Allometry of left ventricular myocardial innervation
Institute of Functional and Applied Anatomy, Hannover Medical School, Biomedical Research in Endstage and Obstructive Lung Disease Hannover (BREATH), Member of the German Center for Lung Research (DZL), Hannover, Germany
Institute of Functional and Applied Anatomy, Hannover Medical School, Biomedical Research in Endstage and Obstructive Lung Disease Hannover (BREATH), Member of the German Center for Lung Research (DZL), Hannover, Germany
Cluster of Excellence REBIRTH (From Regenerative Biology to Reconstructive Therapy), Hannover, Germany
Institute of Anatomy and Cell Biology, University of Gießen, Gießen, Germany
Christian Mühlfeld, Institute of Functional and Applied Anatomy, Hannover Medical School, Carl-Neuberg-Str. 1, 30625 Hannover, Germany. T: + 49 511 5322878; E: firstname.lastname@example.org
Body mass (BM) of terrestrial mammalian species ranges from a few grams in the case of the Etruscan shrew to a few tonnes for an elephant. The mass-specific metabolic rate, as well as heart rate, decrease with increasing BM, whereas heart mass is proportional to BM. In the present study, we investigated the scaling behaviour of several compartments of the left ventricular myocardium, notably its innervation, capillaries and cardiomyocytes. Myocardial samples were taken from 10 mammalian species with BM between approximately 2 g and 900 kg. Samples were analysed by design-based stereology and electron microscopy and the resulting data were subjected to linear regression and correlation analyses. The total length of nerve fibres (axons) in the left ventricle increased from 0.017 km (0.020 km) in the shrew to 7237 km (13 938 km) in the horse. The innervation density was similar among species but the mean number of axons per nerve fibre profile increased with rising BM. The total length of capillaries increased from 0.119 km (shrew) to 10 897 km (horse). The volume of cardiomyocytes was 0.017 cm3 in the shrew and 1818 cm3 in the horse. Scaling of the data against BM indicated a higher degree of complexity of the axon tree in larger animals and an allometric relationship between total length of nerve fibres/axons and BM. In contrast, the density of nerve fibres is independent of BM. It seems that the structural components of the autonomic nervous system in the heart are related to BM and heart mass rather than to functional parameters such as metabolic rate.
The body mass (BM) of mammalian species covers six orders of magnitude: whereas the adult Etruscan shrew has a BM of approximately 2 g, the elephant, the largest terrestrial mammal, has a BM of a few tonnes. The interspecific relationship between various structural and functional parameters on the one hand and BM on the other has provided important insights into animal physiology (Stahl, 1967). Allometric relationships can often be expressed by the mathematical equation y = aBMb, where y is a parameter of interest (e.g. metabolic rate, heart rate), BM is body mass, a is the y value if BM= 1, and b is the slope of the regression line (Lindstedt & Schaeffer, 2002). For example, the relationship between basal metabolic rate and BM has been a source of controversy for many years (Rubner, 1883; Kleiber, 1961; Heusner, 1982) with recent studies arguing that no unifying value of b exists (White et al. 2009) or even questioning the usefulness of classical allometric scaling (Hillman et al. 2013). Nevertheless, in different-sized adult mammals the basal metabolic rate seems to be described best by a value of b =0.75.
The higher basal metabolic rate (per gram body weight) in smaller mammals compared with larger ones forces the heart to perform at a higher level. As such, the resting heart rate scales with BM−0.25 (Holt et al. 1968) and the volume fraction of cardiomyocyte mitochondria with BM−0.044 (Hoppeler et al. 1984). This means that smaller mammals tend to have a higher heart rate (total and per gram BM) and greater volume fraction of mitochondria. As heart mass and stroke volume are proportional to BM (Lindstedt & Calder, 1981), the flow rate of blood (calculated from stroke volume times heart rate) scales according to b =0.79 (Holt et al. 1968; Lindstedt, 1984), although other values for b have been reported (Patterson et al. 1965). However, with increasing metabolic demands, mammals weighing more than 1 kg can increase their heart rate two- to three-fold, whereas animals weighing < 1 kg have a maximum heart rate only about 30% greater than at rest (Kass et al. 1998). As cardiac capacity is defined by heart rate times stroke volume, this implies that cardiac reserve function is lower in smaller than in larger animals.
