Current Osteoporosis Reports

, Volume 11, Issue 3, pp 194–202

Influence of Hormonal Appetite and Energy Regulators on Bone


  • Ee Cheng Khor
    • Bone Regulation, Neuroscience Research DivisionGarvan Institute of Medical Research
  • Natalie Kah Yun Wee
    • Bone Regulation, Neuroscience Research DivisionGarvan Institute of Medical Research
    • Bone Regulation, Neuroscience Research DivisionGarvan Institute of Medical Research
Nutrition and Lifestyle in Osteoporosis (S Ferrari, Section Editor)

DOI: 10.1007/s11914-013-0157-0

Cite this article as:
Khor, E.C., Wee, N.K.Y. & Baldock, P.A. Curr Osteoporos Rep (2013) 11: 194. doi:10.1007/s11914-013-0157-0


Nutritional status is an essential component in determining whole body energy homeostasis. The balance between energy/food intake and metabolism is governed by a range of hormones secreted from various parts of the body. Their subsequent dissemination via the blood results in a wide range of biological responses including satiety, hunger, and glucose uptake. The roles of these systemic hormones also extend to bone regulation with animal and clinical studies establishing a relationship between these regulatory pathways. This review covers the gastrointestinal hormones, ghrelin, PYY, GIP, GLP-1, and GLP-2, and the adipokines, leptin, and adiponectin and their roles in regulating bone homeostasis. Their known actions are reviewed, with an emphasis upon recent advances in understanding. Taken together, this review outlines an expanding appreciation of the interactions between bone mass and the nutritional control of whole body energy balance by gut and adipose tissue.




Energy homeostasis is maintained, in part, by hormones secreted from the gastrointestinal tract and adipose tissue. A number of these hormonal regulators of metabolism, which include gastrointestinal-secreting peptides and the adipose-derived adipokines, are known to influence the skeleton. Through clinical evaluation of metabolic disorders and study of mouse mutant models we are gaining a clearer understanding of the interplay between these factors and the maintenance of bone mass.

Gastrointestinal hormones that regulate or respond to feeding include ghrelin, PYY, GIP, GLP-1, and GLP-2. Postprandial effects on circulating bone turnover markers have been observed showing that food intake and the associated hormones play a role in bone remodelling [1].

Adipokines are factors released from adipocytes in response to nutritional status, obesity, and inflammation [2, 3]. Adipokines play an essential role in energy homeostasis with leptin and adiponectin regulating food intake and insulin sensitivity, respectively [4]. Furthermore, leptin and adiponectin levels are altered in obesity [5, 6] and influence bone homeostasis.

This review will assess the impact that these hormones have on bone metabolism.


The growth hormone (GH)-releasing peptide, ghrelin is an appetite stimulant secreted from the stomach [7]. During fasting, ghrelin levels are increased with the highest levels prior to feeding [8]. After ingestion of a meal, ghrelin secretion is subsequently suppressed via postgastric feedback [9].

Rats infused with ghrelin have increased BMDs [10]; thus, the level of ghrelin when present can be an important determinant in bone metabolism. Ghrelin-null mice have normal bone densities when compared with their wild-type littermates [11]. Similarly, mice lacking ghrelin’s receptor, Ghrs, do not show any differences in BMD and BMC [12]. Thus, Maccarinelli et al proposed that compensatory mechanisms for ghrelin may be present as other factors known to be influenced by ghrelin were also unchanged in these mice [13]. A recent study found an age-dependent bone phenotype in Ghsr–/– mice with reduced cancellous bone volume at 6 months of age [14••]. Similar to previous studies, these mice had a normal bone phenotype at 3 months of age [11, 12, 14••]. Ex vivo analysis showed an osteoclast effect with increased differentiation and fusion in Ghrs–/– mice [14••]. In addition, Ghrelin treatment directly inhibited osteoclastogenesis in culture [14••]. Hence, the ex vivo effects of ghrelin deficiency may be absent or compensated in vivo at 3 months of age. Further exploration of ghrelin receptor deficient (Ghrs–/–) and leptin deficient (ob/ob) mice showed that the age-dependent changes in osteoclast number in leptin deficiency alone was restored to WT levels with the combined deletion of Ghrs. The late onset, leptin-dependent changes in resorption in Ghrs–/– mice suggest the possible involvement of cocaine amphetamine regulated transcript (CART), a hypothalamic neuropeptide known to stimulate bone resorption in leptin deficient mice [15] and implicated in the maintenance of bone mass in humans [16]. This study shows the influence of ghrelin on bone metabolism may be entwined with leptin central-signalling to osteoclasts [14••, 17].

