What about limb long bone nutrient canal(s)? – a 3D investigation in mammals

Abstract

The nutrient arteries, located in the long bone diaphysis, are the major blood supply to long bones, especially during the early phases of growth and ossification. Their intersection with the central axis of the medullary area corresponds to the ossification center, and their opening on the outer bone surface to the nutrient foramen. Nutrient arteries/foramen have essentially been analyzed in humans, and only to a much lesser extent in a few mammals. Some studies have taken measurements of the nutrient foramen; others have investigated the shape and orientation of the nutrient canals, although only partially. No studies have analyzed the nutrient canal in three dimensions inside the bone and the relationships between nutrient foramen, nutrient canal, growth, and physiology require further investigation. The current study proposes to investigate in three dimensions the shape of the nutrient canal in stylopod bones of various mammals. Qualitative and quantitative parameters are defined to discuss the diversity in, for example, morphology, orientation, and diameter encountered, resorting to two different datasets to maximize differences within mammals and then analyze variation within morphologically and phylogenetically closer taxa. This study highlights a strong intraspecific variation for various parameters, with limited biological signal, but also shows trends. It notably provides evidence that canals are generally more numerous and relatively thinner in less elongated bones. Moreover, it shows that the growth center is located distally in the humerus and proximally in the femur, and that the canals are essentially oriented towards the faster growing end, so that the nutrient foramen does not indicate the location of the growth center. This result seems general in mammals but cannot be generalized outside of Mammalia. Further analyses of the features of nutrient arteries in reptiles are required to make comparisons with the trends observed in mammals.

This study proposes qualitative and quantitative parameters to describe the shape of the nutrient canal in three dimensions in stylopod bones of various mammals. It discusses the diversity in e.g., morphology, orientation, and diameter encountered, within a single bone, species and between taxa.

Introduction

Bone is a mineralized connective tissue constituting the skeleton, which provides support and protection, and enables locomotion. Bones can notably be distinguished based on their position within the skeleton and their shape. Limb long bones occur in the stylopod (e.g. femur) and zeugopod (e.g. tibia) regions of the limbs. They are morphologically divided into a shaft bounded by both proximal and distal ends, called epiphyses (with intermediate metaphyses). The diaphysis of long bones is often (but not always) tubular, i.e. compact bone deposits surround a medullary cavity devoid of bone deposits. Conversely, epiphyses are generally spongy (Carter & Beaupré, 2007). Long bones form through two distinct modes of ossification: periosteal, i.e. direct ossification in the periosteum (membrane covering the outer surface of the bone), and endochondral, i.e. following the resorption of a preformed cartilaginous structure (Ross & Pawlina, 2011). In long bones, after the formation of a cartilage model, periosteal bone deposits laterally and centrifugally. The cartilage inside the shaft starts calcifying and blood vessels invade the calcified cartilage. Then resorption occurs and a primary center of ossification develops, from which endochondral ossification starts proximally and distally centrifugally, with synchronous periosteal bone deposition (laterally) (Carter & Beaupré, 2007). The development of secondary centers of ossification in the epiphyses can develop, depending on the taxa (e.g. it occurs in mammals and lepidosaurs but not in turtles or crocodiles; Haines, 1969).

Nutrient foramina are openings through which blood vessels and peripheral nerves connect to the marrow. If there are epiphyseal and metaphyseal arteries, the nutrient arteries are located in the long bone diaphysis. The nutrient arteries are the major blood supply to long bones, especially during the early phases of growth and ossification (Gümüsburun et al. 1994). The ossification center is considered to correspond to the point in the center of the medullary cavity that is reached by the imaginary prolongation of the nutrient canal(s) (Digby, 1916).

If growth is fast symmetrical in the proximal and distal directions, the growth center is localized around the mid‐shaft. Asymmetrical proximo‐distal growth has been reported since the 18th century (Ollier, 1867; Payton, 1932; Bisgard & Bisgard, 1935), with either a rather constant position in a given bone (Pereira et al. 2011) or not (Campos et al. 1987). Moreover, several studies mentioned the occurrence of several nutrient canals (Mysorekar, 1967; Sendemir & Cimen, 1991; Gümüsburun et al. 1994) or the absence of nutrient canals (Longia et al. 1980); these studies did not note any significant relationship between the number of nutrient canals and the bone length, or the number of ossification centers (Patake & Mysorekar, 1977). The number of nutrient canals seems to greatly vary intraspecifically for a given bone (Sendemir & Cimen, 1991; Pereira et al. 2011).

The nutrient arteries are supposed to enter the bone through a discrete foramen, the nutrient foramen, on the diaphysis. This nutrient is considered originally to indicate the position of the growth center; however, when the shaft extends asymmetrically in length, it becomes proximally or distally located relative to the growth center (Hughes, 1952). Considering the possible occurrence of several nutrient foramina and the asymmetrical proximo‐distal growth, the relationship of nutrient foramen, nutrient canal, and growth center requires further investigation.

