Recent developments and the importance of the volume estimation in biomedical sciences

Abstract Introduction Recently, scientists who performed morphological, comparative and experimental studies have tried to get more efficient and accurate information from the interested tissue. The volume estimation is part of this information and an important criterion for the biomedical sciences. It increases the confidence in the data obtained. The volumetric change is an indicator of an organ’s health status. It is also important in the clinical diagnosis of a tumour, therapy planning and control of the tumour’s growth. The important data obtained using the Cavalieri principle is considered the best volume estimation method. This method, a stereological tool, allows precise estimates about the related object. Scientists and clinicians both use this method under in vivo and in vitro conditions. The method could combine in vivo by computed tomography and magnetic resonance images and in vitro after the classical histological tissue processing. The aim of this article was to discuss the recent developments and the importance of the volume estimation in biomedical sciences. Methodology The Cavalieri principle could estimate an object’s volume under in vitro and in vivo conditions. In vitro estimations—First, the tissue is sliced at a random starting point at parallel and equal intervals. Then, the surface areas of these slices (just one and the same side of each slice) are measured by a randomly superposed point grid. The point counting procedure could be done on a computer loaded with stereology software. In vivo estimations—This measurement is done on magnetic resonance and computed tomography images. The parallel and equally sliced images of the related objects are obtained from the magnetic resonance and computed tomography. At the monitor, the software places the point grid on these images and the estimations are calculated. Conclusion The Cavalieri principle estimates the total volume of an organ and its subcomponents more accurately and precisely than the other methods. It runs simply and easily and produces efficient results.


Introduction
Recently, scientists who performed morphological, comparative and experimental studies have tried to get more efficient and accurate information from the interested tissue.The volume estimation is part of this information and an important criterion for the biomedical sciences.It increases the confidence in the data obtained.The volumetric change is an indicator of an organ's health status.It is also important in the clinical diagnosis of a tumour, therapy planning and control of the tumour's growth.The important data obtained using the Cavalieri principle is considered the best volume estimation method.This method, a stereological tool, allows precise estimates about the related object.Scientists and clinicians both use this method under in vivo and in vitro conditions.The method could combine in vivo by computed tomography and magnetic resonance images and in vitro after the classical histological tissue processing.The aim of this article was to discuss the recent developments and the importance of the volume estimation in biomedical sciences.

Methodology
The Cavalieri principle could estimate an object's volume under in vitro and in vivo conditions.
In vitro estimations-First, the tissue is sliced at a random starting point at parallel and equal intervals.Then, the surface areas of these slices (just one and the same side of each slice) are measured by a randomly superposed point grid.The point counting procedure could be done on a computer loaded with stereology software.
In vivo estimations-This measurement is done on magnetic resonance and computed tomography images.The parallel and equally sliced images of the related objects are obtained from the magnetic resonance and computed tomography.At the monitor, the software places the point grid on these images and the estima-

Introduction
The researchers who work in the areas like morphology, comparative anatomy, nutrition, pathology and toxicology sciences are interested in the total or subcomponent volume of organs 1 .The volume estimation is a critical parameter for biomedical sciences [1][2][3] .The volumetric change is an index for studying the health status; it is clinically important because it indicates the functional reserve of an organ and is a sensitive indicator of chemically induced changes to organs [4][5][6][7] .The volume comparison of the organ subcomponents may produce data useful for diseases such as hypertrophy, atrophy and tumour formation in the organs 4,5,8 .Also, it could be used to control the cancer's ongoing treatment by estimating the tumour volume 9 .The volumetric estimation of the related object and subcomponents could be measured with stereological methods.The measurement method-stereologyis an unbiased and efficient combination of the tools for obtaining accurate, precise quantitative structural data from tissue sections.In the 1980s, Gundersen and his friends contributed a great deal to modern stereological methods 10 .The stereological tools have the sensitivity necessary to detect small changes by combining statistical sampling principles with geometric analysis of the tissue's microstructure [10][11] .Different from other morphometric measurement methods, stereology is based on tissue section analysis by providing estimates that are statistically valid, truly three dimensional and refer to the entire organ [10][11] .The precision of the stereological analysis procedure can be predicted; therefore, research could be designed and powered to detect any minimum, potentially toxicologically significant changes [10][11] .
The estimation of this important value should be performed by the Cavalieri principle, the most precise way 10 .This method is a stereological method that relies on systematic uniform random sampling.Systematic uniform random sampling is the best way to sample the organ because it samples each part of the organ, and therefore every part of the organ is evaluated equally 10 .This method can detect small changes in the structure of the organ easily 10 .Before measuring, a pilot sample was performed on one tissue 12 .The result was evaluated by calculating the coefficient of error (CE) 10,12 .CE = SEM (standard error of the mean)/mean 10,12 interested object under the in vivo and in vitro conditions.It allows researchers to estimate the volume of the whole structure, subcomponents or even irregular shapes.

