Tangential Sections Research Articles

Assessing Conifer Ray Parenchyma for Ecological Studies: Pitfalls and Guidelines.

Ray parenchyma is an essential tissue for tree functioning and survival. This living tissue plays a major role for storage and transport of water, nutrients, and non-structural carbohydrates (NSC), thus regulating xylem hydraulics and growth. However, despite the importance of rays for tree carbon and water relations, methodological challenges hamper knowledge about ray intra- and inter-tree variability and its ecological meaning. In this study we provide a methodological toolbox for soundly quantifying spatial and temporal variability of different ray features. Anatomical ray features were surveyed in different cutting planes (cross-sectional, tangential, and radial) using quantitative image analysis on stem-wood micro-sections sampled from 41 mature Scots pines (Pinus sylvestris). The percentage of ray surface (PERPAR), a proxy for ray volume, was compared among cutting planes and between early- and latewood to assess measurement-induced variability. Different tangential ray metrics were correlated to assess their similarities. The accuracy of cross-sectional and tangential measurements for PERPAR estimates as a function of number of samples and the measured wood surface was assessed using bootstrapping statistical technique. Tangential sections offered the best 3D insight of ray integration into the xylem and provided the most accurate estimates of PERPAR, with 10 samples of 4 mm2 showing an estimate within ±6.0% of the true mean PERPAR (relative 95% confidence interval, CI95), and 20 samples of 4 mm2 showing a CI95 of ±4.3%. Cross-sections were most efficient for establishment of time series, and facilitated comparisons with other widely used xylem anatomical features. Earlywood had significantly lower PERPAR (5.77 vs. 6.18%) and marginally fewer initiating rays than latewood. In comparison to tangential sections, PERPAR was systematically overestimated (6.50 vs. 4.92%) and required approximately twice the sample area for similar accuracy. Radial cuttings provided the least accurate PERPAR estimates. This evaluation of ray parenchyma in conifers and the presented guidelines regarding data accuracy as a function of measured wood surface and number of samples represent an important methodological reference for ray quantification, which will ultimately improve the understanding of the fundamental role of ray parenchyma tissue for the performance and survival of trees growing in stressed environments.

Application of white cellulose acetate sheets on fossil wood investigation

Generally, transparent cellulose acetate sheets as a peel technique material are used in the identification of fossils, whereas white cellulose acetate sheets as a biochemistry technique material are applied in serum protein electrophoresis (SPE). Here we report the application of white cellulose acetate sheets for identifying a polished fossil wood from the Upper Mesozoic of West Liaoning, China. Based on the characters of transverse, radial, and tangential sections, the fossil wood is ascribed to a taxon of Protoglyptostroboxylon sp. Compared with transparent cellulose acetate sheets, white cellulose acetate sheets not only provide the similar information as that of the former, but also are more easily acquired in the Chinese market than the former. Because peel technique supported by white cellulose acetate sheets has the advantages of simple, time-saving, safe, reliable, and practical operation with lower material loss, it is a very good choice for the polished fossil wood investigation in labs, museums, geological parks, and handicraft shops. It is also a convenient approach to training students to learn the anatomic structure of fossil wood.

Anatomical changes in the cell-wall structure of Leucaena leucocephala (Lam.) de Wit as caused by the decay fungi Trametes versicolor and Trametes hirsuta

The structural changes in the cell wall and delignification pattern caused by Trametes versicolor and Trametes hirsuta in the sap wood of Leucaena leucocephala were examined by light and confocal laser scanning microscopy. The in vitro decay test was conducted for 12 weeks. Both species of Trametes used in this study caused anatomical characteristics specific to simultaneous white rot. Formation of boreholes, erosion troughs, erosion channels with U-shaped notches in tangential sections and thinning of cell walls were evident in the wood inoculated with each of the fungal species. Cell separation due to removal of middle lamellae occurred at the early stages of infection (30 d) with T. versicolor. In contrast, middle lamellae remained intact in wood inoculated with T. hirsuta and showed cell separation due to degradation of the outer layer of the secondary wall and degradation of the middle lamellae observed only in severely decayed wood at late stages. Confocal microscopy revealed the delignification pattern particularly from cell corners and vessel walls at an advanced stage of decay, indicating strong ligninolytic activity of both species in the sapwood of L. leucocephala.

