Morphology of the nutrient artery and its foramen in relation to femoral bone perfusion rates of laying and non‐laying hens

Abstract

If arteries penetrate bones through foramina, regional artery blood flow rates can be estimated from the foramen sizes. Femoral bone blood flow rates estimated from nutrient foramen sizes were previously not absolute, but only a relative blood flow index (Q _i), because the size relationship between the foramen and the occupying artery was unknown. The current study used vascular contrast and micro‐computerized tomographic scanning to investigate femoral nutrient foramen and nutrient artery sizes in three groups of sub‐adult chickens (non‐laying hens, laying hens, and roosters) of similar ages. The results indicate that the cross‐sectional area of the nutrient artery lumen occupies approximately 20.2 ± 4.1% of the foramen for femora with only one foramen. Artery lumen size is significantly correlated with foramen size. Vascular contrast imaging is capable of estimating blood flow rates through nutrient arteries, as blood flow rates estimated from artery lumen casts are similar to blood flow rates measured by infusion of fluorescent‐labeled microspheres. Laying hens tend to have higher nutrient artery perfusion rates than non‐laying hens, probably due to extra oxygen and calcium requirements for eggshell production, although the calculated blood flow difference was not statistically significant. Histological embedding and sectioning along with vascular contrast imaging reveal variable nutrient foramen morphology and nutrient artery location among femora with more than one nutrient foramen.

We described morphologies and locations of nutrient foramina and nutrient arteries in chicken femoral bones using vascular contrast, micro‐computerized tomographic scanning along with histological sectioning and embedding technique. Nutrient artery blood flow rates of chicken femora are related to energy requirements of the bones. There is a strong correlation between the nutrient foramen and nutrient artery sizes.

1. INTRODUCTION

Mechanical forces created by blood flow and blood pressure determine blood vessel structure. As blood flows through a vessel, it creates a tangential force called shear stress, and blood pressure creates a perpendicular force called circumferential stress to the vessel wall (Jones et al., 2006). The forces acting on the vessel wall control artery sizes and maintain physiological functions of the arteries (Lu & Kassab, 2011). Blood vessel sizes thus reflect regional blood flow rates, which are normally determined by the oxygen requirements of local organs (Wolff, 2008). Nutrient arteries contribute 50%–70% of the blood flow to adult long bones (Trueta, 1963). Long bones are responsible for withstanding loading stresses from locomotion, and they act as a reservoir to maintain extracellular calcium balance. A nutrient artery passes through the cortical bone of a femur shaft through a hole called the nutrient foramen, usually along with a vein (Currey, 2002; Singh et al., 1991). The sizes of vascular foramina are known to correlate dynamically with the sizes of the vessels in them. For example, the size of the internal carotid artery determines the size of the carotid canal in the human skull (Chen et al., 2021; Wyse et al., 2015). Femoral bone blood flow is related to locomotor activity levels in mature terrestrial vertebrates, as relatively larger nutrient foramina tend to occur in animals with higher metabolic rates during locomotion (Allan et al., 2014; Seymour et al., 2012). It is known that elevated stress and strain in bones during locomotion lead to more micro‐damage and enhanced remodeling (Lieberman et al., 2003; Robling et al., 2006). In growing animals, femoral bone blood flow also plays an important role in supporting rapid bone development. For example, substantially larger femoral nutrient foramina occur in in‐pouch kangaroo joeys than in adult marsupials of similar body mass (Hu et al., 2018). In general, higher oxygen demands of bone cells result in higher blood flow rates, which are associated with larger vessels and foramina. The approach of using foramen sizes to evaluate regional blood flow rates is called the ‘foramen technique’ (Hu et al., 2020).

If the size relationship between the foramen and the occupying artery is known, then quantitative blood flow rate can be estimated from theoretical or empirical equations. For example, blood flow rates in the marsupial and primate internal carotid arteries have been estimated from foramen sizes, because the artery occupies the carotid foramen almost entirely (Boyer & Harrington, 2018, 2019; Seymour et al., 2015, 2016, 2019a). However, the relationship between foramen and artery lumen size becomes much more complex when a foramen, such as the femoral nutrient foramen, also passes substantial veins. Previous research on long bone nutrient foramina used an index of blood flow (Q _i), which was assumed to be proportional to absolute blood flow rate (Allan et al., 2014; Hu et al., 2018; Seymour et al., 2012). However, no studies have ever quantified how nutrient arteries occupy the nutrient foramina of long bones, and the assumption remains untested.

To improve the foramen technique on femoral bone blood flows, the size relationship between femoral nutrient arteries and nutrient foramina needs to be investigated. Vascular contrast techniques have been commonly used for studying vascular beds with associated tissues or organs in vertebrates. The technique requires inserting a radiopaque medium into the circulatory system, and the medium can then be detected by X‐ray without tissue corrosion (Sedlmayr & Witmer, 2002). We used high‐resolution micro‐computerized tomographic (Micro‐CT) imaging to measure the cross‐sectional areas of the artery lumen and its nutrient foramen to establish the lumen/foramen area ratio. Histological tissue embedding and sectioning were also used to observe vessel locations inside the nutrient foramen. Commercial chickens were selected because bone blood flow rates of birds are poorly studied compared to mammals. Non‐laying hens, laying hens, and roosters of similar age were selected for examining the relationships among blood flow rates and the sizes of the femoral nutrient artery and its foramen. Additionally, laying birds export calcium partly from the bones into eggshell during reproductive periods. Calcium turnover in commercial layers is much more intense to satisfy rapid egg production. Birds develop medullary bone, which mainly acts as a labile calcium store for eggshell production (Whitehead, 2004). Femora contain medullary bone, so the foramen‐artery size relationship in chickens may relate to blood flow rates of femoral bones associated with these physiological processes. We hypothesized that nutrient foramen sizes in femoral bones correlate with nutrient artery sizes, which reflect blood flow rates of nutrient arteries and the metabolic demands of the shafts of femoral bones.