Aside from information about growth mode, the nutrient canals are also supposed to carry physiological information. Some studies have indeed concluded that a greater blood pressure causes a thickening and strengthening of the walls, as well as an increase in the circumference of vascular canals (Seymour et al. 2011). The nutrient canal could thus be larger in taxa showing a higher metabolic rate.

Nutrient arteries/foramina have essentially been analyzed in humans, and only to a much lesser extent in a few mammals (e.g. Ahn, 2013, in dogs). They have also been visualized in a few turtles (Nakajima et al. 2014). Some studies have taken measurements of the nutrient foramen (Seymour et al. 2011), and others have investigated the shape and orientation of the nutrient canals but only partially, for example using needles inserted through the nutrient foramen to get insights into the diameter (considering the diameter of the largest needle that could be inserted more than 1 cm deep) and the orientation (penetration direction of the needle; Sim & Ahn, 2014), but no study has analyzed the nutrient canal in three dimensions inside the bone.

The current study proposes to investigate the shape of the nutrient canals in stylopod bones of various mammals. It proposes a definition of qualitative and quantitative parameters to discuss the diversity in morphology, orientation, and diameter, etc. We resorted to two different datasets to maximize variation within mammals and then analyze variation within morphologically and phylogenetically closer taxa. This enabled us to discuss the growth mode of the stylopod bones in various mammals, looking for general trends. This study also permits investigation of the biological signal of some features of the nutrient canals. Finally, we discuss the relative degree of interspecific and intraspecific variation observed.

Materials and methods

Material

The material includes humeri and femora from two datasets (see Table 1) already available from previous studies (Houssaye et al. 2018; Houssaye & Botton‐Divet, 2018), and representing adult specimens. The first one (hereafter referred to as QM) consists of 15 quadrupedal mammal species of various sizes, morphologies, locomotor modes, and that are widespread on mammal phylogeny (see Table 1). The aim of this sample is to show diversity, despite a limited sample size. The other sample (hereafter referred to as MU) is more restricted (e.g. in morphology, size, and phylogenetic position). It focuses on mustelids, with 10 species (three in common with the previous sample) illustrating diverse degrees of adaptation to an aquatic lifestyle (terrestrial, semi‐aquatic, aquatic).

Table 1.

List of the material analyzed in this study.

Family	Taxon	Abb.	Dataset	Collection Nb.	Bone
Caviidae	Cavia porcellus	Cp	QM	STIPB Unnumbered	F
Sciuridae	Marmota marmota	Mma	QM	STIPB Unnumbered	H,F
Tupaiidae	Tupaia belangeri	Tb	QM	STIPB Unnumbered	H,F
Erinaceidae	Erinaceus europaeus	Ee	QM	STIPB Unnumbered	H,F
Talpidae	Talpa europaea	Te	QM	STIPB Unnumbered	H,F
Suidae	Sus scrofa	Ss	QM	STIPB M56	H,F
Hippopotamidae	Choeropsis liberiensis	Cl	QM	ZFMK 65 570	H,F
Cervidae	Rangifer tarandus	Rt	QM	STIPB M47	H,F
Cervidae	Dama dama	Dd	QM	STIPB M1	H
Bovidae	Rupicapra rupicapra	Rr	QM	STIPB M1639	H,F
Felidae	Felis silvestris	Fs	QM	UFGK Unnumbered	H,F
Canidae	Vulpes vulpes	Vv	QM	STIPB M12	H,F
Mustelidae	Meles meles	Mme	QM MU	STIPB M4002	H,F
Mustelidae	Martes martes	Mm	QM MU	STIPB Unnumbered	H,F
Mustelidae	Mustela putorius	Mp	QM MU	STIPB Unnumbered	H,F
Mustelidae			MU	MNHN 1997‐440	H,F
Mustelidae			MU	MNHN 2004‐639	H,F
Mustelidae	Mustela eversmannii	Me	MU	MNHN 2005‐668	H,F,F
Mustelidae	Neovison vison	Ne	MU	MNHN 1958‐165	H,F,F
Mustelidae	Pteronura brasiliensis	Pb	MU	MNHN A1918	H,F
Mustelidae			MU	SMNS 1300	H,F,F
Mustelidae	Lontra felina	Lf	MU	MNHN 1884‐874	H,F
Mustelidae			MU	MNHN 1995‐185	H,F,F
Mustelidae	Lontra canadensis	Lc	MU	UAM 53927	H,F
Mustelidae			MU	UAM 67696	H,F
Mustelidae	Lutra lutra	Ll	MU	MNHN 1996‐2466	H,F
Mustelidae	Enhydra lutris	El	MU	MNHN 1935‐124	H,F
Mustelidae			MU	MNHN A12503	H,F

Abb., abbreviations, later used in figures; F, femur; H, humerus; MU, dataset of the mustelids; QM, dataset of the various quadrupedal mammal species. Institutional abbreviations: MNHN, Museum national d’Histoire naturelle, Paris, France; SMNS, Staatliches Museum für Naturkunde Stuttgart, Stuttgart, Germany; STIPB, Steinmann‐Institut, Universität Bonn, Bonn, Germany; UAM, the University of Alaska Museum, Fairbanks, AK, USA; UFGK, Ur‐ und Frühgeschichte Köln, Cologne, Germany; ZFMK, Zoologisches Forschungsmuseum Alexander Koenig, Bonn, Germany.