The importance of age and life-stage transitions upon bone regulation by ghrelin has also been examined in humans [1820]. An investigation of ghrelin, estrogen, and BMD in pre-, peri- and postmenopausal women established that all 3 components have positive correlations between them [18]. Whether ghrelin and estrogen affect BMD by independent or convergent mechanisms has not been shown [18]. As low ghrelin and low estrogen levels were associated with a low BMD, this suggests that ghrelin may be implicated in postmenopausal osteoporosis [18]. Thus, a better understanding of ghrelin’s mechanisms in regulating bone is required and ghrelin supplementation during menopause may potentially be of therapeutic benefit to prevent osteoporosis.

A study of obese and nonobese children and adolescents demonstrated that the influence of acyl and des-acyl ghrelin on whole body BMD and BMC/height was mediated by body composition [21]. Negative correlations between acyl ghrelin and bone mass, and between des-acyl ghrelin and bone mass, were identified in the normal BMI group [21]. No correlation between the 2 isoforms of ghrelin and bone measurements (BMD and BMC) was identified in obese children and adolescents [21].Thus, under normal conditions, ghrelin may be correlated with BMD and BMC, however, under certain conditions such as obesity, the factors governing bone metabolism are altered and ghrelin is no longer an influential factor. These findings indicating an attenuation of ghrelin action in obesity, when combined with the mice findings of a strong effect of ghrelin in leptin deficient conditions mentioned above, suggest an inverse relationship between obesity and ghrelin’s actions to regulate bone mass. Such a proposition is consistent with the reduction in ghrelin levels in obesity and their increase after gastric surgery [22], a period of marked bone loss.

An emerging consideration in patients undergoing bariatric surgery is the effect on bone [23••]. Since most studies demonstrate that circulating fasting and postprandial ghrelin levels are decreased in Roux-en-Y gastric bypass patients and this may be a contributing factor to weight and bone loss [23••]. However, weight loss by nonsurgical methods increases ghrelin promoting osteoblast proliferation and differentiation [24]. Thus, is known to have a positive effect on bone mass. Hence, future studies need to assess the contribution of ghrelin during weight loss, in particular after bariatric surgery.

In summary, ghrelin seems to exert rather positive effects on the skeleton, but its effects are shadowed by other metabolic factors in obesity.

Peptide YY, a Member of the NPY Family

The gastrointestinal hormone, peptide YY (PYY) acts to supress appetite, and is secreted postprandially from the ileum and the colon to limit meal size and overall calorie intake [25]. Consistent with a positive effect upon satiety, PYY levels are elevated in anorexic patients and reduced in obesity. Two forms of biologically active PYY exist: PYY1-36 and PYY3-36. The latter is produced when PYY1-36 is cleaved by DPP-4 [26]. PYY1-36 has a strong affinity for the Y1 and Y2 receptor whilst PYY3-36 has a strong affinity for the Y2 receptor only. Thus, the effects of PYY on bone metabolism may be dependent on the form of the peptide.

Recently, Wong et al demonstrated that PYY has a direct effect on osteoblasts and osteoclasts [27••]. PYY–/– mice showed increased bone mass associated with increased osteoblast activity. Conversely, overexpression of PYY reduced osteoblast activity and increased osteoclast surface in the femoral metaphysis [27••]. Osteoblasts express the Y1 receptor and ERK signalling was increased in response to treatment with PYY and this response was reduced in the presence of a Y1-specific antagonist [27••]. Thus, PYY acts directly on osteoblasts via Y1 signalling. These findings were in contrast to a previous study on PYY knockout mice that observed a decrease in BMD, BMC, and cancellous bone volume [28]. However, the differences observed between these studies may be due to the difficulty in producing mice with genetically altered levels of PYY as PYY overexpression is lethal in embryonic development [29].