2. METHODS

2.1. Animals

Three groups of crossbreed sub‐adult ISA‐brown chickens (non‐laying hens, laying hens, and roosters) with age ranging from 4 to 7 months were obtained under Animal Ethics Committee approval (S‐2017‐058). Non‐laying hens were defined as point‐of‐lay birds but having no developed eggs in their reproductive organs, while laying hens were those that had just begun to lay eggs regularly. Chickens were kept in a constant temperature room at 25℃ before operations. The room was set to have a 16‐h daytime and 8‐h night time cycle. All chickens had free access to water and calcium‐rich layer's pellets.

2.2. Surgical procedures

Chickens were anesthetized with a combination of ketamine (40 mg/kg) and xylazine (4 mg/kg) through intramuscular injection. They were placed on a dissection table on their right side, 20 min after the injection. The left wing was spread and stabilized, and the feathers on the inside of the wing were plucked. A scalpel was used to cut the skin open next to the brachial vein near the humerus, and the brachial vein was isolated and cannulated by a heparinized, 20 ga, Venocan Pencil style IV catheter (Cat. No. 121931, Kruuse) towards the heart. Heparinized saline (2 ml, 125 i.u. ml⁻¹) was injected into the brachial vein through the catheter to heparinize blood throughout the body and to prevent coagulation during the following operations. Two minutes after the injection, chickens were euthanized by injecting an over‐dose of anesthetic into the brachial vein. The catheter was then removed, and both sides next to the injection point were sutured to prevent any liquid from leaking.

Feathers were removed at the left chest region. The first three ribs were exposed by cutting into the chest skin and muscles. The cut was made as small as possible to reduce any blood vessel damage. A self‐retaining Weitlaner retractor was used to open the gap between the second and third ribs to expose the pericardium, which was then removed to expose the heart. A pair of microscissors was used to cut a small hole through the heart wall into the left ventricle. A clear vinyl tube (internal diameter: 1.4 mm; external diameter: 1.9 mm) was inserted into the left ventricle and was stabilized to the heart wall using cyanomethacrylate glue. The same procedure was performed on the right side of the chicken to expose the heart, except that tweezers were used to tear the right atrium open to release blood and perfusate. The whole‐body vasculature was perfused via the tubing into the left ventricle with saline from a reservoir bottle positioned at a vertical distance of 2.03 m above the chicken to produce approximately average systemic arterial blood pressure of 150 mm Hg. The blood‐flushing process lasted for about 15–20 min until little blood remained in the saline solution draining out from the right atrium.

2.3. Vascular contrast medium injection

Immediately after the blood‐flushing process, legs were harvested by cutting across the ilium. During pilot studies, we observed that the femoral nutrient arteries branch from the ischiatic arteries. Because the cross‐sections of the nutrient arteries were too small to observe and cannulate, the contrast medium (BriteVu; Scarlet Imaging) was instead perfused into the ischiatic arteries near the femoral head (Figure S1). The ischiatic artery near the femoral head was isolated and cannulated using a clear vinyl tubing (internal diameter: 0.5 mm; external diameter: 0.9 mm) with a 25 ga needle connecting to the end. A drop of cyanomethacrylate glue was applied at the joint to stabilize the tubing. Because the femoral nutrient arteries are much smaller than the ischiatic arteries, contrast medium sometimes bypassed the nutrient arteries and caused experimental failures. To compensate for this problem, we exposed and ligated the downstream ischiatic artery near the knee (Figure S1).

After cannulation, the leg was placed into a plastic bag, which was put into a warm water bath prior to contrast medium perfusion. One part of BriteVu, 3 parts of water, and 1.5% BriteVu enhancer (Scarlet Imaging) were mixed continuously in a glass beaker with a stirring bar and a thermometer on a magnetic stirrer hotplate, heated to 70–80℃. The contrast medium was injected from a 12 ml syringe containing a collapsed latex balloon that expanded under an applied pressure from a saline‐filled reservoir bottle 2.03 m (i.e., 150 mm Hg, accounting for the density of saline) above the leg of the animal. This produced a physiological pressure to the outlet of the syringe, which was connected to the ischiatic artery. The contrast medium was perfused continuously until it cooled down and no more could be perfused into the leg. The leg was then placed back into the plastic bag in an ice bucket and then into a refrigerator 1 day prior to micro‐CT scanning.

Twenty‐seven out of 38 legs from 6 non‐laying hens, 6 laying hens, and 7 roosters were successfully perfused with contrast medium under physiological pressure. Each of these 19 chickens had at least one leg successfully perfused under physiological pressure. Among the 38 legs, 7 legs were unsuccessfully perfused, and 4 legs (1 leg of 2 non‐laying hens and 2 laying hens) were perfused with contrast medium manually under hand pressure via the ascending aorta, to explore blood vessel distribution surrounding a femur and to examine cross‐sectional area differences collected from physiological and hand pressurized arteries.