Methods

Data acquisition

Bones were scanned using high‐resolution computed tomography (GE_phoenix∣X‐ray v∣tome∣xs 240) at the Steinmann‐Institut, University of Bonn (Bonn, Germany) and at the AST‐RX platform at the Museum national d’Histoire naturelle, Paris (France), with reconstructions performed using DATOX/RES software. Voxel size naturally varies pending on specimen size, from 19 to 246 µm. Image segmentation and visualization were performed from the reconstructed image data using avizo 9.4 (VSG, Burlington, MA, USA).

The nutrient canals were segmented. The limits of the canals were difficult to fix clearly: at the outer surface, notably because of the obliquity of the canal; in the medullary area, because of bone resorption. Some canals were located more distally or proximally on the bone and not linked to the diaphyseal growth center; they thus appeared rather as metaphyseal or epiphyseal canals and were not taken into consideration.

Data analysis

The following parameters (listed in Supporting Information Table S1) were defined qualitatively and quantitatively to characterize the nutrient canals:

• The number of nutrient canals in the bone (NNC).

• Mean diaphyseal radius (R), averaged for the whole diaphysis, based on the averaged sectional area (averaged CSA parameter in bonej), as √(averaged CSA/π).

• The foraminal index (FI): this index was defined by Hughes (1952) to estimate the relative position of the nutrient foramen on the bone; it is calculated as the ratio of the distance between the proximal extremity of the bone and the nutrient foramen (d) over the bone total length (L) (Kizilkanat et al. 2007). Because some epiphyses were incomplete (on the scans), the missing part was estimated based on comparisons with similar bones (e.g. on ArchéoZoothèque; https://www.archeozoo.org), and the points chosen to calculate the distances do not correspond to the most extreme points. In the humerus, the proximal point corresponds to the most distal point between the humeral head and the greater tubercle on the proximal surface; the distal point corresponds to the core of the trochlea. In the femur, the proximal point is the most distal point between the femoral head and the greater trochanter and the distal point is located at the core of the patella groove (Fig. 1).

• Canal diameter (CD), calculated based on the mid‐canal sectional area (CA) obtained in artec studio professional v12.1.5.1 software (Artec 3D2018) with the measuring tool ‘section’, as √(CA/π). The parameter is calculated at the mid‐length of what is preserved (not resorbed) of the canal walls, the section of the canal being usually rather constant except around its extremities.

• Canal diameter at the outer extremity (CDE), to take into consideration the variation of the canal diameter along its length, calculated as for CD but based on the most external section perpendicular to the canal.

• Canal obliquity (CO): this parameter had previously been analyzed based on the insertion of a needle in the canal and the measurement of the angle between the needle and the long bone longitudinal axis (Sim & Ahn, 2014). Here since we have access to the 3D organization of the canal and sometimes observed orientation changes along the canal, we measured the general obliquity as the angle between a line linking the canal extremities as preserved and the horizontal to the bone longitudinal axis.

• Canal cortical height (H): representing the relative height of the reconstructed canal (which could essentially be reconstructed in the cortex) divided by the bone length as measured for FI. Parameters linked to canal length (and thus also volume) could not be obtained because of resorption occurring in the medullary area. Two additional parameters were defined to estimate the bone length and shape: L – bone length, as measured for FI; and LR – bone length (L) divided by the bone mean diaphyseal radius (R).

Figure 1.

3D reconstructions showing how the foraminal index (FI) was calculated for the nutrient canal (in purple), based on bone length (L) and the distance between the proximal extremity and the nutrient foramen (d). (A) Humerus of Rangifer tarandus STIPB M47. (B) Femur of Mustela eversmannii MNHN 2005‐668. Not to scale.

In addition to these quantitative parameters, some qualitative ones were also defined:

• direction: proximal to distal (PD) or distal to proximal (DP);

• shape: defining the global shape of the canal: straight or angled;

• orientation: describing the anatomical orientation of the canal in the bone.

We tested the phylogenetic signal of the continuous parameters in the data. For that, we averaged the values obtained for all canals (when several canals occurred) and all specimens (when several specimens were available) for each species. We then calculated the K‐statistic following Blomberg et al. (2003) for each parameter and performed randomization tests. The K‐statistic compares the observed phylogenetic signal in a trait with the signal under a Brownian motion model of trait evolution. A K‐value > 1 implies more similarity between relatives than expected under Brownian motion; K < 1 highlights convergences. We used the phylogeny from Meredith et al. (2011) and Slater et al. (2012) for the quadrupedal mammal (QM) and mustelid (MU) samples, respectively (Supporting Information Fig. S1).