Clinically, PYY levels are implicated in metabolic disorders. Reduced PYY levels are a common finding in obesity [23••, 25, 30, 31]. These are suggested to decrease feelings of satiety and subsequently results in increased food intake [31]. Conversely, the administration of PYY in obese adults results in increased satiety and decreased food intake [31]. In addition to this, resistance to leptin and ghrelin can develop in obese patients; however, there appears to be no resistance to PYY [31]. Thus, PYY should be further explored as a potential therapeutic for obesity.

Anorexic adolescents have been demonstrated to have increased PYY concentrations and decreased BMD [31, 32]. In particular, Misra et al shows this strong correlation as with an increased sample size in comparison to the studies that went before [31]. In addition, patients that had weight recovery were subsequently retested and found to have a trend of decreased PYY concentrations [31]. Thus, PYY may have a negative relationship with bone mass during periods of reducing meal size, such as anorexia and post gastric surgery. In addition, the greater calorie demand of exercise has been shown to promote the bone loss in exercising women with amenorrhea [33].

As reviewed by Wong et al, a negative correlation between PYY and BMD and BMC has been established using PYY–/– and Y2 receptor deficient mice, and data from obese and anorexic patients [25]. In obese patients, as determined by a high BMI, basal PYY levels are generally decreased in comparison with the control patients whilst an increase BMD is observed [3436]. The converse is observed in patients with anorexia nervosa [31, 37]. Thus, PYY is implicated in obesity and bone metabolism, and may be a causative link between the two. However, the inverse correlation between PYY and BMD suggests that the administration of PYY may have detrimental effects on bone mass.

Postprandial Peptides - GIP, GLP-1 and GLP-2

Bone resorption decreases after a meal (postprandial), leading to the suggestion that gastrointestinal hormones may influence bone regulation [38]. Postprandial hormones of interest with respect to bone metabolism are: glucose-dependent insulinotropic polypeptide (GIP), glucagon-like peptide-1 (GLP-1), and glucagon-like peptide 2 (GLP-2).

GIP has a positive effect on bone. GIP receptors are present on osteoblasts and osteoclasts [39, 40]. Incubation of GIP with osteoblast-like cells results in increased collagen type 1 expression and increased alkaline phosphatase [39]. Supporting this, experiments using GIPR–/– mice and GIP-overexpressing transgenic mice have demonstrated that GIP stimulates bone formation and inhibits bone resorption, thus resulting in increased bone size and mass [39, 4143].

In direct conflict with the observations detailed above, Gaudin-Audrin et al recently demonstrated with a different GIPR–/– mouse model that cancellous bone mass is increased, osteoblast activity, and bone formation rate is increased and there is a decrease in osteoclasts [44]. These observations were found in both young (8-week old) and old (45-week old) mice [44]. These contradicting results suggest that GIP may also have a deleterious effect on bone. However, further investigations into GIP’s effects on bone are required especially to clarify the contradiction observed in GIPR–/– mouse models.

The influence of GLP-1 on bone regulation has been predominantly studied in rodents. The administration of GLP-1 in normal rats had no effect on bone structure [45]. However, in rats that were either type-2 diabetic or insulin-resistant, GLP-1 counteracted certain effects (structure model index and trabecular bone pattern factor) in the femur that are known not to be corrected by insulin treatment [45]. Thus, investigation into modulators of GLP-1 such as GLP-1 agonists and dipeptidyl peptidase-4 (DPP-4) inhibitors may be used in the future to alleviate the changes in bone that are observed in type-2 diabetes, especially since GLP-1 levels are reduced in type-2 diabetic patients [26].

GLP-2 is co-secreted with GLP-1. However, GLP-2 has been less extensively studied in comparison with GLP-1 with respect to bone. Incubation of serum-starved osteoblastic cell line, TE-85 with GLP-2 decreased the level of PINP [46•], suggesting that bone formation may be decreased. However, no changes in ALP levels were present [46•]. Whilst in the MG-63 osteoblastic cell line, no changes in PINP or ALP were present; however a reduction in osteocalcin (OC) was present following 5-day treatment with GLP-2 [46•]. No significant responses were detected in the most mature cell line Saos-2, which was expected as GLP-2R mRNA was not found in the Saos-2 cell line [46•]. Pacheco-Pantoja et al were able to demonstrate the presence of GLP-2 receptor in 2 osteoblastic cell lines, MG63, and TE-85 [46•], however, the responses elicited by GLP-2 appear inconsistent as some markers of bone formation were altered whilst others remained unaffected.