New data about anatomy, branching, and inferred growth patterns in the Early Devonian plant Armoricaphyton chateaupannense, Montjean-sur-Loire, France

This study provides detailed information, based on serial peels, on the anatomy of the primary and secondary xylem, lateral branch formation, and proposed growth pattern of Armoricaphyton Strullu-Derrien et al., an Early Devonian (Pragian) basal euphyllophyte. The centrarch primary xylem strand is circular to oval in cross section and includes P-type tracheids. The pattern of lateral branch departure is described in detail based on serial peels. The secondary xylem, illustrated in transverse, radial and tangential longitudinal sections, includes P-type tracheids with similar pitting in radial and tangential walls. The presence of one-walled spaces interpreted as rays is confirmed. This study also documents the earliest occurrence of secondary xylem at bases of next higher order of branches. A model of growth for this unusual Early Devonian plant is presented, with documented epidogenetic, menetogenetic and possible apoxogenetic phases. The difference in proportion of primary to secondary xylem is postulated to be a result of this mode of growth. The possible implications of xylem size and organization in the lateral organ in Armoricaphyton relative to the early evolution of the megaphyllous leaf are briefly discussed.

Study on origin and authentication of medicinal materials of Dalbergiae Lignum in crude drug's market

The study is aimed to distinguish morphological characteristics of Dalbergiae Lignum collected from crude drug's markets and establish a identification methods and the quality standard for Dalbergiae Lignum. The macroscopic and microscopic features of Dalbergiae Lignum from crude drug's market were observed, analyzed and compared according to Hongmu specification issued by the People's Republic of China in 2000, and by the characteristics recorded in domestic monograph of Mucai Shibie (wood identification). The redwood of Dalbergiae Lignum cut into small pieces as medicinal material are dry heart wood of mahogany (trees from Dalbergia sp.), which characteristics of the small pieces as crude drug are different. There are differences in macroscopic and microscopic features about texture of wood and color, odor, taste, transverse section, radial section, tangential section. The results can provide basis for identification, application and improment of the quality standard of Dalbergiae Lignum as medicinal material.

Fabrication of smart coatings based on wood substrates with photoresponsive behavior and hydrophobic performance

Abstract A smart coating based on wood substrate with photochromic behavior and hydrophobic performance was successfully fabricated by depositing modified organic photochromic material (PM) on wood surface using a simple drop-coating method. The prepared samples were characterized by the scanning electron microscopy (SEM) and attenuated total reflectance–Fourier transformation infrared (ATR–FTIR) techniques. The colorimetric parameters L *, a *, b *, and Δ E * of the samples under ultraviolet (UV) irradiation and visible (VIS) irradiation were measured, respectively. The response time of samples was calculated and the water contact angles (CAs) were also measured. The ATR–FTIR spectra and the SEM analysis demonstrate that PM modified by polyvinyl alcohol and the dextrin deposited on the wood surface, and the resulted coating was firmly adhered to wood by adhesion test results. With the PM concentrations increasing from 0 to 3.0%, the Δ E * values of samples remarkably increased from 3.7 to 58.2. Furthermore, the coloration time and fading time in the cross section were longer than the radial and tangential sections. Through the octadecyltrichlorosilane (OTS) treatment, the sample surface exhibited hydrophobic property with a contact angle of 134°, broadening the applications of the photoresponsive coatings in a harsh environment such as prolonged exposure under UV light or rain.

Identification of Pottery‐Forming Techniques using Quantitative Analysis of the Orientation of Inclusions and Voids in Thin Sections

The relationship between forming techniques and orientation of the components of ceramic materials in the context of pottery technology has long been recognized and used for identification of the techniques employed to create archaeological ceramics. The alignment of inclusions is usually characterized by qualitative categories or ordinal scales. This paper evaluates the potential of quantitative orientation analysis for identification of pottery‐forming techniques. A collection of experimental pottery formed using five forming techniques and combined techniques was analysed. The forming techniques were characterized by the intervals of the mean direction and the circular standard deviations of the orientation of the major axes of the ellipses equivalent to the objects representing random sections of inclusions and voids. The most informative criteria for the identification of pottery techniques are the circular standard deviation of the inclusion/void orientations in the core area of the vessel wall in a perpendicular thin section and the mean direction in a tangential section.

Possibilities and limits of imaging endodontic structures with CBCT.