We tested the influence of size on all parameters, first on all canals independently, then for each specimen, thus grouping data for all canals for each specimen. To do so, we averaged all parameters but also calculated the sum of the canal diameters: CDsum and CDEsum. We performed linear regressions of each parameter to R (lm function). These parameters were then divided by R, once correlation with size had been highlighted, to obtain CDr, CDEr, CDrsum, and CDErsum.

To evaluate how these different parameters drive the variation observable in our samples, we conducted normalized PCAs (David & Jacobs, 2014) for all datasets, those with all canals and those averaged by specimen.

These analyses and additional statistical ones (Student’s t‐test, anova) were performed using statistical software r (R Core Team, 2014; packages ape, FactoMineR, factoextra, picante).

Results

The values obtained for the different parameters, and on which statistical analyses were performed, are discussed below. They are listed in Supporting Information Tables S2–S5.

Discrete parameters

The number of nutrient canals (NNC)

The NNC varies from one to four in our samples. It varies among a single species (e.g. from 1 to 3 in the humerus of Mustela putorius) and between humeri and femora from the same species (one in the humerus and four in the femur of Erinaceus europaeus). Correlation tests between the humerus and femur datasets averaged for each species indicate no correlation between the two bones. anova revealed that the number of canals is always correlated with LR, and thus the bone proportions, and CDr (but not always with CDEr; Table 2). LR decreases when the bone is more robust for a given length. In less elongated bones, canals appear generally more numerous and relatively thinner. However, as shown by the intraspecific variation, this is a common but not an absolute trend.

Table 2.

P‐values from the anova on the link between the number of nutrient canals (NNC) and the various continuous characters (for the datasets including all canals).

D/P	R	FI	CDr	CDEr	CO	H	L	LR
H QM	0.39	0.47	0.001	0.008	0.004	0.68	0.08	0.001
F QM	0.77	0.98	0.02	0.70	0.07	0.20	0.31	0.01
H MU	0.02	0.44	0.04	0.10	0.85	0.67	0.009	0.03
F MU	0.14	0.43	0.003	0.02	0.83	0.27	0.49	0.04

Abbreviations as in Materials and Methods. Values in bold are significant at 5%.

Direction

Canals are mainly directed distalo‐proximally (from the core to the outer surface of the bone) in the humerus (Fig. 2A). There are a few exceptions, with proximo‐distal orientations in Meles meles, one specimen of Meles putorius, Pteronura brasiliensis and Lontra felina, and one of the two canals of the Mustela eversmanni specimen. From our sample, it thus only varies from the common condition in mustelids. In addition, a few canals are sub‐horizontal, which usually corresponds to CO values < 15° (Fig. 2B). This occurs only in bones with several canals (except in the specimen of Lutra lutra). Conversely, in the femur, canals are mainly proximo‐distally directed (Fig. 2C,D). Exceptions occur in Rangifer tarandus, Vulpes vulpes, and one of the canals of Erinaceus europaeus, Rupicapra rupicapra, and M. eversmanni. One horizontal canal is observed among those of Choeropsis liberiensis.

Figure 2.

3D reconstructions showing the number and orientation of the nutrient canals. (A) Two canals distalo‐proximally oriented in the humerus of Dama dama STIPB M1. (B) Four horizontal canals in the humerus of Talpa europaea STIPB Unnumbered. (C) Two canals proximo‐distally oriented in the femur of Lontra felina MNHN 1884‐874. (D) A single canal proximo‐distally oriented in the femur of Felis silvestris UFGK Unnumbered. Not to scale.

Canals are essentially straight, except in Rangifer humerus and femur and in several humeri of mustelids where they are angled: Meles, Martes, two M. putorius, one canal of M. eversmanni, one canal of one Enhydra lutris specimen. Moreover, a humerus of L. felina shows a serpentiform canal. Conversely, all canals in the mustelid femora are straight.

The orientation of the canals in the bone is extremely variable in the humeri and femora of the QM sample; the canals can extend anteriorly, posteriorly, medially, laterally or in‐between. In the humerus of the mustelids, most canals are anteriorly directed, some medially directed and a few posteriorly directed. No canal is laterally oriented. In the mustelid femora, canals are almost always posteriorly oriented, only a few being medially oriented.

Continuous parameters

Phylogenetic signal

There is no phylogenetic signal in the parameters used to describe the canals for the QM dataset (Table 3). However, within mustelids, a phylogenetic signal is observed in some parameters (sometimes with a high K‐value) but not for the same parameters in the humerus as in the femur, except for CDE (Table 3). There is a significant phylogenetic signal for the size index R only for the humerus QM (with no other parameter showing a significant phylogenetic signal in this sample). The occurrence of a phylogenetic signal in the data thus appears clearly independent of size.

