Skip to main content
Download PDF

Effect of athletic fatigue damage and the associated bone targeted remodeling in the rat ulna

BioMedical Engineering OnLine volume 16, Article number: 99 (2017) Cite this article

Abstract

Background

Fatigue damage of the long bones is prevalent in running athletes and military recruits due to vigorous mid- and long-term physical activity. The current study attempted to know the features of bony athletic fatigue damage and to explore the mechanism of fatigue damage repair through bone targeted remodeling process.

Methods

Right ulnae of the Wistar rats were fatigue loaded on an INSTRON 5865 to construct the athletic fatigue damage model, and several time points (i.e. experimental days: 0, 7, 13 and 19) were selected to simulate physiological status, preliminary, mid-term and perennial stage during continuous high-intensive training, respectively. The multi-level responses of rat ulnae under the athletic fatigue loading, including cellular protein expression, micro damage or micro-crack and macro mechanical properties, were tested and statistically analyzed.

Results

Wistar rats, subjected to the athletic fatigue loading protocol, experienced a decrease of ulna fatigue mechanical properties and an active bone resorption of the loaded ulnae in the early stage, whereafter, a hyperactive bone formation and significant improvements of ulnae fatigue mechanical properties were detected. However, a deterioration of quasi-static mechanical properties in the subsequent period implied limitations of bone remodeling to maintain the bearing capacity of bone during long-term strenuous exercise.

Conclusions

In summary, after athletic fatigue loading, bone targeted remodeling is activated and proceeds to repair fatigue damage, but only to a certain extent.

Background

Bones experience various mechanical environments in daily human activities, with exceptional mechano-sensitivity resulting from bone remodeling by an activity “balance” between osteoblasts (OBs) and osteoclasts (OCs) [1,2,3]. A large proportion (approximately 70%) of bone remodeling is stochastic, participating in biochemical regulation and balancing calcium salt, and the other 30% is targeted remodeling, which is specialized to repair damage or microcracks in bones according to their load situation and demands [4,5,6]. There are common or universal mechanisms of bone damage and targeted remodeling processes among species that are based on the local strain or stress distribution [1, 7].

Long bone fatigue damage is prevalent in running athletes and military recruits due to vigorous mid- and long-term physical activity [8, 9]. It is characterized as generation, accumulation and coalescence of microcracks; the deterioration of mechanical properties; or even stress fractures [10, 11]. Loading intensity, frequency (f), and number of cycles (N) are critical factors that influence bone fatigue damage [12, 13], and there also seems to be a threshold of local peak strain that leads to destructive bone damage and bearing invalidation [14,15,16].

In the present study, we hypothesized that 8000 cycles of dynamic loading producing a 3000 με peak strain on the rat ulna could imitate athletic fatigue damage and activate the bone targeted remodeling process, and based on our earlier experiments, we constructed an athletic fatigue damage model of the rat ulna, and attempted to explore the features of bony athletic fatigue damage and the mechanism of fatigue damage repair through bone targeted remodeling process.

Methods

Animals and materials

Female Wistar rats (3 months old) were obtained from the laboratory animal center of the Academy of Military Medical Sciences in Beijing, China. The experiments performed were within the animal welfare regulations and guidelines for the Academy of Military Medical Sciences. ELISA Kits for rat estradiol (E2), bone gamma-carboxyglutamic-acid-containing protein (BGP) and tartrate-resistant acid phosphatase 5b (TRAP-5b) were purchased from Cloud-Clone Corporation in Wuhan, China.

Experimental design

A total of 33 female Wistar rats were randomly divided into four groups by athletic fatigue loading duration, including a physiological intensity group (i.e. Group Day 0 or the Control group, 9 rats) and three high-intensity groups (Group Day 7, Day 13 and Day 19; 8 rats/group). Rats in the control group were fed normally with no fatigue loading, while the right ulnae of the rats in the high-intensity groups were fatigue-loaded on an INSTRON 5865 with general anesthesia every other day for 8000 cycles at a frequency of 1.5 Hz and a constant strain amplitude of 3000 με over a period of 20 days (a total of nine loading days starting from the second day), and data of σ–ε were recorded every 500 loading cycles (Fig. 1). Samples of rat ulnae and serum were obtained from the rats sacrificed on day 7 (Group Day 7), day 13 (Group Day 13) and day 19 (Group Day 19). Histological and morphometric analyses were performed using hematoxylin–eosin (HE) staining on non-decalcified ulna slices. Concentrations of serum proteins (E2, BGP and TRAP-5b) and mechanical properties were also analyzed.