An adequate portrayal of the root canal anatomy by diagnostic imaging is a prerequisite for a successful diagnosis and therapy in endodontics. The introduction of dental cone beam computed tomography (CBCT) has considerably expanded the scope of imaging diagnostics. The aim of the following study was to evaluate the imaging of endodontic structures with CBCT. One hundred and twenty teeth were examined with a CBCT device (ProMax 3D). Subsequently, the findings of the three-dimensional images were evaluated and compared to those of dental radiographs and tangential section preparations of the examined teeth. Results with high prevalence, such as existing roots and root canals, as well as results with low prevalence, e.g., extremely fine anatomical structures of the endodontic tissue, could be visualized precisely by dental CBCT; side canals, ramifications, communications, pulp stones, and obliterations could also be detected. Additionally, the length of curved root canals could be determined accurately. Likewise, root fractures were visualized reliably with CBCT. However, carious lesions could not be diagnosed adequately, and the evaluation of fillings and prosthetic restorations was complicated due to scattered X-ray artifacts. CBCT datasets qualify to visualize and diagnose small anatomical structures of the endodontic tissue.

Determination of the tangential surface profile of Toroidal beam line mirrors with polarization phase-shifting Twyman–Green interferometer

A new technique for the measurement of the tangential surface profile of Toroidal mirrors (TMs) used in synchrotron radiation beam lines is proposed. A cylindrical lens placed in the collimated input (He–Ne laser) beam of a polarization Twyman–Green interferometer (TGI) forms line foci in the reference and test arms. The effect of the sagittal curvature of the TM is eliminated by adjusting a line focus on the surface of the TM, along the central tangential section. Thus, a toric test wavefront (TTW) with sagittal curvature identical to that of the incident cylindrical wavefront and tangential curvature with slope twice that of the TM, is produced along the reflection direction. The TTW interferes with a reference cylindrical wavefront, generated by retroreflecting the incident cylindrical wavefront from a reference plane mirror in the reference arm of the TGI and having identical curvature in the sagittal direction. Polarization phase-shifting interferometry has been applied to obtain the tangential surface profile of the test TM. Results are compared with other methods. The advantages of the technique are that only a plane reference mirror is needed to generate the reference beam, and the technique is suitable for TMs with long tangential radii of curvature in the kilometer regime.

Analysis of Hyperbolic Transition Curve Geometry

After the description of the basic geometry and relationships of the hyperbolic transition curve geometry we made further analysis. In this paper we analyzed the possible minimal length of the transition curve based on the dynamical characteristics. We determined the relationship between the dynamical parameters and the p parameter of the transition curve. For transition curves between tangential sections and curves we compared the minimal lengths of the hyperbolic geometry to the clothoide and cosine ones. The results show that according to the considered regulations the hyperbolic geometry gives shorter transition curve length. This has significant practical consequences as it makes the design more flexible.

Co-localization of glutamic acid decarboxylase and vesicular GABA transporter in cytochrome oxidase patches of macaque striate cortex.

The patches in primary visual cortex constitute hot spots of metabolic activity, manifested by enhanced levels of cytochrome oxidase (CO) activity. They are also labeled preferentially by immunostaining for glutamic acid decarboxylase (GAD), γ-aminobutyric acid (GABA), and parvalbumin. However, calbindin shows stronger immunoreactivity outside patches. In light of this discrepancy, the distribution of the vesicular GABA transporter (VGAT) was examined in striate cortex of two normal macaques. VGAT immunoreactivity was strongest in layers 4B, 4Cα, and 5. In tangential sections, the distribution of CO, GAD, and VGAT was compared in layer 2/3. There was a close match between all three labels. This finding indicates that GABA synthesis is enriched in patches, and that inhibitory synapses are more active in patches than interpatches.

Possibilities and limits of imaging endodontic structures with CBCT.

An adequate portrayal of the root canal anatomy by diagnostic imaging is a prerequisite for a successful diagnosis and therapy in endodontics. The introduction of dental cone beam computed tomography (CBCT) has considerably expanded the scope of imaging diagnostics. The aim of the following study was to evaluate the imaging of endodontic structures with CBCT. One hundred and twenty teeth were examined with a CBCT device (ProMax 3D). Subsequently, the findings of the three-dimensional images were evaluated and compared to those of dental radiographs and tangential section preparations of the examined teeth. Results with high prevalence, such as existing roots and root canals, as well as results with low prevalence, e.g., extremely fine anatomical structures of the endodontic tissue, could be visualized precisely by dental CBCT; side canals, ramifications, communications, pulp stones, and obliterations could also be detected. Additionally, the length of curved root canals could be determined accurately. Likewise, root fractures were visualized reliably with CBCT. However, carious lesions could not be diagnosed adequately, and the evaluation of fillings and prosthetic restorations was complicated due to scattered X-ray artifacts. CBCT datasets qualify to visualize and diagnose small anatomical structures of the endodontic tissue.