Functional adaptation of the heart to increasing demands is modulated by the autonomic nervous system. For example, several arguments support the notion that exercise limitation in heart transplant recipients is caused by denervation and the loss of sympathetic positive chronotropy and inotropy (Andreassen, 2008). However, little is known about interspecific variation and the allometric relationships of nerve fibres in the myocardium of various mammals. The atria are richly supplied by sympathetic and parasympathetic nerve fibres, whereas ventricles are mainly innervated by noradrenergic sympathetic nerve fibres. The perikarya of the postganglionic neurons are located mainly in the paravertebral ganglia of the cervical sympathetic trunk. Studies on the superior cervical ganglion in different mammals have shown that the dendritic complexity of sympathetic neurons and convergence of their input is greater in larger than in smaller mammals (Forehand, 1985; Purves & Lichtman, 1985; Loesch et al. 2010). In line with this, the number of neurons in the superior cervical ganglion was found to increase with rising BM, but less steeply (Ribeiro et al. 2004).
Here, we hypothesized that the allometric relationship of the innervation of the left ventricular myocardium is not proportional to BM or heart mass. There are two alternative possibilities: (i) the lower adaptability of the heart of smaller mammals makes an equally high support with nerve fibres unnecessary and, consequently, the innervation density is smaller; and (ii) the impossibility of the heart of smaller mammals to increase its beating frequency to a similar degree as larger-sized mammals requires a higher degree of innervation in the left ventricle to meet the metabolic demands. To test this hypothesis, we used ventricular myocardium from 10 mammalian species and estimated the total length of nerve fibres and axons by design-based stereology. In addition, several parameters characterizing capillaries and cardiomyocytes were quantified to see whether one or more of these structures show a similar scaling to that of nerve fibres.
Materials and methods
All analyses were performed on archive material from the Institute of Anatomy at the University of Bern, Switzerland, and kindly provided by Prof. Hans Hoppeler. The following 10 species (n = 1 each) were employed in the stereological investigation: Etruscan shrew (Suncus etruscus), woodmouse (Apodemus sylvaticus), rat (Rattus rattus), cat (Felis catus), fox (Vulpes vulpes), coyote (Canis latrans), wolf (Canis lupus), dog (Canis familiaris), horse (Equus caballus), cattle (Bos taurus). All heart samples were previously investigated in a number of research projects not related to this study (Hoppeler et al. 1984). All animals received anaesthesia and analgesia and were killed with a minimum of painful procedures. All of the original studies underwent a bioethical evaluation and were approved by the respective authorities.
In short, the hearts were excised from the animals within a few minutes, washed, and weighed. Transmural samples were taken from the left ventricular apex, immersed in aldehyde fixative subsequently and processed for transmission electron microscopy (Hoppeler et al. 1984). As the samples were taken from the left ventricle only, the heart weight was multiplied by two-thirds to obtain an estimate of the left ventricular weight as the reference space. The rationale for using a constant multiplication factor of two-thirds is based on the fact that the sum of the mass of the left ventricular free wall and the interventricular septum varies only slightly across mammalian species (Lee et al. 1975). The mass of the left ventricle was further divided by the density of muscle tissue (taken to be 1.06 g cm−3, see Mendez & Keys, 1961) to obtain the volume of the left ventricular myocardium as the reference volume.