Table 3.

K‐statistics with the associated P‐values for the continuous parameters.

Dataset/Parameter	FI	CD	CDE	CO	H	R
Humerus QM	K = 0.44	K = 0.65	K = 0.45	K = 0.32	K = 0.46	K = 1.40
	P = 0.22	P = 0.08	P = 0.15	P = 0.80	P = 0.32	P < 0.001
Femur QM	K = 0.46	K = 0.42	K = 0.40	K = 0.41	K = 0.36	K = 0.48
	P = 0.24	P = 0.47	P = 0.43	P = 0.66	P = 0.80	P = 0.23
Humerus MU	K = 1.01	K = 1.34	K = 1.41	K = 0.73	K = 0.73	K = 0.74
	P = 0.049	P = 0.003	P = 0.002	P = 0.08	P = 0.11	P = 0.10
Femur MU	K = 0.81	K = 0.84	K = 1.46	K = 0.69	K = 1.57	K = 0.73
	P = 0.07	P = 0.10	P = 0.03	P = 0.10	P = 0.005	P = 0.13

Values in bold are significant at 5%.

Influence of size

Linear regressions clearly show that in all datasets the canal diameter is correlated with size, whereas its geometry is not (Table 4). For further analyses, we used ratios for the canal diameter parameters, dividing their values by R (CDr, CDEr, CDrsum, CDErsum).

Table 4.

Results of the linear regressions performed on the datasets (with R as a size estimate).

Dataset/Parameter	FI	CD	CDE	CDsum	CDEsum	CO	H
Humerus QM AC	r = −0.21	r = 0.79	r = 0.59	–	–	r = 0.20	r = 0.35
	P = 0.37	P < 0.001	P = 0.01			P = 0.40	P = 0.13
Femur QM AC	r = 0.04	r = 0.82	r = 0.93	–	–	r = −0.26	r = 0.16
	P = 0.86	P  < 0.001	P < 0.001			P = 0.22	P = 0.47
Humerus MU AC	r = 0.09	r = 0.86	r = 0.65	–	–	r = −0.10	r = −0.01
	P = 0.68	P < 0.001	P < 0.001			P = 0.67	P = 0.98
Femur MU AC	r = 0.24	r = 0.56	r = 0.51	–	–	r = −0.03	r = 0.20
	P = 0.22	P < 0.001	P  = 0.005			P = 0.88	P = 0.30
Humerus QM I	r = −0.28	r = 0.80	r = 0.63	r = 0.90	r = 0.85	r = −0.01	r = 0.36
	P = 0.34	P < 0.001	P = 0.02	P < 0.001	P < 0.001	P = 0.98	P = 0.21
Femur QM I	r = 0.23	r = 0.83	r = 0.94	r = 0.92	r = 0.85	r = −0.08	r = 0.48
	P = 0.43	P < 0.001	P < 0.001	P < 0.001	P < 0.001	P = 0.79	P = 0.07
Humerus MU I	r = 0.22	r = 0.88	r = 0.59	r = 0.85	r = 0.53	r = −0.12	r = −0.10
	P = 0.43	P < 0.001	P = 0.02	P < 0.001	P = 0.03	P = 0.66	P = 0.71
Femur MU I	r = 0.35	r = 0.58	r = 0.46	r = 0.86	r = 0.70	r = −0.01	r = 0.33
	P = 0.13	P = 0.01	P = 0.04	P < 0.001	P < 0.001	P = 0.95	P = 0.15

AC, all canals; I, averaged by individual. Values in bold are significant at 5%.

Values of the parameters

The continuous parameters are discussed based on datasets considering all canals (Fig. 3). The foraminal index (FI) is clearly higher in humeri than in femora (t‐tests; P < 0.001; Fig. 3A). It is also slightly lower in the QM sample than in the MU one (t‐tests; P < 0.001; Fig. 3A). For the canal diameter parameters, no significant difference was observed between the various datasets (Fig. 3B,C). The canal obliquity (CO) and the canal cortical height (H) are much higher in mustelid femora (t‐tests; P < 0.001; Fig. 3D,E).

Figure 3.

Boxplots illustrating the variation of the various parameters depending on the samples. CDr, relative canal diameter; CDEr, relative canal diameter at the outer extremity; CO, canal obliquity; FI, foraminal index; H, canal cortical height; R, bone mean diaphyseal radius.

Principal component analyses (PCA)

PCA enable not only the study of the distribution of the different specimens in the morphospace, but also and above all in our study, the analysis of the relative contribution of each parameter compared with the others and comparisons of the results obtained based on the different datasets.