2.4. Micro‐CT scanning

A Skyscan 1276 Micro‐CT scanner (Bruker microCT) was used to measure areas of both nutrient foramina and nutrient arteries infused with contrast medium. Femur shafts were firstly scanned using a lower resolution (~20 µm) to observe foramen numbers and locations. Each nutrient foramen was then scanned using a higher resolution (~10 µm). After scanning, NRecon 1.6.10.4 (Bruker microCT) was used for image reconstruction. The scan parameters were 95kV source voltage, 200 µA source current, 715 ms exposure, aluminum‐copper filter, no frame averaging. Image pixel sizes were 20.5 and 10.3 µm, and rotation step angles were 0.4 and 0.2 degrees for femur shafts and nutrient foramina, respectively. The reconstruction settings were smoothing 2, ring artifacts reduction 10, beam hardening correction 30%, and contrast limits 0–0.04. Cross‐sectional areas of arteries and foramina were collected and measured using both DataViewer 1.5.2.4 (Bruker microCT) and Fiji (www.fiji.sc). Areas of nutrient arteries filled with contrast medium were measured separately from the foramina as sometimes the artery pathways did not perfectly align with the foramen pathways. Radii were calculated from the foramen areas, assuming the areas were perfect circles. Methods that measure foramen size are well described in Hu et al. (2020).

2.5. Histology study

Another three laying hens were used for histological sectioning of the femoral nutrient foramina. The same surgical operation procedures were performed on these chickens. Immediately after the blood flushing process, 10% formalin was perfused for 15 min via the left ventricle from a reservoir bottle at a different vertical distance of 1.87 m (i.e., 150 mm Hg). After formalin perfusion, most feathers were removed, and chickens were placed in 10% formalin solutions for 2 weeks. After whole‐body fixation, femora were harvested. Most attached tissues were removed, except for the tissues at the bone shaft, covering the nutrient foramina. Femur shafts were scanned using the micro‐CT scanner at 20 µm resolution to detect foramen locations and numbers. Femora were then placed into Cal‐Ex decalcifying solution for 3 weeks. After decalcification, tissues were carefully removed, and femur shafts with foramina were separated from the whole bones and placed in 70% ethanol prior to histological embedding and sectioning. Femur shafts were embedded in paraffin and sectioned serially with 7 µm slice thickness through the whole cortical region, where the foramen is located (Figure S2), using a rotary microtome. Masson's trichrome stain was used to stain the tissues, to distinguish bones, vessel walls, and nerves. A light microscope (Z2197, Olympus) connected to a 5MP digital imager (#44422, Celestron) and a computer was used to take microphotographs of the foramen slices.

2.6. Statistical analysis

Most biological factors are related to body mass in non‐linear ways. When comparing data such as foramen size, vessel size, and blood flow data among chickens with different body mass, data need to have the effect of body mass removed. The scaling of blood flow index (Q _i) in the femoral bone of cursorial birds on body mass has an exponent of 0.89 (Allan et al., 2014). As derived from Poiseuille's Law, Q _i = r ⁴/L, where Q _i (mm³) is blood flow index, r (mm) is foramen radius substituting for vessel radius, and L (mm) is an arbitrary length, assuming that femur length is geometrically similar to vessel length (Allan et al., 2014; Seymour et al., 2012). The units of Q _i are mm³ and are assumed to be proportional to blood flow rate. Any length scales with body mass or volume to the 0.33 power, and area scales to the 0.67 power if the shape is constant. Therefore, assuming that Q _i is proportional to body mass to the 0.89 power and L to the 0.33 power, then foramen radius should scale to the (0.89 + 0.33)/4 = 0.305 power, and area to the 0.61 power, in birds. The raw size data were converted to mass‐independent radii (mm/kg^0.305) and areas (mm²/kg^0.61) for analysis.

Pearson's correlation coefficient (Pearson's r) was calculated to measure the strength of a linear correlation between areas of nutrient foramina and nutrient artery lumen in femora successfully perfused under physiological pressure. Lumen/foramen area ratio was calculated by dividing a nutrient artery lumen area by a foramen area for each properly perfused foramen. Some femora had more than one foramina or more than one perfused nutrient artery. To estimate the area and radius data of these femora, foramen and nutrient artery areas were summed, and radii for these femora were estimated from the summed foramen and artery areas. Sizes of nutrient arteries were collected only from femora with contrast medium successfully perfused in the artery lumina inside the foramina. To compare artery areas and radii among the 19 chickens, only arteries that were perfused under physiological pressure were included in the analysis. If nutrient arteries of both femora were well‐perfused under physiological pressure, size data of the nutrient arteries were averaged from both femora, otherwise, one femur's artery was a datum. Foramen areas and radii were averaged from both femora of the 19 chickens. Mass‐independent areas of nutrient foramina and nutrient artery lumina were compared among three chicken groups using ANOVA in statistical software (Prism 6.0; GraphPad Software). If there was a significant difference, Tukey's multiple comparisons test was used for comparing means between any two groups. All error statistics are 95% confidence intervals (CI).