The majority of studies into bone regulation by GLP-2 are clinical studies, as reviewed by Wong et al [39]. Subcutaneous GLP-2 injections produced a dose-dependent reduction in bone resorption markers, whilst bone formation was unaltered [25, 47, 48]. Similarly, in healthy postmenopausal women the administration of GLP-2 had a positive effect on hip and trochanter BMD with decreases in serum CTX and no change in serum OC [4951]. Thus, having demonstrated the positive effects of GLP-2 on bone, a recent study has focused on the ideal method for the administration of GLP-2 as a future intervention for osteoporosis [52]. Askov-Hansen et al evaluated intravenous injections at 3 different concentrations, subcutaneous injection and the administration of sitagliptin (DPP-4 inhibitor) followed by a subcutaneous injection of GLP-2 [52]. Interestingly, the subcutaneous injection was most effective with a longer exposure of circulating GLP-2 and a longer suppression of CTX [52]. However, sitagliptin did not increase the efficacy when GLP-2 was injected subcutaneously [52]. Thus, it was determined that a long exposure time to GLP-2 was more effective than a high concentration injected intravenously.

To date, these postprandial peptides require further study on their role in bone homeostasis. However, GLP-2 is emerging as a possible therapeutic target against bone loss.

Leptin and NPY

Leptin is primarily secreted from adipocytes, hence the levels of circulating leptin are positively correlated with percentage body fat [53]. Additionally, neuropeptide Y (NPY), a known regulator of energy and bone homeostasis is a critical downstream mediator of leptin-deficient starvation signalling in the hypothalamus. Leptin is implicated clinically with higher serum leptin levels in obesity and lower leptin after massive weight loss from bariatric surgery [23••]. Leptin signalling deficiency in the mutant (ob/ob) mice or inactivation of the leptin receptor Ob-Rb (db/db) leads to an obese phenotype in mice, secondary to central starvation responses in the absence of leptin feedback to the hypothalamus, including a marked increase in NPY and reduction in CART expression [54, 55]. Aside from its effects on metabolic homeostasis, leptin has an established role in bone mass regulation. ob/ob mice display a complex bone phenotype, with reduced cortical bone mass and increased cancellous bone [56, 57], as well as shorter long bones and longer vertebrae [58]. Thus, it appears that leptin has opposing effects on cancellous and cortical bone [59]. However, the route of action on bone mass has been controversial in recent years.

Circulating leptin passes through the blood-brain barrier to bind to the long form of the leptin receptor Ob-Rb in the hypothalamus [60]. Leptin was shown to indirectly influence cancellous bone through this pathway [61]. This was demonstrated with intracerebroventricular (icv) infusion of leptin in wild-type and ovariectomized ob/ob mice, which reduced cancellous bone volume [61]. An icv injection of adeno-associated virus expressing leptin rescues the metabolic and bone phenotypes of ob/ob mice [62]. Further support of a neuronal pathway in leptin signalling to bone was shown in parabiosis experiments between ob/ob mice, where the mouse receiving icv infusion of leptin (with no leptin detected in the circulation) had reduced cancellous bone volume whereas the partner was not affected [63]. It was established that hypothalamic leptin signalling to the cancellous bone involved the sympathetic nervous system releasing adrenaline and noradrenaline to osteoblasts and osteoclasts that express the β2-adrenergic receptor [15, 63, 64].

The mechanism by which leptin regulates cortical bone was not explained until recently. Hypothalamic neuropeptide Y (NPY) is upregulated in leptin-deficient ob/ob mice [65] demonstrating that leptin negatively regulates central NPY expression [66]. NPY deficiency in mice results in a high bone mass phenotype in both cancellous and cortical bone [6769]. Thus, increased NPY signalling in leptin deficiency could contribute to the reduction in cortical bone. This was initially supported by NPY Y2 receptor knockout in ob/ob mice (Y2–/–ob/ob) having greater cortical bone formation compared with ob/ob mice [57]. More recently, this was confirmed with the ablation of the leptin-deficient increase in NPY expression with NPY knockout in ob/ob mice (NPY–/–ob/ob). NPY–/–ob/ob mice had increased cortical bone mass compared with ob/ob mice and this was not associated with body weight changes [70••]. The lack of changes in cancellous bone in NPY–/–ob/ob suggests that the leptin-mediated adrenergic pathway has a dominant effect on cancellous bone.