Quadrupedal mammals

The first two axes of the humerus PCA including all canals (representing 87.1% of the total variance; Fig. 4) show that several canals from the same specimen can be either close (as for Talpa; Te) or very distant (as for Choeropsis; Cl). The intrabone variation seems thus potentially very high. In this small sample, the intraspecific variation seems essentially driven by the canal geometry (H, CO, FI). The two canal diameter parameters co‐vary. H and FI vary antagonistically. When data are averaged for each specimen, the relationships between the variables remain similar.

Figure 4.

Distribution of the specimens in the morphospace and contribution of the various parameters along the two first axes of the humerus PCA for the quadrupedal mammal (all canals) sample. Abbreviations as in Fig. 3 and Table 1.

The first two axes of the femur PCA including all canals (representing 78.6% of the total variance; Fig. 5A) also show a strong co‐variation between the two canal diameter parameters. The obliquity (CO) and canal cortical height (H) also strongly co‐vary. As for the humerus, the intrabone variation varies between taxa (rather weak in Talpa [Te], high in Erinaceus [Ee] and Rupicapra [Rr]) and appears clearly affected by various parameters depending on the specimens. Whereas CDr and CDEr rather co‐vary with CDrsum and CDErsum for the humerus when data are averaged for each specimen, this is not the case for the femur, where the first drive variability essentially along the first axis and the others along the second axis (Fig. 5B). The relationships between the variables are rather consistent between the two femur PCA, with the averaged CDr and CDEr replacing the CDr and CDEr values. The addition of the CDrsum and CDErsum does not greatly change the relative distribution of the specimens in the morphospace.

Figure 5.

Distribution of the specimens in the morphospace and contribution of the various parameters along the two first axes of the femur PCA for the quadrupedal mammal sample. (A) All canals; (B) all specimens. Abbreviations as in Fig. 3 and Table 1.

Mustelids

The first two axes of the PCA for all canals of the humeri (representing 82.3% of the variance; Fig. 6A) clearly show that variation can be greater within a bone than between specimens (e.g. in E. lutris [El], Lontra canadensis [Lc]). In this taxonomically narrower sample, the relationships between the different variables are similar to those in the QM sample, with a slightly lower co‐variation between CDr and CDEr. When data are grouped by specimens, the CDEr and CDErsum variables separate from the CDr and CDrsum variables that strongly co‐vary (Fig. 6B). The distribution of the specimens in the morphospace is this time different between the two samples (e.g. Meles [Mm]).

Figure 6.

Distribution of the mustelid specimens in the morphospace and contribution of the various parameters along the two first axes of the humerus PCA. (A) All canals; (B) all specimens. Yellow: Mustelinae; Blue: Lutrinae. Abbreviations as in Fig. 3 and Table 1.

The first two axes of PCA for all canals of the femora (representing 90.7% of the variance) tend to separate otters (lutrines) from other mustelids, with a limited overlap. H and FI strongly co‐vary, slightly less with CO, whereas at about right angle to those variables, CDr and CDEr also strongly co‐vary. As for the humerus, variation within a bone can be higher than between bones of a same species and even between species (Fig. 7). When canals from single specimens are globally considered, all canal diameter variables co‐vary and with the same relationship to the other variables as CDr and CDEr in the previous analysis. The distribution of the specimens is also similar.

Figure 7.

Distribution of the mustelid specimens in the morphospace and contribution of the various parameters along the two first axes of the femur PCA on all canals. Yellow: Mustelinae; Blue: Lutrinae. Abbreviations as in Fig. 3 and Table 1.

Considering the divergence between lutrines and mustelines in the mustelid sample of femora and based on the strong differences in femur shape and proportions between these two groups (Botton‐Divet et al. 2016), we analyzed the possible correlation between bone proportions and the various parameters, assuming a possible link with the canal geometry parameters. For that analysis, we performed linear regressions of all datasets with L and LR (Table 5).

Table 5.

Results of the linear regressions performed on the datasets with L and LR.