3. RESULTS

3.1. Relationships between femoral nutrient foramen and nutrient artery sizes

Four chickens with only one nutrient foramen on each femur were perfused with contrast medium under physiological pressure on one leg and hand pressure on the other leg. The areas of the nutrient artery lumina between both legs of these four chickens were not significantly different (p = 0.30), suggesting higher hand pressure did not affect lumen size measurements inside the nutrient foramina. However, the sizes of nutrient arteries that were perfused using hand pressure were excluded in the following analysis, to prevent systematic errors. The areas of the nutrient foramen and the nutrient artery lumen were measured in 20 femora that had one nutrient foramen (Figure 1). There is a significantly positive correlation between the nutrient foramen and nutrient artery lumen areas (r = 0.51; p = 0.02). When a linear regression was forced through the origin, as a foramen of zero area must have an artery of zero area, the slope of the line was 0.183 ± 0.032, indicating that the lumen area calculated from the regression occupies, on average, 18.3% of the foramen area. The broad variation of the dataset can be partly explained by the narrow size ranges of the foramina and lumina and experimental error. Nevertheless, the 95% CI of the slope of the regression (0.151–0.215) aligns with area data from individual nutrient arteries. The lumen occupies 22.5 ± 4.0% of the foramen area in 39 nutrient arteries perfused under both physiological and hand pressure. Knowledge is incomplete about how nutrient arteries supply femora with more than one foramen, so lumen/foramen area ratios of femora with only one foramen were compared among three chicken groups, to achieve direct ratio comparison. Only 19 samples processed under physiological pressure were chosen for this ratio comparison. Average lumen/foramen area ratio of these femora was 0.202 ± 0.041. Among the 19 femora, there were 8, 5, and 6 samples belonging to non‐laying hens, laying hens, and roosters, respectively. This ratio was not significantly different among three chicken groups (F _{2, 16} = 3.2, p = 0.07), with non‐laying hens being 0.168 ± 0.055, laying hens being 0.274 ± 0.133, and roosters being 0.186 ± 0.056 (Figure S3).

FIGURE 1.

Relationship between areas (mm²) of nutrient artery lumina and foramina. The linear regression (artery lumen area = 0.183 × foramen area) is constrained to pass through the origin. Dashed lines represent the 95% confidence intervals of the slope (0.151–0.216)

Absolute foramen areas (non‐laying hens: 0.42 ± 0.11 mm²; laying hens: 0.41 ± 0.13 mm²) and radii (non‐laying hens: 0.36 ± 0.05 mm; laying hens: 0.36 ± 0.06 mm) of two hen groups were not significantly different from each other (area: p = 1.00; radius: p = 0.99). Absolute foramen areas (0.64 ± 0.12 mm²) and radii (0.45 ± 0.04 mm) of roosters were significantly higher than the non‐laying hens (area: p = 0.01; radius: p = 0.01) and laying hens (area: p = 0.01; radius: p = 0.01; Figure 2a,b).

FIGURE 2.

Absolute cross‐sectional areas and radii of nutrient foramina (a and b) and nutrient artery lumina (c and d) among 6 non‐laying hens, 6 laying hens and 7 roosters. Error bars represent 95% confidence interval (CI) of the means

The significant differences in absolute foramen size among the three chicken groups were apparently related to body mass. There were no significant differences in mass‐independent areas (F _{2, 16} = 1.65, p = 0.22) and radii of nutrient foramina (F _{2, 16} = 1.73, p = 0.21; Figure S4A,B).

Size data of nutrient arteries were only collected from arteries perfused under physiological pressure for artery size comparison among three chicken groups. Lumen areas were 0.06 ± 0.02, 0.10 ± 0.03, and 0.10 ± 0.03 mm² for 6 non‐laying hens, 6 laying hens and 7 roosters, respectively. Non‐laying hens had significantly smaller lumen areas than the roosters (p = 0.02). Lumen areas were not significantly different between non‐laying hens and laying hens (p = 0.07), or between laying hens and roosters (p = 0.88). Lumen radii were 0.13 ± 0.03, 0.17 ± 0.03, and 0.18 ± 0.03 mm for non‐laying hens, laying hens and roosters, respectively. Non‐laying hens had significantly smaller lumen radii than the laying hens (p = 0.04) and roosters (p = 0.01; Figure 2c,d). When the effect of body size was removed, there were no significant differences in mass‐independent areas (F _{2, 16} = 1.45, p = 0.26) and radii (F _{2, 16} = 2.11, p = 0.15) of nutrient artery lumina among three chicken groups (Figure S4C,D).

3.2. General observations of chicken femoral nutrient arteries and nutrient foramina

As the descending aorta passes into the abdominal region, it gives rise to external iliac and ischiatic arteries running into the legs, and the femoral arteries branch off the external iliac arteries (Midtgård, 1982; Xu et al., 2010). The femoral artery and ischiatic artery are the major arteries of the thigh, with the femoral artery often supporting the proximal muscles, and ischiatic artery providing the main blood supply of the hind limb. Femoral nutrient arteries of chickens branch off the ischiatic arteries (Figures 3 and 4). After a single nutrient artery enters a femur shaft through a nutrient foramen, it bifurcates into ascending and descending arteries (Figure 4b,c). Most femora had only one nutrient foramen located at the mid‐shaft region. In addition to the 38 femora of the three chicken groups, we scanned another 10 femora and recorded foramen numbers and locations. Of 48 femora scanned in this study, 28 femora had a single foramen, 17 femora had two, and 3 femora had three. Nutrient artery locations and foramen shapes were complex in femora with more than one nutrient foramen. Therefore, femora with more than one foramen are described separately below.