To quantify myocardial composition, design-based stereological methods were applied (reviewed in Mühlfeld et al. 2010a). Fields of view for investigation were obtained by systematic uniform random sampling (Mayhew, 2008) at linear magnifications of ×2800 or 14 000 using a transmission electron microscope (Morgagni; FEI, Eindhoven, the Netherlands). At the lower magnification, the volumes of blood vessels (including all types of vessel) and cardiomyocytes and their mitochondria and myofibrils, the volume of capillary lumen, the surface densities of capillary endothelial cells and cardiomyocytes as well as the length of capillaries were estimated using standard stereological procedures (Weibel, 1979). Surface area and length estimations rely on the randomness of tissue orientation in 3D. Unbiased stereological methods to generate isotropic uniform random sections from the samples are the orientator (Mattfeldt et al. 1990) and the isector (Nyengaard & Gundersen, 1992). As these methods were not available at the time the samples were collected (Hoppeler et al. 1984), we have relied on haphazard orientations of tissue blocks during processing (Stringer et al. 1982).
For volume and surface area estimations, a grid consisting of 12 line segments was projected onto the fields of view. The endpoints of the line segments were regarded as test points. For volume estimation, the number of test points hitting a structure of interest (e.g. cardiomyocytes) was counted and divided by the number of points hitting the reference volume (e.g. left ventricular tissue), resulting in the volume density of a structure related to a reference volume [e.g. VV(cardiomyocyte/left ventricle]. To obtain the total volume [e.g. V(cardiomyocyte, left ventricle), the volume density was multiplied by the reference volume, V(left ventricle)]. For surface area estimations, the number of intersections of the line segments with the cardiomyocyte plasma membrane and the luminal capillary endothelium was counted and related to the total length of test line segments hitting the reference space using SV = 2*I/(lT/2*P), where SV is the surface density referred to a reference volume, I is the number of intersections, lT is the individual length of a line segment, and P is the number of points hitting the reference volume. The total surface area was calculated by multiplying the density by the reference volume (Fig. 1).
For length estimation, the number of capillary profiles was counted within an unbiased counting frame (Gundersen, 1977). The length density of capillaries was calculated by LV(cap/lv) = 2*Q/(P(CF)*a(p)) with Q being the number of capillary profiles, P(CF) the number of edges of the counting frame hitting the reference space and a(p) the counting frame area per point, i.e. the area of the total counting frame divided by 4. Under the explicit and simplifying assumption of a cylindrical supply or diffusion zone around each capillary, the mean radius of this cylinder [R(diff)] was calculated according to the formula R(diff) = 1/√(π*LV) with LV being the length density of the capillaries (Weibel, 1984; Nyengaard et al. 1996). This radius conforms to that of the physiological concept known as the Krogh cylinder (see Weibel, 1984).
At the higher magnification, the length of nerve fibres and axons as well as the mean number of axons per nerve fibre profile was estimated in a manner similar to the method described earlier (Mühlfeld et al. 2010b). In short, the number of nerve fibre profiles and the number of axons per nerve fibre profile were counted within an unbiased counting frame. The total lengths of nerve fibres and axons were estimated according to the equation given for capillary length. The mean number of axons per nerve fibre was obtained as the arithmetic mean (Fig. 2).
The stereological and BM data were log-transformed before undertaking linear regression analyses. Following log-transformation, allometric relationships were expressed in the form of y = axb. Here, x represents the independent variable (BM) and y one of various stereologically determined dependent variables. The term a is a constant determined by x and y. The exponent (or scaling factor) b represents the slope of the regression line and provides information on the growth relationship between y and x. If b < 0, x and y are inversely related. A b-value of < 1 indicates that the growth of y is slower than that of x and, if b >1, y grows faster than x. The standard error of the mean (SEM) for b helps to decide whether the exponent is significantly different from a given value (e.g. b =1). The non-linear correlation between the stereological estimates and BM was carried out with Spearman's rho test, which provided a coefficient of correlation (r) and a measure of statistical significance (P). The significance level was P < 0.05.