D/P	FI		CDr		CDEr		CDrsum		CDErsum		CO		H
Var	L	LR	L	LR	L	LR	L	LR	L	LR	L	LR	L	LR
H QM AC	R = −0.20	R = 0.15	R = −0.16	R = 0.72	R = −0.06	R = 0.45	–	–	–	–	R = 0.41	R = 0.63	R = 0.36	R = 0.08
	P = 0.40	P = 0.53	P = 0.50	P < 0.001	P = 0.79	P = 0.047					P = 0.08	P = 0.003	P = 0.12	P = 0.73
F QM AC	R = 0.06	R = −0.16	R = −0.08	R = 0.44	R = −0.09	R = 0.08	–	–	–	–	R = −0.12	R = 0.26	R = 0.27	R = 0.06
	P = 0.79	P = 0.46	P = 0.71	P = 0.03	P = 0.69	P = 0.70					P = 0.56	P = 0.22	P = 0.20	P = 0.78
H MU AC	R = 0.19	R = 0.20	R = 0.10	R = 0.37	R = 0.07	R = 0.31	–	–	–	–	R = −0.05	R = 0.13	R = −0.07	R = −0.21
	P = 0.40	P = 0.37	P = 0.65	P = 0.09	P = 0.75	P = 0.17					P = 0.83	P = 0.56	P = 0.75	P = 0.36
F MU AC	R = −0.03	R = −0.60	R = −0.32	R = 0.56	R = −0.21	R = 0.60	–	–	–	–	R = −0.14	R = −0.28	R = −0.14	R = −0.70
	P = 0.89	P < 0.001	P = 0.09	P = 0.002	P = 0.28	P < 0.001					P = 0.47	P = 0.14	P = 0.47	P < 0.001
H QM I	R = −0.28	R = 0.23	R = −0.46	R = 0.64	R = −0.19	R = 0.31	R = −0.56	R = 0.21	R = −0.23	R = 0.00	R = 0.18	R = 0.46	R = 0.39	R = −0.02
	P = 0.33	P = 0.43	P = 0.10	P = 0.01	P = 0.52	P = 0.27	P = 0.04	P = 0.48	P = 0.44	P = 1.00	P = 0.55	P = 0.10	P = 0.17	P = 0.95
F QM I	R = 0.25	R = −0.24	R = −0.12	R = 0.39	R = −0.12	R = 0.06	R = −0.23	R = −0.06	R = −0.19	R = −0.32	R = 0.07	R = 0.23	R = 0.57	R = −0.15
	P = 0.39	P = 0.40	P = 0.67	P = 0.17	P = 0.68	P = 0.84	P = 0.42	P = 0.84	P = 0.52	P = 0.27	P = 0.82	P = 0.43	P = 0.03	P = 0.61
H MU I	R = 0.34	R = 0.24	R = 0.09	R = 0.55	R = 0.04	R = 0.46	R = 0.09	R = 0.55	R = −0.39	R = 0.72	R = −0.05	R = 0.19	R = −0.18	R = −0.23
	P = 0.20	P = 0.37	P = 0.75	P = 0.03	P = 0.89	P = 0.07	P = 0.75	P = 0.03	P = 0.14	P = 0.001	P = 0.84	P = 0.47	P = 0.50	P = 0.40
F MU I	R = 0.04	R = −0.71	R = −0.38	R = 0.52	R = −0.3	R = 0.56	R = −0.23	R = 0.45	R = −0.12	R = 0.55	R = −0.14	R = −0.26	R = −0.05	R = −0.82
	P = 0.85	P < 0.001	P = 0.10	P = 0.02	P = 0.20	P = 0.01	P = 0.32	P = 0.047	P = 0.62	P = 0.01	P = 0.56	P = 0.26	P = 0.84	P < 0.001

D/P, dataset/parameter; Var, variable; other abbreviations as in Table 2. Values in bold are significant at 5%.

These analyses reveal that there is no correlation between bone length (L) and the canal parameters (there are only two significant results for distinct parameters and datasets), but also no general correlation between bone proportions, i.e. notably between small and large bones vs. elongated ones, and the canal parameters. Indeed, only CDr shows a significant link and moreover only for three of the four datasets. However, it is clear that the link is stronger for mustelid femora, all parameters except CO showing a significant correlation with LR in both datasets. The canal features (except CO) are thus strongly linked with the bone proportions in the mustelid femora.

Correlation tests between the humerus and femur datasets averaged for each species indicate, for both datasets, a significant correlation for the canal diameter parameters but not for the others (Supporting Information Table S6).

Discussion

Our study is the first one, to our knowledge, to analyze in three dimensions both qualitatively and quantitatively the nutrient canals in limb bones thanks to the use of microtomography. We proposed various parameters to describe their features and analyzed their values in two mammal samples to discuss their biological significance.

General comparisons

We did not observe a general phylogenetic signal in the quantitative parameters used to describe the canals. Indeed, a phylogenetic signal was observed for some parameters in the MU sample, but not for the same parameters in the two bones (except CDE). Moreover, no parameter showed a significant phylogenetic signal in the QM sample. The occurrence of a phylogenetic signal thus seems highly dependent on the sample.

In all our analyses, intraspecific variation and even intrabone variation were often very high, sometimes much higher than interspecific variation. As a consequence, the nutrient canals appear to be poor indicators of biological features of a taxon or even organism. Nevertheless, some specific features could be identified, such as the correlation between the canal features and the bone proportions in the MU femora (and not in other samples) notably distinguishing lutrines and mustelines. This raises potential interest in analyzing in detail the biological signal of nutrient foramina in taxonomically smaller taxa. The parameters CD and CDE were co‐varying in all analyses, so that we would suggest the use of only one of these parameters in further studies. The other parameters analyzed appear suitable to describe the diversity of the canal shape.