FIGURE 3.

Schematic of the vessel patterns surrounding the femur (medial view). The diagram is drawn based on Midtgård (1982) descriptions and our own observations [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 4.

Micro‐CT images of blood vessel distribution surrounding femora. (a) Main arteries surrounding a femur. (b) Ischiatic vein and ischiatic artery connected to the vein and nutrient artery inside a femur shaft. (c) A cross‐sectional image of a femur mid‐shaft, with a nutrient foramen and a nutrient artery passing through it. Nutrient artery outside the foramen in image (c) does not appear due to sample orientation. The scales for (a and b) only represent approximate lengths as both images are 3D images [Colour figure can be viewed at wileyonlinelibrary.com]

3.2.1. Femora with one nutrient foramen

A single nutrient foramen contained a nutrient artery, a vein, and a nerve (Figure 5a). Most femora with only one nutrient foramen observed from histological sections did not reveal a vein inside the foramen, but exposed a large space between the artery and the foramen (Figure 5b). We believe veins in these foramina detached during processing because of their thin, fragile walls, as veins could be observed in some other sections (Figure 5a) and on micro‐CT images (Figure 4b). Areas of these nutrient foramina appeared to be pear‐shaped or elliptical, and the nutrient artery was located at the smaller end (Figure 6a–c). Nutrient foramen passages did not branch inside the cortical region in most cases. However, both femora of one chicken revealed a foramen passage that was single on the periosteal surface and branched into two passages within the cortical bone. One passage contained the nutrient artery and the other empty foramen probably contained the vein (Figure 7).

FIGURE 5.

Microphotographs of histological nutrient foramen cross‐sections with occupying tissues. (a) A nutrient artery, a vein and a nerve occupy a nutrient foramen. (b) A nutrient artery and a nerve occupy a nutrient foramen, leaving a large space between the foramen wall and the occupying tissues. Histological foramen and vessel cross‐sections were not sliced perpendicularly to either the foramen passage or the vessels. No histological nutrient arteries retained pressurized appearance despite being fixed under physiological pressure. The scale represents 0.5 mm [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 6.

Different shapes of nutrient foramina with occupying vessel lumina filled with contrast medium (BriteVu) observed from micro‐CT images. (a and b) Pear‐shaped foramina with nutrient artery locating at the smaller area of the “pear”. (c) A pear‐shaped foramen with both a nutrient artery and a vein partially filled with contrast medium. (d) An “empty” round‐shaped foramen. (e) A round‐shaped foramen with a vein. (f) A round‐shaped foramen with a nutrient artery. Scales represent 0.5 mm [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 7.

Tangential cross‐sections of nutrient foramen passages in two femora of a single chicken. From left to right, the cross‐sections were collected from 4 positions along a foramen passage, starting closer to the bone surface and ending closer to the bone marrow. An invisible vein may be present in the “empty” space of each foramen. Scales represent 0.5 mm [Colour figure can be viewed at wileyonlinelibrary.com]

3.2.2. Femora with more than one foramen

In some cases when a femur had more than one foramen, only one foramen passed the nutrient artery with its lumen filled with contrast medium. Other foramina appeared to be empty or to have irregular‐shaped lumen areas (Figure 6d,e). This could be because the contrast medium failed to perfuse into the arteries inside these foramina or because these foramina contained only a vein. Veins were not perfused intentionally with contrast medium in this study, but contrast medium entered veins in some cases, possibly through anastomoses or ruptures (e.g. Figure 4b). One femur, which had two nutrient foramina, showed an ischiatic vein partially perfused with contrast medium. One foramen of this femur contained a nutrient artery traced to the ischiatic artery and the other foramen contained the vein, which was traced to the ischiatic vein. Both of these foramina were round‐shaped. This sample indicated the possibility for a femur to have two nutrient foramina, with one occupied by an artery and other occupied by a vein. Another case showed a femur containing two foramina, each with a nutrient artery. In this specific example, the areas of the two nutrient artery lumina were similar, but one foramen was round‐shaped and the other one had a much larger area with a pear shape, suggesting that it may have contained a vein (Figure 8). After these arteries ran into the femur shaft, one artery turned into an ascending artery and the other turned into a descending artery. No direct connections were observed between the two arteries inside the femur. A similar pattern occurred in the histological study of two femur shaft sections that contained two foramina (Figure S5). These observations suggested that femora with two nutrient foramina could both contain an artery.

FIGURE 8.