Table 1 provides basic data on BM and heart dimensions. Tables 2-4 show the summarized stereological data and Table 5 reports the results of the correlation and regression analyses. Figure 3 shows the log–log plots for a selection of various parameters relative to BM. As known from other studies, the heart mass scales with BM in direct proportion, the exponent b being not significantly different from 1. The volume of cardiomyocytes, myofibrils and mitochondria as well as the surface area of cardiomyocytes were significantly correlated with BM. For total volume and surface area of cardiomyocytes, myofibril volume and capillary volume, surface area and length, the b-values in the regression analysis were also not significantly different from 1. Total mitochondrial volume showed a b-value of 0.885, similar to the value of 0.9 described by Hoppeler et al. (1984) for the same set of material. Similarly, mitochondrial volume density was inversely correlated with BM. The functionally most relevant volume and surface density of capillaries were inversely correlated with BM, whereas the length density failed to reach significance levels. Also, although the diffusion radius around the capillaries grew at a far slower rate than BM and ranged between about 7.1 μm in the woodmouse to 10.5 μm in the wolf, the species differences were not consistent in terms of BM alone.
Table 2. Stereological data on myocardial innervation
LV(nf/int), length density of nerve fibres per unit volume of interstitial space; L(nf,lv), total length of nerve fibres in the left ventricle; LV(axon/int), length density of axons per unit volume of interstitial space; L(axon,lv), total length of axons in the left ventricle; QQ(axon/nf), mean number of axons per nerve fibre profile.
Table 3. Stereological data on cardiomyocytes
VS-ratio (myo) (cm3 m−2)
VV, volume density; V, total volume; myo, cardiomyocyte; lv, left ventricle, mf, myofibrils; mi, mitochondria; SV, surface density; S, total surface area; VS-ratio, volume-to-surface ratio.
Table 4. Stereological data on myocardial blood supply
VV, volume density; V, total volume; vessel, blood vessels incl. all types of arteries, capillaries and veins; lv, left ventricle; cap, capillary; int, interstitium; LV, length density; L, total length; R(diff), capillary diffusion radius; SV, surface density; S, total surface area.
Table 5. Correlation analysis using Spearman's rho test and linear regression analysis of various parameters vs. body mass
NS, not significantly different from b =1.
0.971 (0.034) NS
Nerve fibre length density
Axon length density
Nerve fibre length
1.040 (0.044) NS
1.088 (0.043) NS
Mean number of axons per nerve fibre
Volume of cardiomyocytes
0.961 (0.036) NS
Volume density of myofibrils
Volume of myofibrils
0.983 (0.039) NS
Volume density of mitochondria
Volume of mitochondria
Surface density of cardiomyocytes
Surface area of cardiomyocytes
0.963 (0.033) NS
Volume density of capillary lumen
Volume of capillary lumen
0.969 (0.030) NS
Length density of capillaries
Length of capillaries
0.929 (0.044) NS
Surface density of capillary endothelium
Surface area of capillary endothelium
0.920 (0.036) NS
When the largest and lowest densities were compared, the length density of nerve fibres and axons varied greatly between the species, with a maximum factor of 2.6 for nerve fibres and 3.6 for axons. However, there was no systematic relationship between BM and nerve fibre/axon length density. The total length of nerve fibres and axons increased from 0.0166 km of nerve fibres (0.0199 km of axons) in the Etruscan shrew with rising body mass to 7237 km of nerve fibres (13 938 km of axons) in the horse. Both parameters were significantly correlated with BM and, in both cases, the power law equation had a b-value not significantly different from 1. Interestingly, the mean number of axons per nerve fibre profile was significantly correlated with BM, thus contributing to a higher b-value of total axon length than total nerve fibre length and indicating a greater complexity of the axonal arborization in larger-sized mammals.
As nerve fibre length, axon length, cardiomyocyte volume, myofibril volume, cardiomyocyte surface area and capillary volume, surface and length all scaled to BM as b =1, it follows that the cardiomyocyte and capillary dimensions scale to nerve fibre and axon length as b =1.
Left ventricular sympathetic innervation mainly serves to increase the contractility of cardiomyocytes (positive inotropy) via noradrenergic transmission and β1-adrenoreceptor activation (Burnstock, 1969; Momose et al. 2001). Due to the differences in heart rate and cardiac reserve function between differently sized mammals, we hypothesized that the relationship between BM and left ventricular innervation is not directly proportional. In particular, the possibility that the higher cardiac reserve requires a stronger degree of sympathetic innervation in larger animals would mean that the exponent b in the power law equation y = aBMb is larger than 1. Our data indicate that the total length of nerve fibres is essentially in direct proportion to BM. However, due to an increase in the mean number of axons per nerve fibre with rising BM, the total length of axons appears to scale with BM according to b =1.088. No significant correlation was observed between innervation density and BM.