Mechanism of changes in grain inclination in wood produced by storeyed cambium

The changes in cell orientation in the cambium of <i>Entandrophragma</i> producing wood with interlocked type of grain, and in the cambium of <i>Tilia</i> in a spirally girdled stem are traced through serial tangential sections of wood. In <i>Entandrophragma</i> the changes result from the intrusive growth of a fusiform cell whih repeatedly produces a new pointed tip from one side of the existing tip which disappears. This causes a sort of creeping of cell ends of one storey past those of the adjoining storey. The oppositely directed ends of the cells belonging to one storey creep in opposite directions so that the position of the cell centres remains constant and only the angle between the cells and the stem axis changes. The stratification of short rays in <i>Entandrophragma</i> represents an adaptation to the changes in celi orientation involved in the formation of interlocked grain. The mechanism of changes in grain inclination in <i>Tilia</i> is intermediate between that based on the creeping of cell ends and that based on pseudotransverse division and intrusive elongation which is known in non-storeyed cambia.

Visual Interhemispheric and Striate-Extrastriate Cortical Connections in the Rabbit: A Multiple Tracer Study.

Previous studies in rabbits identified an array of extrastriate cortical areas anatomically connected with V1 but did not describe their internal topography. To address this issue, we injected multiple anatomical tracers into different regions in V1 of the same animal and analyzed the topography of resulting extrastriate labeled fields with reference to the patterns of callosal connections and myeloarchitecture revealed in tangential sections of the flattened cortex. Our results extend previous studies and provide further evidence that rabbit extrastriate areas resemble the visual areas in rats and mice not only in their general location with respect to V1 but also in their internal topography. Moreover, extrastriate areas in the rabbit maintain a constant relationship with myeloarchitectonic borders and features of the callosal pattern. These findings highlight the rabbit as an alternative model to rats and mice for advancing our understanding of cortical visual processing in mammals, especially for projects benefiting from a larger brain.

Cell events i n cambium, connected with the formation and existence of a whirled cell arrangement

The history of cambium development was reconstructed on the basis of serial tangential sections of a woody tumour of <i>Picea excelsa</i> (Lam.) Lk. On the area with whirled arragement of the tracheids intrusive growth was found to occur at the lateral radial and longitudinal edges apart from its normal occurrence at the radial apical edges. Intrusive .growth at the radial lateral edge leads to forking of the fusiform initial in the cambium plane. The growth which appears on longitudinal lateral edges oocurs between the tangential walls of cells in neighbouring storeys. In such places a drastic reconstruction of the cell arrangement in neighbouring annual rings was observed. Intrusive growth. between the tangential walls leads to a whirled arrangement of tracheids.