Fig. 1
figure 1

The athletic fatigue loading of rat ulna (a) and compressive σ–ε curves recording (b) on an INSTRON 5865

Full size image

Development of the athletic fatigue damage model in the rat ulna

Loading parameters for the athletic fatigue damage model were determined using preliminary results. The average loading frequency (f = 1.5 Hz) was calculated based on sports data and the standard statistics of male Chinese running athletes and military recruits (Table 1). The local strain distribution (Fig. 2) and fatigue behavior of the rat ulna under a specific loading intensity (εmax = 3000 με) was simulated using 3D reconstruction and finite element analysis (FEA) [17]. The percent decrease in the secant modulus (Es) and the associated cyclic energy dissipation (Hc) were common indices of material fatigue behavior [12, 18, 19]. In the present study, the number of fatigue loading cycles was determined by an in vitro fatigue test of rat ulnae, and we considered a 25% decrease in the Es [20,21,22] with significant Hc changes as validation of the athletic fatigue damage model, which could activate bone targeted remodeling.

Table 1 Determination of the athletic fatigue loading frequency based on Chinese sports statistics
Full size table
Fig. 2
figure 2

Local strain distribution in rat ulna under specific loading amplitude using FEA

Full size image

Histology and morphometric analysis

Hematoxylin–eosin staining on non-decalcified slices of the middle sections of the ulnae were performed by XueBang Pathology Corporation in Beijing, China. A qualitative observation of ulnar micromorphology was performed on an optical microscope (Olympus, Japan), and the percentage of empty osteocyte lacunae was quantitatively analyzed and compared between different groups.

Tests of serum protein expression and ulnar mechanical behavior

ELISA kits for TRAP-5b and BGP were used to detect bone resorption and formation, respectively. The influence of estrogen on bone remodeling [17, 23, 24] was also determined by assaying serum estradiol with an E2 ELISA Kit. The quasi-static mechanical properties of the ulnae were tested on an INSTRON 5865 (Instron Corporation, England) with the following parameters: (1) 0.5 N preload, 5 uniaxial loading cycles of displacement with a loading rate of 1%/min to a maximum of 0.4%; (2) a loading rate of 5%/min to fracture. Compressive modulus (E), strength (σb) and fracture energy (Hf) were determined. Fatigue mechanical properties, including cyclic Es, Hc and cycles to fatigue (Nf), were evaluated based on the stress–strain (σ–ε) data recorded during fatigue loading. Es was the slope of the line through the start and end points in the loading stage of the σ–ε loop. Hc was the area of the σ–ε loop, determined by integration, and Nf was the number of fatigue loading cycles at 25% Es decrease, determined by interpolation.

Statistical analysis

Data are presented as the mean ± SD and were from at least three independent experiments. The research was designed and simplified from a two-independent-variable experiment based on the theory of “mechanostat” [1]. Significant differences were evaluated with a one-way analysis of variance (ANOVA) followed by a least significant difference (LSD) t test. Significance was defined as p < 0.05.

Results

Values of Es were calculated and standardized (Es’) based on the 500th cycle,and curves of Es’–N and Hc–N are shown in Fig. 3. The ulnae in all groups experienced fatigue successively, with Es’ falling to the fatigue line (25% decrease) (Fig. 3a), and there were obvious decreases in Hc with increasing fatigue loading cycles (Fig. 3b). Therefore, the model of athletic fatigue damage was validated.