Micro‐CT images of a femur with two nutrient arteries passing through two nutrient foramina. (a) A femur shaft with two nutrient arteries. Arrows represent foramen locations. Arteries disappeared outside the bone because of vessel collapse. (b and c) The two nutrient arteries and their foramina cross sections of the femur shown in (a). Both nutrient artery lumina are filled will contrast medium (BriteVu). An artery apparently fills the foramen in image (b). A vein may be located in the foramen “empty” space of image (c). The scale represents approximately 5 mm for image (a) as it is a 3D image. The scale represents 0.5 mm for both foramen images (b and c) [Colour figure can be viewed at wileyonlinelibrary.com]

Foramen shapes and artery locations may be even more complex when a femur has more than two foramina. Foramen arrangements could vary among three‐foramen femora (Table 1). Femora with three foramina were rare, and only two 3‐foramen femora were successfully perfused with contrast medium. Both femora had one foramen containing one nutrient artery and two other empty foramina. We are not certain about what vessels occupied the other two empty foramina. All observed foramen shapes, artery locations, and foramen arrangements are summarized in Table 1.

TABLE 1.

Observed nutrient foramen shapes, nutrient artery locations and foramen arrangements of femora with different foramen numbers based on this study. Foramen shapes are diagrammatic, not dimensionally accurate. Small circles represent nutrient artery lumen locations inside nutrient foramina. For foramen arrangements, smaller circles represent general foramen locations on the shafts of 48 femora scanned in this study. The observed numbers refer to femora with different foramen arrangements

Foramen numbers on femur shaft	Foramen shapes and nutrient artery location	Foramen arrangements	Observed femur numbers
1			28
2			17
3			2
			1

3.3. Foramen area comparison between femora with different foramen numbers.

We also examined foramen number and area data of another 50 chicken femora reported in another study (Hu et al., 2021). Of 98 femora analyzed in both studies, 64 had one nutrient foramen, 30 had two, and 4 had three. Total foramen areas from right and left femora were compared in 15 chickens that had one foramen on one side and two foramina on the other side. Since different methods were involved in both studies, total foramen areas between the left and right femora were compared using paired t‐test. No significant difference in summed areas (p = 0.36) and estimated radii (p = 0.29) existed between two femora with different foramen numbers (Figure 9a,b), suggesting the summed vessel area and nutrient blood supply may be similar in femora with different foramen numbers.

FIGURE 9.

Nutrient foramen area (a) and radius (b) comparison between both femora of 15 chickens, with one femur containing one foramen and the other femur containing two foramina. Foramen areas of femora with two foramina are summed areas of both. Foramen radii were calculated from summed areas. Data collected are from (Hu et al., 2021) and this study. Error bars represent 95% confidence interval (CI) of the means

4. DISCUSSION

The main objective of this investigation was to determine the size relationships between the nutrient arteries and the nutrient foramina by micro‐CT imaging and histological techniques. The underlying aim was to determine if the size of the foramen can be used to evaluate the rate of blood flow through it. This ‘foramen technique’ was quantitatively validated for the internal carotid arteries, which occupy the carotid foramina almost entirely in mice, rats, and humans (Seymour et al., 2015). The technique was initially controversial, but subsequently used by others, and improvements were made by replacing theoretical equations with empirical ones (Seymour et al., 2019a). The limitations of the technique have been well described in Hu et al. (2020). Where arteries pass through foramina and do not fill the opening, absolute blood flow rates could not be obtained. Instead, an index of blood flow rate (Q _i) has been calculated under the assumption that it is proportional to absolute blood flow rate (Seymour et al., 2012), but the assumption has not been verified. The present study measures the sizes of pressurized nutrient arteries in their foramina in chickens (1) to examine nutrient foramen anatomy and to determine how the artery occupies the foramen, (2) to calculate absolute blood flow rates from lumen radius in nutrient arteries, (3) to relate femoral bone perfusion to chicken physiological processes, particularly in relation to eggshell production in laying hens, and (4) to observe the effects of multiple foramina.

4.1. The sizes of the femoral nutrient artery and foramen

Micro‐CT scans of the nutrient foramina in this study reveal variable anatomy, with some foramina containing only an artery, others with space around the artery presumably occupied by a vein, and others with no artery (Figure 6). Arteries could be accompanied by veins or run separately from them (Figure 7). Inside of the cortical bone, a single artery divides into ascending and descending branches (Figure 4b,c). Alternatively, the nutrient artery could divide outside of the bone and enter at two points (Figure 8; Figure S5).

Histological sections confirmed that arteries and veins could pass through a single foramen (Figure 5). Unfortunately, artery size is not available from histological sections due to shrinkage. Nevertheless, micro‐CT scans reveal inflated arterial lumen radius (r _i), and the wall thickness can be estimated from the distance between the lumen and the closest foramen wall. Assuming that nutrient arteries are circular and fill a section of a noncircular foramen (Figure 10a) or a circular foramen (Figure 10b), the “outer circumference” of the nutrient artery was measured subjectively using Fiji and converted into artery outer radius (r _o). Wall thickness is r _o – r _i, and the ratio of wall thickness to lumen radius is w = (r _o − r _i)/r _i. Average wall thickness‐lumen ratio, estimated from 39 chicken femoral nutrient foramina was 0.59 ± 0.09. This value is significantly higher than 0.3, which is the value estimated from humans (Hu et al., 2020). However, a 1.95 kg chicken has an approximately 54% higher systemic arterial blood pressure (Seymour & Blaylock, 2000) than a 1.95 kg mammal (White & Seymour, 2014), which should result in a higher ratio (w = 0.46) if avian arteries have the same mechanical properties as mammalian arteries and transmural pressure is directly proportional to wall thickness according to Law of Laplace (Westerhof et al., 2019). Still, the apparent wall thickness from this study is probably overestimated. Locating the artery's “outer circumference” as well as the fuzzy boundary of the lumen on the CT images are somewhat subjective, so it is difficult to define both the inner and outer artery radii precisely.