Discussion
The total and subcomponent volume of an organ is a parameter that is used widely in biomedical sciences [1][2][3] .Researchers in these sciences generally use stereological methods to measure the tissue, thus collecting more precise data [1][2][3] .Stereology is a science that gathers true and precise information from two-dimensional slides of three-dimensional objects 10,12 .Stereological methods are independent of the size of the whole structure and examine the volumetric relation between a structure's subcomponents 10,12 .The Cavalieri principle is one example 10,12 .Researchers who are interested in morphology frequently and commonly use this method 1,8,14 .Recent in vitro studies showed that morphological research concentrates generally on the differences between the paired organs, breed and sex differences 1,8,14,18 .For example, several veterinary anatomy researchers compared the total and subcomponent volume of the kidneys of animals such as cattle, horse and sheep 1,8,19 .In addition, researchers explored the volume of some experimental animals' kidney subcomponents using this method.Researchers also compared the effects of the fixation to the volume on rabbit kidneys and differences between the water displacement method and Cavalieri principle on dog testicles 14,20 .Subcomponent differences in the sex and paired kidneys were observed in the chinchilla kidney and hippocampus of the guinea pigs before puberty 18,21 .On humans, the renal parameters were searched on the normal and anencephalic foetuses, and the findings were compared 22 .A group of researchers also described the volume of the myelinated fibres in the rat cortex and in The point counting procedure could be done on a computer loaded with stereology software.The slides that contain tissue fragments are placed under the light microscope, and the image is sent to the computer by a microscope camera.Then, the software adjusts the intervals of the point grid and places the grid on the images, and the point counting is performed on these consecutive slide images 2,3,10 .
It is calculated by the formula below: The formula shows the calculation of the total volume.The volume of the related object (V) is estimated from parallel sections separated by a known distance (t), by summing up the surface areas of all sections of the object and multiplying the distance (t).The t value must contain the section sampling fraction if performed (i.e.selection of the every second slice, every third bar, etc.).The transparent test probe is superposed on the slices to estimate the surface area of the slices.This probe consists of regularly spaced points in a known distance (a/p).For estimates of the areal fraction of the profile, all points that hit the profile (ΣP) are counted 2,3,10 .

In vivo estimations
This measurement is done on MR and CT images.The parallel and equally sliced images of the related objects are obtained from the MR and CT.At the monitor, the software places the point grid on these images, and the estimations are done with the following formula 9,16,17 : In this formula, t symbolises the section thickness, SU is the scale unit (the real length of the scale marked on the MRIs), d is the distance between two points in the point grid, SL is the scale length (the actual measure of the scale on MRIs) and ΣP is the number of points counted 9,16,17 .
The Cavalieri principle is the best way to obtain detailed data from the The CE is the safety belt of the study to determine whether the sampling and results are appropriate.The Cavalieri principle required CE values of less than 3%.This percentage was obtained by counting the 200 points on 7 to 10 sections of one organ.The study was performed after calculating the CE and controlling the sampling steps [10][11][12] .
The total volume of the organ could be estimated directly and accurately using the water displacement method, the Archimedean principle, at the same time 10 .However, this method does not allow an estimation of the total volume of hollow organs like lungs that do not displace the water and small organs (< 5-6 mm 3 ) because of the capillary effect [13][14][15] .However, the Cavalieri principle solved these problems because it estimates the total volume of hollow or very small organs or structures, even those with an irregular shape 10 .The other advantage of the Cavalieri principle is its ability to estimate the volume of an organ's subcomponents 10 .For example, it could measure renal components such as the cortex, medulla and pelvis one by one and allow researchers to make true comparisons 1 .It could also measure arbitrarily shaped objects more precisely 10 .In addition, the Cavalieri principle could run under in vivo conditions in combination with the magnetic resonance (MR) and computed tomography (CT) images 16 .The Cavalieri principle has very special features.Therefore, this article observes the recent developments about this method and its use.