Fig. 3
figure 3

Changes of standardized secant modulus (Es’) (a) and cyclic energy dissipation (Hc) (b) in different groups with fatigue loading cycles

Full size image

Qualitative observation of the HE-stained, non-decalcified ulnae slices from different groups showed deterioration of the bone microstructure under athletic fatigue loading (Fig. 4). Microcrack generation (Fig. 4b), growth (Fig. 4c, d) and even coalescence (Fig. 4e) in the interstitial bone reflected an aggravation of bone fatigue damage. Significant increases in the percent of empty osteocyte lacunae were also detected (Fig. 4f) in the high intensity groups, suggesting apoptosis of osteocytes.

Fig. 4
figure 4

Non-decalcified slices of rat ulnae and empty osteocyte lacunae statistics. Few empty osteocyte lacunae and almost no obvious microcracks were detected in the Control Group (a), while generation, growth and coalescence of microcracks (black arrows) were observed sequentially in Group Day 7 (b), Group Day 13 (c) and Group Day 19 (d, e). Significant increases of empty osteocyte lacunae, especially around microcracks, were also detected (white arrows) and statistically verified (f)

Full size image

The concentrations of serum proteins (E2, TRAP-5b and BGP) were assayed and are listed in Table 2. No significant differences in serum E2 levels were detected; therefore, the possible influence of estrogen on bone targeted remodeling could be disregarded in our study. A significant increase in serum TRAP-5b in Day 7 suggested fatigue damage and the activation of bone targeted remodeling, and reduced serum TRAP-5b and increased serum BGP from Day 7 to Day 19 demonstrated a process of continuous bone targeted remodeling.

Table 2 ELISA assay of serum E2, BGP and TRAP-5b
Full size table

Fatigue mechanical behavior of the ulnae (Es and Hc) were sensitive to fatigue loading, and significant changes were detected from Day 7, while the quasi-static mechanical properties (E, σb and Hf) seemed to be hysteretic and did not experience significant changes until Day 13 or even Day 19 (Fig. 5). Nf was also statistically analyzed and the results are shown in Fig. 6. Decreases in Nf were detected in all fatigue loading groups, with the valley value on Day 7, which implied a rapid deterioration of the fatigue mechanical properties after fatigue loading and effective improvements by subsequent bone targeted remodeling.

Fig. 5
figure 5

Histogram of ulnar mechanical properties in different fatigue loading groups

Full size image
Fig. 6
figure 6

Statistical analysis of Nf on each loading day

Full size image

Finally, we summarized the relative changes of several key indices of bone targeted remodeling at different levels (Fig. 7) and achieved a systematic understanding of the bone targeted remodeling process under athletic fatigue loading. This understanding could likely offer effective insights regarding to the training of athletes and military recruits.

Fig. 7
figure 7

Sketch of index changes during fatigue damage induced bone targeted remodeling

Full size image

Discussion

The basic principles of bone remodeling are universal regardless of bone dimensions [1, 7], but there are huge differences in the metabolism rates of rats and humans [23]. When we determined the athletic fatigue loading parameters (loading duration, amplitude and sampling intervals), its effect on the bone targeted remodeling process had been fully considered.

We originally designed the experiment with two independent variables (periods and exercise), and simplified it (during sampling, assay and analysis) as a single variable (athletic fatigue loading duration) experiment based on Frost’s theory of the “mechanostat” [1]. Despite of the weight increase, daily activities of the 3-month-old rats in the control group could produce a physiological deformation of ulnae (with a 200–1000 με axial peak strain [25]), which would not disturb the metabolism balance between bone resorption (osteoclasts activities) and bone formation (osteoblasts activities), or lead to a detectable change of bone mechanical properties within 1 month.

Dynamic compressive loading on the long bones is common during daily activities [14, 19], and the decrease in the secant modulus is mostly a result of bone damage or microcracks [22]. The athletic fatigue loading protocol used in the present study resulted in significant decreases in bone fatigue mechanical properties (Figs. 3, 5 and 6); the generation of microcracks in the interstitial bone (Fig. 4b); and an imbalance between bone resorption and bone formation (Table 2) in the early stage (Group Day 7). Our hypothesis on bone fatigue damage and the associated targeted remodeling was therefore confirmed.