The postganglionic neurons of the sympathetic nervous system receive a greater input and have a higher dendritic complexity in larger mammals than in smaller ones (Purves & Lichtman, 1985). This goes along with changes in the localization of the incoming synaptic contacts in that in larger mammals the number of dendritic synapses increases, whereas the somatic innervation decreases (Forehand, 1985). As shown by Ribeiro et al. (2004), the number of neurons in the superior cervical ganglion increases from approximately 19 000 in the rat (BM ≈ 200 g) to over 1 520 000 in the capybara (BM ≈ 40 kg) and 3 393 000 (BM ≈ 200 kg) in the horse. When these data are scaled to BM, the exponent b =0.77. In the dog, most of the ganglion cells are located in the middle cervical ganglion (Armour & Hopkins, 1981), whereas in many other species the majority of neurons projecting to the heart reside in the stellate ganglion (Wallis et al. 1996). Given a similar morphology (Peruzzi et al. 1991) and number (Cavalcanti et al. 2009) of superior cervical and stellate ganglion cells, it appears to be justified to relate the available allometric/interspecies data on the superior cervical ganglion to cardiac innervation. The increase in the mean number of axons per nerve fibre with rising BM matches the greater dendritic complexity of neurons in larger mammals and indicates that the degree of axonal arborization also increases with greater BM.
One could expect that an allometric relationship also exists for the mean size of ganglion cells; however, this does not seem to be the case, as the variation in neuronal size among three different species shows no systematic pattern (Ribeiro et al. 2004). However, as these size estimates were restricted to the soma of the cells, this does not necessarily provide information on dendritic complexity and axonal arborization. Neither nerve fibre nor axonal density showed an allometric relationship in our study, indicating that the distribution of innervation within a certain unit of myocardium is relatively stable. This appears reasonable because regional heterogeneity of cardiac innervation has been described in animal and human studies on cardiac hypertrophy and failure (Himura et al. 1993; Kimura et al. 2007; Mühlfeld et al. 2013) and was repeatedly put in the context of ventricular arrhythmias (Cao et al. 2000; Kimura et al. 2007). To achieve a similar degree of innervation, it is obvious that the number of axon branches must rise when the number of ganglion cells does not increase in proportion to BM. In a series of studies on the mouse heart, it was shown that experimental cancer cachexia leads to a lower level of cardiac innervation (Mühlfeld et al. 2011). However, this was not related to BM, as comparisons of alimentary loss or gain of BM did not provide evidence of quantitative changes in left ventricular innervation (Gruber et al. 2012a,b).
An additional aspect is the lifestyle of the species. For example, whereas the BM of cattle exceeds that of the horse by 77%, the left ventricular mass of the horse is 5% higher and the total length is 13% greater than that of cattle. The greater innervation of the horse myocardium may well be related to the active lifestyle of the horse in comparison with the sedentary lifestyle of cattle. Similarly, the total length of axons in the woodmouse is far greater than that observed in laboratory mice in previous studies (Mühlfeld et al. 2011, 2013; Gruber et al. 2012a,b). Thus, environmental conditions may also influence innervation.