FIGURE 10.

Outer circumferences of nutrient arteries. Estimated outer circumference of a nutrient artery in a pear‐shaped nutrient foramen (a) and a round‐shaped nutrient foramen (b). Yellow circles represent the outer circumferences [Colour figure can be viewed at wileyonlinelibrary.com]

This study indicates that the arterial lumen area occupies about 20% of the foramen area in femora with single foramen. Larger foramina tend to have larger arteries, and the regression slope indicates 18.3% (Figure 1). Despite the narrow size ranges of our foramina and lumina, the 95% confidence intervals of the regression line revealed a positive correlation between the two variables. Therefore, the assumption that foramen size is related to arterial blood flow rate receives some support.

4.2. Blood flow estimation from nutrient artery radii

Blood flow rates (Q̇, cm/s) can be estimated from artery lumen radius (r _i, cm) using theoretical and empirical approaches. The theoretical approach is through Poiseuille's “shear stress equation”:

$$\dot{Q}=(\tau \pi r_{\mathrm{i}}^3)/\left(4\eta \right)$$ (1)

where τ is wall shear stress (dyn cm⁻²) and η is blood viscosity (dyn s cm^{− 2}; Lehoux & Tedgui, 2003). Some previous foramen studies used this equation to estimate blood flow rates in human internal carotid arteries with assumed values for τ and η (Seymour et al., 2015, 2016, 2019a). Q̇ can also be estimated from artery radii empirically. Seymour et al. (2019b) collected 92 points that related artery lumen radius with blood flow rate in the same animal among nine mammalian species. The data included 22 named systemic arteries varying in r _i from 3.65 μm to 1.12 cm. The empirical equation describes a log‐quadratic relationship between blood flow rate (Q̇, cm³ s^{− 1}) and artery lumen radius (r _i, cm):

$$\log \dot{Q}=‐0.20{(\log r_i)}^2+1.91\log r_i+1.82$$ (2)

Both approaches produce similar results for blood flow rates in primate internal carotid arteries, if the scaling of wall shear stress is known (Seymour et al., 2019a). However, Equation (2) is preferable because it requires only radius to calculate blood flow rate.

Nutrient artery blood flow rates in this study were estimated from lumina that were cast under physiological pressures, according to the empirical Equation (2), although the equation is based on blood vessels of mammalian species. If a femur had more than one nutrient artery, blood flow rate of this femur was estimated by summing the estimated blood flow rate of each artery. The results of these estimations based on contrast imaging are compared among three chicken groups to perfusion rates of femur shaft collected using fluorescent microspheres in another study (Hu et al., 2021), as the nutrient arteries supply mainly the femur shafts. There was no significant difference in absolute blood flow rates derived from the two methods (Figure 11a; Figure S6); however, the data between the two studies belonged to different chicken individuals.

FIGURE 11.

Nutrient artery blood flow rates estimated from artery lumina perfused by vascular contrast imaging (I, open circles) and absolute femur shaft blood flow rates determined with fluorescent microspheres (M, solid dots) among non‐laying hens, laying hens and roosters. Absolute blood flow rates are shown in (panel a) and mass‐independent flow rates are shown in (panel b). Animals used between the two studies are different individuals. Absolute blood flow rates in this study were calculated based on artery lumen radii of 19 chickens represented in Figure 2d, according to Equation (2). Error bars represent 95% CI of the means

Both vascular contrast and fluorescent microsphere methods thus appear capable of providing similar estimates of absolute blood flow rates through femur shafts. However, this may be a fortuitous result of studying very small arteries. Larger arteries have thicker and more elastic vessel walls, which may compress contrast medium to a smaller volume before it solidifies. Choosing different casting materials may also affect cast vessel sizes. One study compared in vivo and cast vessel sizes using magnetic resonance imaging (MRI), corrosion casting, and pressure fixation methods in rabbit aorto‐iliac region, and the results indicated that the lumen diameter of the pressurized‐fixed sample was 18%–29% smaller, and the cast vessel diameter was 5%–17% smaller than the ones collected from in vivo MR images (Moore et al., 1999).

4.3. Perfusion of chicken femora in relation to eggshell formation

Absolute blood flow rates in the nutrient arteries are higher in laying hens than in non‐laying hens, however, laying hens weighed more. For proper comparison, it is necessary to remove the effect of body mass and calculate mass‐independent values of blood flow rate (Figure 11b). This is done by dividing the blood flow rate by body mass raised to the exponent evident in the regression across all three chicken groups (Figure 12). The scaling exponent is 1.22 ± 0.84, which is not significantly different from the 1.32 ± 0.93 scaling exponent reported in our study of femur perfusion measured with microspheres (Hu et al., 2021). The value of 1.3 used in Hu et al.'s (2021) study was selected to compare mass‐independent blood flow rates between the two studies. Mass‐independent blood flow rates of nutrient arteries, therefore, have a unit of ml min⁻¹ kg^−1.3. The average mass‐independent blood flow rates of nutrient arteries in three chicken groups are 0.17 ml min⁻¹ kg^−1.3 (non‐laying hens), 0.21 ml min⁻¹ kg^−1.3 (laying hens) and 0.16 ml min⁻¹ kg^−1.3 (roosters; Figure 11b). Although the mean for laying hens is greater than that for non‐laying hens, the difference is not significant (p = 0.67). However, the difference is significant when measured with microsphere infusion (p = 0.04; Hu et al., 2021). The relationships between blood flow rates calculated from imaging and microspheres are shown in the Supporting Information (Figure S6).