An osteon in the cortical bone acts not only as a stress concentrator that accounts for microcrack generation [25,26,27] but also as a guard against microcrack growth to maintain the load-bearing capacity of the bone during daily activity [28, 29]. During continuous vigorous activity, however, microcracks will grow and even develop to the macro scale, leading to a stress fracture [9, 21, 30]. Our study supported these results. From Day 7 to Day 13, small microcracks were observed (Fig. 4b, c), and fatigue mechanical properties also improved (Figs. 5, 6). At Day 19, larger microcracks grew and coalesced (Fig. 4d, e), and significant decreases in quasi-static mechanical properties were detected (Fig. 5), which affected the load-bearing capacity and increased the risk of stress fractures.

The integrity of osteocytes is vital for the structural and functional stability of bone [31]. There seems to be a threshold of microdamage or local strain [16] over which fatigue loading or the necessity of bone targeted remodeling could lead to the apoptosis of osteocytes [23, 24, 32]. In the current study, we confirmed the stable apoptosis of osteocytes in the high-intensity groups during fatigue loading through the significant increase in the percentage of empty osteocyte lacunae (Fig. 4f) along the microcracks near osteons (Fig. 4b–d) when compared with the Control group. However, there might be different mechanisms of osteocyte apoptosis in different groups. The apoptosis observed at Day 7 and Day 13 might result from the necessity of bone targeted remodeling at the early stage because small microcracks and active bone resorption were detected. By contrast, at Day 19, larger linear microcracks were observed despite hyperactive bone formation; therefore, it was likely the severe fatigue damage in the interstitial bone that sequentially prompted osteocyte apoptosis.

Finally, the responses of the bone at different levels under various mechanical conditions should compose a unified model. We achieved a systematic understanding of the process of bone targeted remodeling under athletic fatigue loading, as illustrated in Fig. 7. Strenuous activity in the early stage (3 days in rats or 1 month in humans [23]) would cause rapid microdamage, decreases in fatigue mechanical properties and obvious bone resorption in the long bones. With increasing time, the risks of stress fracture would increase with the deterioration of the quasi-static mechanical properties of the bone despite a continuous bone targeted remodeling process, suggesting a limitation or a maximum ability to repair excessively damaged bone. For this reason, excessive early-stage training or long-term intensive training without appropriate rests should be avoided to prevent the risk of accumulative fatigue damage or even stress fractures.

Conclusion

An athletic fatigue damage model of rat ulna was successfully established. Fatigue damage was aggravated in the loading process, with osteocyte apoptosis, microcrack accumulation, and a decrease in mechanical properties. Bone targeted remodeling was activated after athletic fatigue loading and progressively leaned towards bone formation and away from bone resorption to repair fatigue damage, though to some extent.

Abbreviations

OBs:

osteoblasts

OCs:

osteoclasts

E2:

estradiol

BGP:

bone gamma-carboxyglutamic-acid-containing protein

TRAP-5b:

tartrate-resistant acid phosphatase 5b

FEA:

finite element analysis

References

  1. Frost HM. Bone ‘‘mass’’ and the ‘‘mechanostat’’: a proposal. Anat Rec. 1987;219(1):1–9.

    Article  Google Scholar 

  2. Burger EH, Klein NJ, Smit TH. Strain-derived canalicular fluid flow regulates osteoclast activity in a remodeling osteons—a proposal. J Biomech. 2003;36(10):1453–9.

    Article  Google Scholar 

  3. Noble BS, Peet N, Stevens HY, Brabbs A, Mosley JR, Reilly GC, Reeve J, Skerry TM, Lanyon LE. Mechanical loading: biphasic osteocytes survival and targeting of osteoclasts for bone destruction in rat cortical bone. Am J Physiol-Cell Physiol. 2003;284(4):C934–43.

    Article  Google Scholar 

  4. Frost HM. Bone microdamage: factors that impair its repair. In: Uhthoff HK, editor. Current concepts of bone fragility. Berlin: Springer-Verlag; 1985. p. 123–48.