The complexity of the autonomic nervous system allows changes in the nervous system input at various levels, e.g. in the quantitative contribution of sympathetic/parasympathetic nerve fibres at different sites (Crick et al. 1996a), the noradrenalin uptake mechanisms from the intercellular space (Bengel, 2011) or the expression levels of enzymes for transmitter production (Meerson et al. 1970; Peyronnet et al. 1999). Furthermore, the increase in heart rate and left ventricular function upon exercise do not rely solely on cardiac innervation but also on circulating catecholamines released from the adrenal medulla and the interaction between parasympathetic and sympathetic neurons both at the organ level and within the central nervous system. Importantly, several qualitative and quantitative immunohistochemical studies on various species, including the rat (Corr et al. 1990), guinea pig (Anderson, 1972; Crick et al. 1996b), cat (Qayyum, 1973), human (Crick et al. 1994) and pig (Crick et al. 1999), have highlighted that species differences exist with respect to the innervation density of different regions of the heart, in particular, to the innervation of the conduction system. Besides species differences, these studies have shown that the innervation of the cardiac conduction system is significantly denser than that of the surrounding myocardium. As cardiac capacity relies on heart rate and cardiac output, innervation differences of the conducting system among species have additional effects on cardiac adaptability by the autonomic nervous system.
A potential limitation of this study is the fact that all nerve fibres/axons ramifying between cardiomyocytes of the left ventricle were quantified irrespective of potential subpopulations, such as cholinergic or presumably sensory (calcitonin-gene-related-peptide- or nitric oxide synthase-containing) nerve fibres (Sosunov et al. 1995). However, despite the frequent presence of sensory nerve fibres around blood vessels and in the endocardium and epicardium, they are very rare in the left ventricular myocardium (Gerstheimer & Metz, 1986; Crick et al. 1999). In addition, it was not possible to distinguish between different subpopulations of the nerve fibres based on their morphology.
The present study further evaluated some quantitative parameters relating to cardiomyocytes and capillaries. As already known from older studies (Hoppeler et al. 1984; Schaper et al. 1985; Barth et al. 1992), the volume fraction of mitochondria was inversely related to BM, a fact which can be explained by the higher basal metabolic rate of small mammals. Similarly, the volume and surface density of capillaries were significantly inversely correlated with BM. The Krogh cylinder radius did tend to rise with BM, but at a very slow rate, the exponent b being very small [0.021 (0.01)]. A clear correlation of capillary density had been observed in skeletal muscle (Schmidt-Nielsen & Pennycuik, 1961) and can also be attributed to delivery of oxygen to mitochondria and therefore to basal metabolic rate (Conley et al. 1987). In previous studies on alimentary over- or undernutrition (Gruber et al. 2012a,b), it was observed that those cardiomyocyte and capillary parameters that are related to energy metabolism are mostly altered in the same way and to a similar degree but that innervation was independent of these changes. Thus, mitochondrial and capillary content seem to be influenced by metabolism, whereas left ventricular sympathetic innervation depends rather on the mass of the left ventricle as the target tissue. The latter can best be explained by the importance of nerve growth factor release from the target tissue because it has been shown that the compartment of nerve fibres in the heart strongly relies on the release of nerve growth factor from the myocardium itself (Smeyne et al. 1994; Hassankhani et al. 1995; Kaye et al. 2000; Kimura et al. 2010).
In summary, our study provides the first quantitative evaluation of left ventricular innervation in a variety of mammalian species. The allometric scaling reveals that increases in total nerve fibre length are commensurate with increases in BM from the adult shrew (2.4 g) to adult cattle (920 kg). Due to an increasing number of axons per nerve fibre in larger mammals, the total axon length also scales with BM, with b not significantly different from 1. We propose that the structural components of the autonomic nervous system in the left ventricle are related to body/heart mass rather than to functional parameters such as metabolic rate or heart rate.
The authors wish to thank Prof. Hans Hoppeler at the Institute of Anatomy, University of Bern, Switzerland, for kindly providing us with the study material. We further wish to thank Franziska Graber (Bern), Gerhard Kripp (Gießen) and Christa Lichtenberg (Hannover) for excellent technical support.
This work was funded by the German Research Foundation (Cluster of Excellence REBIRTH) and German Ministry for Education and Research (BMBF) via the German Center for Lung Research (DZL).
J.S. and T.M.M. collected data and participated in the statistical analysis and interpretation of the findings. C.M. provided the concept and design of the study, participated in the collection of data and statistical analysis as well as interpretation of findings. All authors contributed to the writing and preparation of the manuscript and approved its submission in the final form.
Conflict of interest
The authors declare that they have no competing interests.