Use of wood characters in the Identification of Terminalia spp in Sri Lanka

250 timber species are being used by the timber industry in Sri Lanka and among them major timber consumers are housing developer, furniture manufacturer and wood fabricators. Once the tree is felled, the identification of the tree become very difficult and need of relying on their macroscopic/ microscopic features and physical properties of timber become necessary. Timber identification is necessary for right use of timber and to check on fraud in timber trading as some timber traders mix or sell low price different type of timber species deceiving customers implying them to be valuble timbers in order to increase their profit margin. 0 Five timber species of Terminalia namely Terminalia arjuna (Kumbuk), Terminalia bellirica (Bulu), Terminalia catappa (Kottamba), Terminalia chebula (Aralu) and Terminalia parviflora (Hampalanda) of the family of Combretaceae were studied anatomically in search of sufficient features by which one Terminalia sp can be separated from the other . The examination of the transverse section of wood with a hand lens (x25) does not provide adequate reliable information to differentiate one species from the other for identification due to resemblance of wood structure of five Terminalia spp. Hence for the anatomical examination, transverse section (T.S.), radial longitudinal section (R.L.T.) and tangential longitudinal section (T.L.S.) were obtained using the microtome. In this study, some important wood anatomical and non anatomical features were studied according to IAWA ( 1989). It was found that all the Terminalia spp had diffuse porous wood having vessels mainly solitary and occasionally in 2 -3 vessels of radial multiples. Mean vessel diameter and vessel diameter range were recorded respectively as 241 µm and 172-331 µm in Terminallia arjuna, 169 µm and 107-204 µm in Terminalia bellirica , 240 µm and 169-309 µm in Terminallia catappa, 115 µm and 68-175 µm inTerminalia chebula and 124 µm and 75-159 µm in Terminalia parviflora. Mean vessel frequency were observed as 3 per mm2 in Terminallia arjuna, 4 per mm2 in Terminalia bellirica , 3 per mm2 in Terminallia catappa, 6 per mm2 in Terminalia chebula and 5 per mm2 in Terminalia parviflora. Mean rays frequency, mean ray height and mean ray width were found respectively as 9 per mm, 206 µm, 24 µm in Terminallia arjuna, 11 per mm, 283 µm, 24 µm in Terminalia bellirica , 8 per mm, 280 µm, 25 µm in Terminallia catappa, 13 per mm, 239 µm, 31 µm in Terminalia chebula and 10 per mm, 235 µm, 30 µm in Terminalia parviflora. Ray cell arrangement is mostly uniseriate and occasionally byseriate in Terminalia bellirica, Terminalia parviflora, Terminallia arjuna. Ray cell arrangement is mostly multiseriate and occasionally uniseriate in Terminallia catappa. Terminalia chebula has uniseriate ray cell arrangment . Different type of axial parenchyma types were found in each terminalia species from which the prominent type of axial parenchyma was identified from each species as follows; Terminalia bellirica had axial parenchyma band (more than three cells wide). Terminalia parviflora and Terminalia catappa had aliform/ vasicentric type axial parenchyma which can be differentiated from confluent parenchyma type in Terminalia chebula . Vasicentric (halo) parenchyma type were found mainly in Terminallia arjuna. Finally, It can be concluded that ray cell arrangement and axial parenchyma types can be used together as baseline to distinguish Terminalia spp in Sri Lanka for the purpose of timber identification.

Anatomical studies on two species of Dracaena in southeastern Nigeria

Anatomical studies of transverse, tangential and radial longitudinal sections of roots, stems and leaves of two species of Dracaena present in southeastern Nigeria were investigated, to determine their anatomical features with regards to arrangement of vascular bundles in their roots, stems and leaves and type of secondary growth occurring in them using standard method. T- test was used for the analyses. Result showed that the number of vascular bundles in the leaves and roots of D. arborea are more in number than those of D. mannii but the reverse is the case in the stem. Secondary growth occurs in both D. mannii and D. arborea. The overall analyses showed no significant statistical difference in the anatomy of the two Dracaena species. The implication is that the two species are closely related and this justified their placement under the same genus Dracaena while the slight differences between them suggest the reason for their separation into different species.

3D image analysis of plants using electron tomography and micro-CT.