    Google Scholar 

  5. Mori S, Burr DB. Increased intracortical remodeling following fatigue damage. Bone. 1993;14(2):103–9.

    Article  Google Scholar 

  6. Burr DB. Targeted and nontargeted remodeling. Bone. 2002;30(1):2–4.

    Article  MathSciNet  Google Scholar 

  7. Frost HM. The mechanostat: a proposed pathogenetic mechanism of osteoporoses and the bone mass effects of mechanical and nonmechanical agents. Bone Miner. 1987;2(2):73–85.

    Google Scholar 

  8. Chapurlat RD, Delmas PD. Bone microdamage: a clinical perspective. Osteoporos Int. 2009;20(8):1299–308.

    Article  Google Scholar 

  9. Green JO, Wang J, Diab T, Vidakovic B, Guldberg RE. Age-related differences in the morphology of micro-damage propagation in trabecular bone. J Biomech. 2011;44(15):2659–66.

    Article  Google Scholar 

  10. Danova NA, Colopy SA, Radtke CL, Kalscheur VL, Markel MD Jr, Vanderby R, McCabe RP, Escarcega AJ, Muir P. Degradation of bone structural properties by accumulation and coalescence of microcracks. Bone. 2003;33(2):197–205.

    Article  Google Scholar 

  11. Chapurlat RD. Bone microdamage. Osteoporos Int. 2009;20(6):1033–5.

    Article  Google Scholar 

  12. Yamamoto E, Paul CR, Chan DD, Keaveny TM. Development of residual strains in human vertebral trabecular bone after prolonged static and cyclic loading at low load levels. J Biomech. 2006;39(10):1812–8.

    Article  Google Scholar 

  13. Pasqualini M, Lavet C, Elbadaoui M, Vanden BA, Laroche N, Gnyubkin V, Vico L. Skeletal site-specific effects of whole body vibration in mature rats: from deleterious to beneficial frequency-dependent effects. Bone. 2013;55(1):69–77.

    Article  Google Scholar 

  14. Kotha SP, Hsieh YF, Strigel RM, Müller R, Silva MJ. Experimental and finite element analysis of the rat ulnar loading model-correlations between strain and bone formation following fatigue loading. J Biomech. 2004;37(4):541–8.

    Article  Google Scholar 

  15. Nagaraja S, Couse TL, Guldberg RE. Trabecular bone microdamage and microstructural stresses under uniaxial compression. J Biomech. 2005;38(4):707–16.

    Article  Google Scholar 

  16. McNamara LM, Prendergast PJ. Bone remodeling algorithms incorporating both strain and microdamage stimuli. J Biomech. 2007;40(6):1381–91.

    Article  Google Scholar 

  17. Li H, Li RX, Wan ZM, Xu C, Li JY, Hao QX, Guo Y, Liu L, Zhang XZ. Counter-effect of constrained dynamic loading on osteoporosis in ovariectomized mice. J Biomech. 2013;46(7):1242–7.

    Article  Google Scholar 

  18. Haddock SM, Yeh OC, Mummaneni PV, Rosenberg WS, Keaveny TM. Similarity in the fatigue behavior of trabecular bone across site and species. J Biomech. 2004;37(2):181–7.

    Article  Google Scholar 

  19. Sobelman OS, Gibeling JC, Stover SM, Hazelwood SJ, Yeh OC, Shelton DR, Martin RB. Do microcracks decrease or increase fatigue resistance in cortical bone? J Biomech. 2004;37(9):1295–303.

    Article  Google Scholar 

  20. Burr DB, Turner CH, Naick P, Forwood MR, Ambrosius W, Hasan MS, Pidaparti R. Does microdamage accumulation affect the mechanical properties of bone? J Biomech. 1998;31(4):337–45.

    Article  Google Scholar 

  21. Diab T, Vashishth D. Effects of damage morphology on cortical bone fragility. Bone. 2005;37(1):96–102.

    Article  Google Scholar 

  22. Muir P, Sample SJ, Barrett JG, McCarthy J Jr, Vanderby R, Markel MD, Prokuski LJ, Kalscheur VL. Effect of fatigue loading and associated matrix microdamage on bone blood flow and interstitial fluid flow. Bone. 2007;40(4):948–56.