FIGURE 12.

Relationship between nutrient artery blood flow rate (Q̇, ml/min) and chicken body mass (M _b, g). Three different symbols represent three different chicken groups. The regression equation set to all groups is Q̇ = 3.6 × 10⁻⁵ M _b ^1.22±0.84. Dotted lines represent 95% confidence intervals for the regression mean. Data are plotted on logarithmic scales

Regional blood flow rates are normally associated with the energy requirements of local tissues, as higher metabolism requires more oxygen and blood flow. Laying hens may require extra blood flow to deliver oxygen, which is essential for medullary bone metabolism associated with calcium deposition and mobilization. Medullary bone is a special bone type acting as calcium reserves in birds and crocodilians, and it replaces trabecular bone in chicken leg bones as they reach sexual maturity (Whitehead, 2004). Medullary bone is capable of being absorbed and renewed rapidly (Bain et al., 2016), in order to maintain calcium balance in bones of domestic chickens. Laying hens transport about 2.2 g of calcium into eggshell of each egg (Bouvarel et al., 2011) and about 20%–40% of this calcium passes through bone (Bar, 2009). This study shows a trend for greater bone perfusion that probably relates to intense calcium turnover in laying hens. The relationship between chicken femoral bone blood flow and bone metabolism has been described in more detail in Hu et al. (2021).

4.4. Effect of single and multiple nutrient foramina

If a femur has more than one nutrient foramen, we cannot determine artery radius or estimate blood flow rates from foramen size directly. However, the summed foramen areas of paired‐femora with one and two foramina are not significantly different (Figure 9a,b), which aligns with no significant difference in total blood flow rates into left and right femora measured by microsphere infusion (Hu et al., 2021). This suggests that nutrient artery blood flow rates to the left and right femora should be similar, even when they have different foramen numbers. Therefore, we can estimate absolute blood flow rates of nutrient arteries from multiple‐foramen femora by assuming summed foramen areas as a single imaginary foramen area, and artery lumen areas of these femora can then be estimated using the lumen/foramen area ratio of 20%.

In cases where the surface of the femur is lost or obscured, particularly with fossil bones, all foramina may not be visible. If one foramen is found, there is a possibility that additional foramina could be lost. If only the largest is found, it is of interest to evaluate the effect of the missing ones. To investigate how much error can be introduced in this case, 34 multiple‐foramen chicken femora were selected. For all multiple foramen femora, the largest foramen accounted for 68 ± 4.5% of the summed foramen area of individual femur, ranging from 44% to 90%. Considering only femora with two foramina (n = 30), their largest foramen accounted for 70 ± 4.5% of the summed foramen area, and for femora with three foramina (n = 4), the largest accounted for 53 ± 9.9%. Therefore, foramina that have been missed during measurement can lead to substantial underestimation of femoral bone blood flow. The impact increases as the missing foramen number increases. Additionally, the lumen/foramen area ratio in the largest foramen of a multiple‐foramen femur can vary, and it would introduce more errors into the blood flow estimation. To obtain accurate femoral bone blood flow, foramen numbers need to be carefully identified for each bone specimen.

In conclusion, this study shows that the ratio of lumen area to foramen area in femora with single foramina is 20.2 ± 4.1%, and there is a significant positive correlation between lumen area and foramen area with a slope of 0.183. Therefore, the radius of the artery lumen can be obtained from the foramen area, and blood flow rate can be calculated from theoretical or empirical equations. The vascular contrast technique is capable of estimating blood flow rates by imaging pressurized nutrient arteries. Estimated blood flow rates are not significantly different from flow rates measured with fluorescent microspheres. Blood flow rates in the nutrient arteries tend to be higher in laying hens than in non‐laying hens, albeit not significantly, but consistent with significant differences in rates measured with microspheres. This may be related to extra calcium mobilization during laying periods. Absolute blood flow rates can be estimated from nutrient foramen size alone, without imaging the artery lumen. However, femora with multiple foramina that may contain arteries and/or veins cannot be reliably used to estimate blood flow rate. Nutrient foramen numbers and sizes need to be carefully determined for each bone specimen to avoid errors in the estimation of blood flow rate.

COMPETING INTERESTS

No conflict of interests are declared.

AUTHOR CONTRIBUTION

Q.H. conducted experiments, analyzed data, wrote the initial manuscript draft, and edited subsequent drafts. T.J.N. assisted in the experiments, helped with data collection, literature research, and provided feedback for the manuscript. R.S.S. provided guidance for experiments and contributed to the writing of the manuscript.

Supporting information

Fig S1

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Supplementary material

Hu, Q. , Nelson, T.J. & Seymour, R.S. (2022) Morphology of the nutrient artery and its foramen in relation to femoral bone perfusion rates of laying and non‐laying hens. Journal of Anatomy, 240, 94–106. 10.1111/joa.13535

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon request.