Number and diameter of the nutrient canals

This study showed in limb bones a number of nutrient canals varying from one to four, but more generally between one and two, in its samples. Previous studies on human long bones described a majority of humeri with a single nutrient foramen and of femora with one or two nutrient foramina; some also showed up to nine or even no foramen at all (Longia et al. 1980; Sendemir & Cimen, 1991; Nagel, 1993; Gümüsburun et al. 1994; Kizilkanat et al. 2007). During our study, we observed that some metaphyseal canals exit the bone in the diaphysis, so that some nutrient foramina on the diaphysis belong to metaphyseal rather than diaphyseal nutrient canals.

In our samples, the number of canals also varies within a single species (e.g. from 1 to 3 in the humerus of M. putorius) and between humeri and femora from the same species. This parameter thus appears to be strongly variable intraspecifically. However, our study reveals a trend for nutrient canals to be generally more numerous and relatively thinner in less elongated bones. As for the canal diameter, the diameters taken at mid‐length or at the periphery co‐vary. These parameters are also the only ones to co‐vary between the humeri and the femora. This shows that the diameter of the canals is rather constrained. Seymour et al. (2011) suggested a link between blood vessel circumference and metabolic rates (larger blood vessels servicing higher flow rates) and thus that the diameter of the nutrient canals would be linked to the physiology of the organisms. Our results confirm that the size of the canals appears constrained and rather homogeneous within a specimen.

Canal direction and orientation

In humeri, canals are essentially distalo‐proximally directed, whereas the opposite is true in the femur. However, foraminal indices are much higher in humeri than in femora, in accordance with studies on human bones (Pereira et al. 2011). This is because the growth center is located much more distally in the humerus than in the femur (in our samples). The nutrient canal seems thus generally oriented towards the mid‐diaphysis. Unfortunately, because the centralmost part of the bones generally underwent resorption, the medialmost extension of the nutrient canals is not observable. As a consequence, the position of the growth center cannot be ascertained precisely. If in the case of straight canals it would be tempting to extend the canal up to the core of the shaft, the occurrence of some bending in a few canals or of a slight change of orientation close to the growth center (e.g. femur of Enhydra) prevents the use of such an approach. When several canals occur, the intersection of the canals can also be ascertained as the position of the growth center. Despite the difficulty in determining the exact position of the growth center, the position of the medialmost extension of the canal clearly shows that the growth center is much distal (at about 70% of the bone length for both samples) in the humerus, and much proximal (at about 30% for QM and 40% for MU) in the femur. Growth is thus clearly not symmetrical in most taxa of our sample, being much more intense proximally in the humerus and distally in the femur. This confirms previous observations made on humans (e.g. Ollier, 1867) and also preliminary observations made on fossil whales (Houssaye et al. 2015). However, a proximal growth center has been observed in the humerus of turtles (Nakajima et al. 2014). As a consequence, although our results appear to be rather general in mammals, they cannot be generalized outside of Mammalia and further studies are required to investigate this question in other amniotes.

Canals are generally straight, with only a few exceptions. The relative extension of these canals along the diaphyseal cortex (H) is limited (< 15% L with average values between 3 and 9% L). However, this corresponds to minimal estimates, since the position of the growth center cannot be ascertained precisely. Moreover, a few taxa display high values (e.g. 26% L in Choeropsis humerus, and 15% in Rangifer and L. felina femur). Our study also clearly reveals that horizontal or sub‐horizontal canals are rare. The nutrient foramen thus does not indicate the location of the growth center. It has been assumed that the nutrient foramen was originally located at the level of the growth center but that an asymmetrical growth could engender the foramen to move proximally or distally, towards the faster growing end (Hughes, 1952; Henderson, 1978). Our results confirm that the canals are essentially oriented towards the faster growing end.

There is a high variation in the orientation of the canals in the bone within mammals. However, it was interesting to note preferential or absent orientations in the mustelid sample, which probably reflect morphological constraints during development that would be specific to these taxa and thus would imply stronger constraints at smaller taxonomical scales. Similarly, the much higher canal obliquity and cortical height in mustelid femora than in the other samples could also reflect specific developmental constraints. As a consequence, if the biological information could be flooded in a large sample of diverse taxa, more specific patterns might be revealed at a smaller taxonomic scale.

Supporting information

Fig. S1. Phylogeny including the species used in this study. (A) The quadrupedal mammal (QM) sample, based on Meredith et al. (2011). (B) The Mustelidae (MU) sample, based on Slater et al. (2012).

Table S1. List of the qualitative and quantitative parameters used in this study.

Table S2. Values of the parameters for the humerus QM dataset.

Table S3. Values of the parameters for the femur QM dataset.

Table S4. Values of the parameters for the humerus MU dataset.

Table S5. Values of the parameters for the femur MU dataset.

Table S6. Results of the correlation tests performed on the parameters averaged by species between the humerus and femur datasets.

Data availability statement

All scans are available under request