Early studies ruled out a possible direct interaction between leptin and bone cells, since leptin signalling in osteoblasts could not be detected [61]. In contrast, other studies have shown leptin receptor expression and direct signalling in osteoblasts, osteoclasts, and chondrocytes [7173]. Leptin has proliferative and differentiating effects on osteoblasts and chondrocytes [71, 74, 75], whereas it has inhibitory direct effects on osteoclastogenesis [71]. Although the possible central effects of leptin cannot be ruled out, the osteogenic effect of leptin was seen with leptin administration increasing bone mass in ob/ob mice [73]. In ovariectomized rats, continuous subcutaneous administration of leptin reduced the bone loss induced by the estrogen deficiency by altering osteoprotegerin (OPG) and Receptor activator of NF-κB ligand (RANKL) expression [76]. The protective effects of leptin on estrogen deficiency appeared to require peripheral leptin signalling, as ovariectomized rats with adeno-associated virus-leptin gene expression in the hypothalamus failed to attenuate the bone loss [77]. The evidence of direct leptin actions in bone indicate that leptin promotes bone formation, which was not consistent with the ob/ob mice cancellous bone phenotype reported by Ducy et al [61].

The debate on central and peripheral leptin-signalling in bone regulation was revisited recently in a study that showed subcutaneous administration or hypothalamic expression of leptin in ob/ob mice increased bone formation rate and restored the bone phenotype close to WT levels [78••]. This study emphasizes that circulating and hypothalamic leptin favors bone formation. Subsequent bone marrow transplant experiments with leptin receptor-deficient db/db bone marrow in lethally irradiated WT mice, neatly demonstrated the direct actions of leptin in bone formation rate in vivo. WT mice transplanted with db/db bone marrow lowered bone formation rate similar to db/db mice [78••]. Interestingly, leptin signalling deficiency in the bone marrow did not alter energy homeostasis, which seems to suggest that peripheral leptin directly regulates bone formation whereas central leptin signalling mainly responds to altered energy metabolism [78••]. This further suggests that the centrally mediated effects on bone mass by leptin are primarily a response to the effects on energy expenditure. Indeed, the role of NPY, a known energy homeostatic neuropeptide, in correcting the large cortical bone deficiency in ob/ob, suggests that the starvation circuits triggered by a reduction in central leptin signalling, in ob/ob and db/db mice, are the primary central skeletal response in these models. Thus, during obesity, direct leptin signalling may dominate, with leptin insensitivity reducing central signalling [79], while during starvation, the central circuits are activated, with hypothalamic NPY reducing cortical mass. However, the biological significance of the elevation in cancellous bone in ob/ob, mediated by adrenergic signalling [15, 63, 64], and also evident in caloric restriction [80], remains elusive.

Studies on humans have yet to confirm the role of leptin in bone. Examination of congenitally leptin deficient children has not revealed short stature or other skeletal changes evident in ob/ob mice, suggestive of altered actions of leptin in humans and mice [81]. There has been mixed results in the association between leptin concentration and BMD in males and females, showing either a positive or no association [59, 8284]. In leptin replacement therapy, hypoleptinaemic women with hypothalamic amenorrhea showed an increase in BMD in the lumbar spine after 2 years of leptin treatment [85]. Furthermore, the reduced serum leptin seen after massive weight loss by bariatric surgery was associated with increased bone resorption [23••]. However, leptin replacement failed to reverse the weight-loss associated changes in bone remodelling markers, NTX, and osteocalcin [86].


Adiponectin, like leptin, is an adipokine, being secreted from adipocytes into the circulation. Unlike leptin however, serum adiponectin levels are negatively correlated with fat mass and BMI with low expression in adipose tissue from obese mice and humans [6, 87]. Metabolically, adiponectin improves insulin sensitivity [4]. Adiponectin has been shown to have direct effects on bone remodelling. Osteoblasts and osteoclasts express both adiponectin and its receptors AdipoR1 and AdipoR2 [8890], however, there are conflicting views on the function of adiponectin in bone homeostasis. Studies have shown a positive effect on osteoblast proliferation and differentiation by adiponectin through the AdipoR1 receptor in vitro [6, 8789]. Adiponectin was also shown to directly inhibit RANKL-induced osteoclastogenesis [87]. In an animal model, systemic treatment of the adiponectin expressing adenovirus in mice increased trabecular bone mass along with reduced osteoclast number and activity [87]. On the other hand, recombinant adiponectin was reported to indirectly enhance osteoclast formation through the upregulation of RANKL and suppression of OPG expression in osteoblasts. There was no direct effect of adiponectin on osteoclast differentiation in that study [91].