    Article  Google Scholar 

  23. Tomkinson A, Gevers EF, Wit JM, Reeve J, Noble BS. The role of estrogen in the control of rat osteocyte apoptosis. J Bone Miner Res. 1998;13(8):1243–50.

    Article  Google Scholar 

  24. Verborgt O, Gibson GJ, Schaffler MB. Loss of osteocyte integrity in association with microdamage and bone remodeling after fatigue in vivo. J Bone Miner Res. 2000;15(1):60–7.

    Article  Google Scholar 

  25. Burr DB, Milgrom C, Fyhrie D, Forwood M, Nyska M, Finestone A, Hoshaw S, Saiag E, Simkin A. In vivo measurement of human tibial strains during vigorous activity. Bone. 1996;18(5):405–10.

    Article  Google Scholar 

  26. Akkus O, Rimnac CM. Cortical bone tissue resists fatigue fracture by deceleration and arrest of microcrack growth. J Biomech. 2001;34(6):757–64.

    Article  Google Scholar 

  27. Park HC, Lakes RS. Cosserat micromechanics of human bone: strain redistribution by a hydration sensitive constituent. J Biomech. 1986;19(5):385–97.

    Article  Google Scholar 

  28. Mosekilde L. Consequences of the remodelling process for vertebral trabecular bone structure: a scanning electron microscopy study (uncoupling of unloaded structures). Bone Miner. 1990;10(1):13–35.

    Article  Google Scholar 

  29. Vashishth D, Behiri JC, Bonfield W. Crack growth resistance in cortical bone: concept of microcrack toughening. J Biomech. 1997;30(8):763–9.

    Article  Google Scholar 

  30. Turnbull TL, Baumann AP, Roeder RK. Fatigue microcracks that initiate fracture are located near elevated intracortical porosity but not elevated mineralization. J Biomech. 2014;47(12):3135–42.

    Article  Google Scholar 

  31. Herman BC, Cardoso L, Majeska RJ, Jepsen KJ, Schaffler MB. Activation of bone remodeling after fatigue: differential response to linear microcracks and diffuse damage. Bone. 2010;47(4):766–72.

    Article  Google Scholar 

  32. Galley SA, Michalek DJ, Donahue SW. A fatigue microcrack alters fluid velocities in a computational model of interstitial fluid flow in cortical bone. J Biomech. 2006;39(11):2026–33.

    Article  Google Scholar 

Download references

Authors’ contributions

LH and LRX made substantial contributions to conception and design, analysis and interpretation of data, and manuscript drafting; HB carried out the ulnar fatigue loading and mechanical property tests; ZB and HBH conducted assays of the selected biochemistry index; LYJ was responsible for manuscript revising and polishing; ZXZ, who was the corresponding author, gave financial support and final approval of the version to be submitted. All authors read and approved the final manuscript.

Acknowledgements

This research is supported by the Major Program of the National Natural Science Foundation of China (No. 11432016) and the General Programs of the National Natural Science Foundation of China (No. 31370942 and No. 31470935).

Competing interests

The authors declare that they have no competing interests.

Data availability statements

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Statement on ethics approval

The experiments on the Wistar rats performed in the current study were within the animal welfare regulations and guidelines for the Academy of Military Medical Sciences, China.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Author information

Authors and Affiliations

  1. Institute of Medical Equipment, Academy of Military Medical Sciences, Tianjin, China

    Li Hao, Li Rui-Xin, Han Biao, Liu Ying-Jie & Zhang Xi-Zheng

  2. Department of Orthopaedics Trauma, First Hospital of Jilin University, Changchun, China

    Zhao Bin & Hao Bao-Hui

Authors
  1. Li Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Rui-Xin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Han Biao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhao Bin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hao Bao-Hui
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Liu Ying-Jie
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Zhang Xi-Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhang Xi-Zheng.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hao, L., Rui-Xin, L., Biao, H. et al. Effect of athletic fatigue damage and the associated bone targeted remodeling in the rat ulna. BioMed Eng OnLine 16, 99 (2017). https://doi.org/10.1186/s12938-017-0384-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1186/s12938-017-0384-1

Keywords

BioMedical Engineering OnLine

ISSN: 1475-925X

Contact us