Methodology
The Cavalieri principle could estimate an object's volume under in vitro and in vivo conditions 1,16 .

In vitro estimations
First, the tissue is sliced at a random starting point at parallel and equal intervals.Then the surface areas of these slices (just one and the same side of each slice) are measured by a randomly superposed point grid.
Researchers previously reported that the volume of the tumour could be measured easily using the MRI or CT images in a few minutes per subject.The Cavalieri principle was performed on the cerebral, skin and renal originated tumours.Previous studies showed the Cavalieri principle could run under both in vivo and in vitro conditions for tumour volume estimation 9,37 .

Conclusion
The Cavalieri principle estimates the total volume of an organ and its subcomponents more accurately and precisely than other methods.It runs simply and easily and produces efficient results.The use of the Cavalieri principle in the biomedical sciences is very wide.Researchers of the in vitro and in vivo conditions could use this method aimed at contributing the data of their studies.Other than study planning it could be used in tumour treatments.The method runs perfectly in single uses or in combination, but the application research in radiographic and ultrasound images is not adequate yet.Future research should plan on the development of this method from these aspects.The researchers could use this method in their studies safely.the quantitative evaluation of brain atrophy because their superior contrast resolution facilitates discrimination of the grey and white matter 31 .The in vivo comparative morphological research collects data from the newborn's total brain, cerebrum, cerebellum and bulbus/pons to try to explain the origin of neurodevelopmental mental disorders 30 .The volume of the brain, cerebellum and brain stem was also observed in the young subjects 33 .Researchers measured the total and subcomponent volume of the cerebrum and cerebellum in Alzheimer's disease 31 .In Chiari type I malformation, the volume of the posterior cranial fossa, cerebellum and tonsils was evaluated using the same combinations 34 .In epileptic patients, the temporal lobe/ telencephalon volume in temporal lobe epilepsy was evaluated by this method 32 .The volume estimation of the cerebella in schizophrenia and vertigo patients was also measured.Besides these, the sport sciences also have used this method on athletes.Researchers evaluated the volume of the lateral and medial epicondyle of the humerus of volleyball players to determine the effects of excessive loading during games and training 35 .
On the other side, the MR images and Cavalieri principle were combined to measure the volume of another hollow organ, the heart.The scientists reported that the Cavalieri principle is the best and most accurate way to estimate the heart's volume, and therefore they applied this method.According to researchers, the Cavalieri Principle with MR combination perfectly measures left ventricular parameters such as enddiastolic volume and end-systolic volume 36 .
The definition of the tumour volume is critically important in radiotherapy and surgical planning.Precision in the estimation of the tumour volume will lead to the future of the therapy.Any fault in the estimation allows inaccurate delivery.the white matter using the Cavalieri principle [23][24] .
Experimental research in the nutritional, toxicological and pathological fields also uses the Cavalieri principle to obtain more accurate data [25][26] .Previous research in these fields concentrated generally on the brain and kidney for the volume estimations because of their subcomponent structures [25][26] .Researchers related to the neuronal system investigated the effects of advanced age and alcohol use on the volume of the hippocampal regions 26 .One toxicological study investigated the effects of formaldehyde exposure from airways to one of the brain compartments' dentate gyrus on the rats after birth 2 .Another group of researchers observed the effects of formalin on the volume of the hippocampal cell layer and hemispheres in rats 27 .In addition, several researchers studied the specificity and extent of volume loss of the major forebrain regions in epileptic rats months after kainateinduced status epilepticus and detected some important statistically changes on the amygdala, olfactory cortex, septal region, hippocampus and thalamus 28 .The Cavalieri principle was also performed on the organs to detect the side effects of drugs 25,29 .The scientists investigated normal and diabetic rat kidneys to observe the drugs' side effects 25,29 .The cortex, medulla and the kidney's whole volume were measured using the Cavalieri principle 25,29 .Moreover, the spleens of obese rats were subjected to nutritional studies 3 .It would be easy to evaluate in vitro the effects on the rats' spleen by feeding them a fatty diet 3 .
The in vivo research focused specifically on the brain imaging, with the goal of explaining mental disorders 30 .The imaging techniques are beneficial for brain research and neurological disorders such as Alzheimer's disease, epilepsy and tumoural formation 9,31,32 .The imaging techniques give useful data for