The actions of adiponectin differed between its autocrine/paracrine and endocrine signalling. Although adiponectin-deficient mice showed no bone phenotype, cultures of adiponectin-deficient bone cells had reduced osteogenesis suggesting an osteogenic effect in the paracrine/autocrine pathway. Transgenic mice over expressing the adipokine in the liver (as a model for endocrine activity of adiponectin) showed no bone phenotype, yet, it was shown that recombinant adiponectin inhibited osteogenesis in vitro [90]. Overall, the data suggests that adiponectin may act through 2 opposing pathways, the autocrine/paracrine and endocrine pathways.

Clinical studies indicate that adiponectin has antiosteogenic effects on the skeleton. There is a negative relationship with serum adiponectin levels and bone mineral density (BMD) [8890]. Weight loss after 12 months postbariatric surgery was associated with an increase in adiponectin levels and reduction in BMD [88]. Thus, weight-loss from reduced food intake after bariatric surgery can affect bone mass with a change in adiponectin levels.


Overall, the secretion of gastrointestinal hormones and adipokines are not just important regulators of energy homeostasis but have strong effects on bone metabolism, often through direct signalling pathways.

There are a number of gastrointestinal hormones involved in food intake that have effects on bone metabolism as shown in Table 1. In general, the gastrointestinal hormones inhibit osteoclastic bone resorption. This demonstrates links between bone resorption and feeding states. Indeed, bone resorption markers are increased in the fasted state and decreased upon feeding coinciding with postprandial increases in the gastrointestinal peptides [1, 26].
Table 1

The response of gastrointestinal hormones to fasting and feeding and their known effects on bone




Effect on bone




Inhibition of osteoclastogenesis [14••]

Increased BMD [10]

Knockout mice - age dependent [14••]




Knockout mice - Increased bone mass and osteoblast activity [27••]

PYY overexpression - Reduced osteoblast activity [27••]




Increased osteoblast differentiation [39]

Inhibits bone resorption [39, 41, 42]

Negatively regulates bone mass [44]




Change in SMI trabecular bone pattern factor in rats [45]




Reduction in bone resorption markers Bone formation unaltered [47, 48]

Body weight is known to have a positive effect on bone. However, there is controversy as to the effect of high fat mass, as seen in obesity, on bone. Our understanding of the relationship between bone and adiposity is maturing as we refine our knowledge of the known effects of the adipokines, leptin, and adiponectin, on bone homeostasis. Obesity is associated with increased leptin and reduced adiponectin serum levels. In the case of leptin, its direct effects appear to promote bone formation, which correlates with changes in bone mass in obesity and weight loss. The centrally mediated effects of leptin on bone are unclear although it may be secondary to its pronounced effects on energy intake and hypothalamic neuropeptide signalling. The effects of adiponectin would be diminished in obesity and clinical studies indicate that adiponectin may have counteracting actions with leptin in regards to bone. Interestingly, PYY and ghrelin have been implicated in obesity-induced bone effects through NPY- and leptin-signalling respectively, linking appetite regulation to whole body energy homeostasis and obesity. It is apparent that interactions between gut hormones and adipokines should be considered in investigating bone effects in metabolic states, as well the response to gastric surgery and anorectic states.

This review reinforces our emerging understanding of the fundamental interrelationship between bone and nutritional/energy homeostatic machinery. Notwithstanding this increase in knowledge, further work is required to clarify conflicting studies. However, investigations into these hormonal regulating factors have demonstrated the complex interactions between energy and bone homeostasis and have allowed for the identification of possible drug targets based upon the roles of these hormones in metabolic and bone diseases.

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Conflict of Interest

EC Khor declares that he has no conflicts of interest. NKY Wee declares that she has no conflicts of interest. PA Baldock declares that he has no conflicts of interest.

Human and Animal Rights and Informed Consent

This article does not contain any studies with human or animal subjects performed by any of the authors.

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© Springer Science+Business Media New York 2013