heteromodal ("higher") cognitive centers.

Mammillary Bodies in Alzheimer's Disease: A Golgi and Electron Microscope Study

Alzheimer's disease (AD) is a progressive neurodegenerative disorder, characterized by irreversible memory decline, concerning no rarely spatial memory and orientation, alterations of the mood and personality, gradual loss of motor skills, and substantial loss of capacities obtained by previous long education. We attempted to describe the morphological findings of the mammillary bodies in early cases of AD. Samples were processed for electron microscopy and silver impregnation techniques. The nuclei of the mammillary bodies demonstrated a substantial decrease in the neuronal population and marked abbreviation of dendritic arbors. Decrease in spine density and morphological abnormalities of dendritic spines was also seen. Synaptic alterations were prominent. Alzheimer's pathology, such as deposits of amyloid-β peptide and neurofibrillary degeneration, was minimal. Electron microscopy revealed mitochondrial alterations and fragmentation of Golgi apparatus, associated frequently with synaptic pathology.

What has electron microscopy contributed to Alzheimer's research?

Electron microscopy has enlarged the visual horizons of the morphological alterations in Alzheimer's disease (AD). Study of the mitochondria and Golgi apparatus in early cases of AD revealed the principal role that these important organelles play in the drama of pathogenic dialog of AD, substantially affecting energy production and supply, and protein trafficking in neurons and glia. In addition, study of the morphological alterations of the dendritic arbor, dendritic spines and neuronal synapses, which are associated with mitochondrial damage, may reasonably interpret the clinical phenomena of the irreversible decline of the mental faculties and an individual's personality changes. Electron microscopy also reveals the involvement of microvascular alterations in the etiopathogenic background of AD.

The hypothalamus in Alzheimer's disease: a Golgi and electron microscope study

Alzheimer's disease (AD) is a progressive neurodegenerative disorder, characterized by irreversible decline of mental faculties, emotional and behavioral changes, loss of motor skills, and dysfunction of autonomic nervous system and disruption of circadian rhythms (CRs). We attempted to describe the morphological findings of the hypothalamus in early cases of AD, focusing our study mostly on the suprachiasmatic nucleus (SCN), the supraoptic nucleus (SON), and the paraventricular nucleus (PVN). Samples were processed for electron microscopy and silver impregnation techniques. The hypothalamic nuclei demonstrated a substantial decrease in the neuronal population, which was particularly prominent in the SCN. Marked abbreviation of dendritic arborization, in association with spinal pathology, was also seen. The SON and PVN demonstrated a substantial number of dystrophic axons and abnormal spines. Alzheimer's pathology, such as deposits of amyloid-β peptide and neurofibrillary degeneration, was minimal. Electron microscopy revealed mitochondrial alterations in the cell body and the dendritic branches. The morphological alterations of the hypothalamic nuclei in early cases of AD may be related to the gradual alteration of CRs and the instability of autonomic regulation.

Quantitative assessment of angiogenesis, perfused blood vessels and endothelial tip cells in the postnatal mouse brain

During development and in various diseases of the CNS, new blood vessel formation starts with endothelial tip cell selection and vascular sprout migration, followed by the establishment of functional, perfused blood vessels. Here we describe a method that allows the assessment of these distinct angiogenic steps together with antibody-based protein detection in the postnatal mouse brain. Intravascular and perivascular markers such as Evans blue (EB), isolectin B4 (IB4) or laminin (LN) are used alongside simultaneous immunofluorescence on the same sections. By using confocal laser-scanning microscopy and stereological methods for analysis, detailed quantification of the 3D postnatal brain vasculature for perfused and nonperfused vessels (e.g., vascular volume fraction, vessel length and number, number of branch points and perfusion status of the newly formed vessels) and characterization of sprouting activity (e.g., endothelial tip cell density, filopodia number) can be obtained. The entire protocol, from mouse perfusion to vessel analysis, takes ∼10 d.

What to report: information to be included in the publication of a stereological study

In publications of stereological studies, descriptions of the method and data are often incomplete. This article discusses how to describe a stereological study in such a way that allows readers and reviewers to access the quality of the data and reproduce the study.

Counting and measuring ultrastructural features of biological samples

Ultrastructural features of cells can be fractions of a micrometer in diameter, and electron microscopy is needed to resolve them to a degree that is compatible with stereological techniques. Because the focal depth of transmission electron microscopy (TEM) images is thousands of times greater than the thickness of the sections used with TEM, virtual sectioning of sections suitable for TEM is not possible, as it is with light microscopy and the optical disector probe. With features the size of neuronal synapses, for example, this necessitates the use of physical sections and physical disectors. Regardless of how the imaging is performed, the design of stereological studies for quantifying ultrastructural features will be essentially the same as that used in the example described here, which uses physically separated ultrathin sections viewed with conventional TEM to estimate the number and size of synapses in a particular brain region.

Optimizing the sampling scheme for a stereological study: how many individuals, sections, and probes should be used

Stereology provides meaningful quantitative descriptions of the geometry of three-dimensional (3D) structures from measurements that are made on two-dimensional (2D) images. A pilot stereological study will provide information that can be used to rationalize how many individuals, sections, and probes should be used to ensure that one is sampling enough, but not too much, to achieve the goal of a study. This general approach is exemplified in the thought experiment described here, which involves a comparison of the means of estimates of the total number of neurons N in two groups, using the simplest of statistical tests, the Student's t-test. It is also applicable to studies involving other estimates of total quantities such as volume, surface, and length obtained from a parallel series of sections.

Estimating length in biological structures

Length estimates of particular features of biological tissues can be useful in evaluating function. Such estimates have been notoriously difficult to obtain because of the requirement for an isotropic interaction between the area probes and the linear features of cells and tissues, which are most likely not isotropically oriented. For complex embedded structures, such as subdivisions of the brain, the turning of the tissue before sectioning that is needed to ensure an isotropic interaction has made it difficult to delineate many regions of interest and limited the number of unbiased stereological studies of length. The recent development of a virtual isotropic spherical probe, the spaceball, makes it relatively easy for the isotropic interaction between probe and structure to be realized. This article describes the use of the spaceball probe to estimate length, and gives an example of estimating total capillary length in CA1 stratum radiatum of the human hippocampus.

Getting started in stereology

Stereology involves sampling structural features in sections of tissue with geometrical probes. This article discusses some practical issues that must be dealt with when getting started in stereology, including tissue preparation methods and determining how many tissue sections and probes are needed to make a stereological estimate.

Estimating surface area in biological structures

Stereological estimates of surface have led to important insights into normal and pathological processes. This article describes the process of estimating surface area in biological structures. It includes a discussion of relationship equations for estimating surface and procedures for estimating surface area of components of organ systems. It also provides an example of estimation of the area of the pial surface of the human brain.

Estimating volume in biological structures

Estimates of volume can be useful in comparative and experimental studies of tissues and organs. In this article, a simple procedure for making unbiased estimates of total volume using Cavalieri's principle is described. This is followed by a description of how point probes can be used to make unbiased estimates of the areas of sectional profiles and how, when combined with Cavalieri's principle, point counting can be used to make an unbiased estimate of the volume of a structural feature.