Precise control of the cell division plane is a prerequisite for plant development. The division site (the position of the division plane insertion) in plant cells is the site along which the cell plate margin joins the parental cell walls. How this division site is determined and established during cell division is an essential question in plant morphogenesis. Herein we demonstrate how computer tomography techniques can aid in understanding nano-machines involved in determination of the division site and in analysing air space development after cytokinesis. The preprophase band (PPB) is a cytokinetic nano-machine used to determine the plant division site. The PPB appears as a broad microtubule (MT) band in the G2 phase and the MT band narrows during the prophase to establish the specialized belt zone in the cell cortex (cortical division zone, [CDZ]). The MT band disappears at prometaphase, but some memories remain in the CDZ throughout the process of cell division, and this is the site of attachment of the newly formed cell plate. We have examined PPB development of high-pressure frozen onion cotyledon epidermis using dual-axis electron tomography. MTs as well as actin microfilaments (MFs) and membrane systems can be preserved well by high-pressure freezing [1]. Since detection of ∼100 vesicles and ∼40 MT ends was possible in a tomogram of the PPB surface (0.25 mm × 0.25 mm) obtained from 250-nm-thick tangential sections of epidermal cells, we were able to quantitatively analyze the frequencies of various types of vesicles and MT ends in the PPB [2]. The results clearly showed that endocytosis is active [2,3] and MTs are very dynamic in the late PPB. Light microscopic studies with fluorescent probes have demonstrated that actins are among the main components of PPB. Electron tomography analysis showed that one actin configuration in the PPB is a relatively short single MFs running parallel to the plasma membrane. The actin MFs connecting two adjacent MTs help to promote MT bundling. Cell plate attachment to the parental wall leads to the fusion of the newly formed middle lamellae in the cell plate to the middle lamella of parental cell wall, and a three-way junction is created. Air space develops from the three-way junction. To determine 3D arrangement of cells and air spaces, we used X-ray micro-CT at the SPring-8 synchrotron radiation facility. Using micro-CT available in BL20XU (8 keV, 0.2 µm/pixel), we were able to elucidate ∼90% of the cortical cell outlines in the hypocotyl-radicle axis of arabidopsis seeds [4] and to analyze cell geometrical properties. As the strength of the system X-ray is too strong for seed survival, we used another beam line BL20B2 (10-15 keV, 2.4-2.7 µm/pixel) to examine air space development during seed imbibition [4,5]. Using this system, we were able to detect air space development at the early imbibition stages of seeds without causing damage during seed germination. AcknowledgmentThe author would like to thank Dr. Ichirou Karahara (Univ. Toyama), Dr. L. Andrew Staehelin (Univ. Colorado), Ms. Naoko Kajimura, Dr. Akio Takaoka (Osaka Univ.), Dr. Kazuyo Misaki, Dr. Shigenobu Yonemura (RIKEN CDB), Dr. Kazuyoshi Murata (NIP), Dr. Kentaro Uesugi, Dr. Akihisa Takeuchi, Dr. Yoshio Suzuki (JASRI), Dr. Miyuki Takeuchi, Dr. Daisuke Tamaoki, Dr. Daisuke Yamauchi, and Ms. Aki Fukuda (Univ. Hyogo) for their collaborations in the work presented here.

Evaluation of microvasculature at the auditory midbrain--the benefits of sectioning at a tangential angle.

Vascular remodeling in the brain occurs as a plastic change following neural over-activity. The auditory midbrain (or inferior colliculus, IC) is an ideal place to study sound-induced vascular changes because it is the brain's most vascularized structure and it is tonotopically organized. However, its micro-vascular pattern remains poorly understood. Since the IC is a sphere-like structure, the histological assessment of vasculature could depend on the angle of sectioning. Here, we studied the effects of cutting the IC at different angles on microvascular assessment, specifically: micro-vascular density and the shape of microvascular lumen. Photomicrographs were taken from 5 µm toluidine blue-stained histological sections obtained at two angles of sectioning: (a) the conventional coronal sectioning, and (b) a novel "tangential" sectioning (tangential to the dorso-medial surface of the IC). Results showed that the tangential sections, in comparison with the coronal sections, yielded (a) a higher count of micro-vascular density and (b) a higher proportion of round-shaped micro-vascular lumens. This discrepancy in results between two cut angles is likely related to the spatial pattern of blood vessels supplying the IC. We propose that the tangential sectioning should be adopted as standard for the accurate study of microvasculature in the IC.

Segmental differences in the orientation of smooth muscle cells in the tunica media of porcine aortae.

The orientation of vascular smooth muscle cells of porcine aortae was assessed to test the widely accepted assumption that these smooth muscle cells are arranged in two helices. We used tangential histological sections of 82 samples of five anatomical segments of thoracic and abdominal porcine aortae and three age groups in animals ranging in age from 5 to 210 days. The distribution of the orientation of smooth muscle cell nuclei in five proximodistal segments of the porcine aortae was determined using an algorithm that fitted a mixture of one to five von Mises probability distributions of the data retrieved from histological micrographs. Automated tracking of the nuclei was confirmed by and consistent with manual histological analysis. The orientation of the vascular smooth muscle cells was successfully fitted using two von Mises distributions in most of the samples with different ages, wall thicknesses, and anatomical positions, which corresponds to two populations of vascular smooth muscle cells. A minor fraction of samples also required a tertiary von Mises distribution to describe the orientation of the smooth muscle cell nuclei. The distribution of vascular smooth muscle cells in five aortic segments ranging from the thoracic ascending aorta to the abdominal intrarenal aorta exhibited similar main directions but different shapes. These results are consistent with the widely used model of two muscular helices intermingling in the arterial wall. Furthermore, we calculated the central angles of symmetry and the mean value of angles between the two assumed smooth muscle directions. We also successfully approximated the orientation of the smooth muscle cells using a mixture of von Mises distributions and our open-source software named dist_mixtures. This method is openly available to researchers who are interested in mathematically assessing the orientation of cell nuclei in various tissues.