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Redmond AK, Davies TM, Schofield MR, Sheard PW. New tools for the investigation of muscle fiber-type spatial distributions across histological sections. Skelet Muscle 2023; 13:7. [PMID: 37087439 PMCID: PMC10122286 DOI: 10.1186/s13395-023-00316-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Accepted: 04/16/2023] [Indexed: 04/24/2023] Open
Abstract
BACKGROUND The functional and metabolic properties of skeletal muscles are partly a function of the spatial arrangement of fibers across the muscle belly. Many muscles feature a non-uniform spatial pattern of fiber types, and alterations to the arrangement can reflect age or disease and correlate with changes in muscle mass and strength. Despite the significance of this event, descriptions of spatial fiber-type distributions across a muscle section are mainly provided qualitatively, by eye. Whilst several quantitative methods have been proposed, difficulties in implementation have meant that robust statistical analysis of fiber type distributions has not yielded new insight into the biological processes that drive the age- or disease-related changes in fiber type distributions. METHODS We review currently available approaches for analysis of data reporting fast/slow fiber type distributions on muscle sections before proposing a new method based on a generalized additive model. We compare current approaches with our new method by analysis of sections of three mouse soleus muscles that exhibit visibly different spatial fiber patterns, and we also apply our model to a dataset representing the fiber type proportions and distributions of the mouse tibialis anterior. RESULTS We highlight how current methods can lead to differing interpretations when applied to the same dataset and demonstrate how our new method is the first to permit location-based estimation of fiber-type probabilities, in turn enabling useful graphical representation. CONCLUSIONS We present an open-access online application that implements current methods as well as our new method and which aids the interpretation of a variety of statistical tools for the spatial analysis of muscle fiber distributions.
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Affiliation(s)
- Anna K Redmond
- Department of Mathematics & Statistics, University of Otago, Dunedin, 9016, New Zealand
| | - Tilman M Davies
- Department of Mathematics & Statistics, University of Otago, Dunedin, 9016, New Zealand.
| | - Matthew R Schofield
- Department of Mathematics & Statistics, University of Otago, Dunedin, 9016, New Zealand
| | - Philip W Sheard
- Department of Physiology, University of Otago, Dunedin, 9016, New Zealand
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2
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Mpampoulis T, Methenitis S, Papadopoulos C, Papadimas G, Spiliopoulou P, Stasinaki AN, Bogdanis GC, Karampatsos G, Terzis G. Weak Association Between Vastus Lateralis Muscle Fiber Composition and Fascicle Length in Young Untrained Females. Sports (Basel) 2021; 9:56. [PMID: 33925196 PMCID: PMC8146508 DOI: 10.3390/sports9050056] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Revised: 04/17/2021] [Accepted: 04/26/2021] [Indexed: 12/20/2022] Open
Abstract
The aim of the study was to investigate the relationships between vastus lateralis muscle fiber length and fiber type composition in individuals with minimal exposure to systematic resistance/power training. In sixty female physical education students (age: 21.03 ± 2.1 years, body weight: 59.8 ± 9.7 kg, body height: 166.2 ± 6.5 cm), with no experience in systematic training, lean body mass, VL muscle architecture and fiber composition type, countermovement jumping (CMJ) performance, and isometric leg press rate of force development were evaluated. Data were analyzed for all participants, as well as two equally numbered groups assigned according to their maximum countermovement jumping power (High-Power or Low-Power group). Significant but low correlations were found between type II muscle fiber percentage and fascicle length (N = 60, p < 0.05). Significant correlations were found between type IIa and IIx muscle fiber percentage cross-sectional area (%CSA) and fascicle length (N = 60; r = 0.321, and r = 0.378; respectively, p < 0.05). These correlations were higher for the High-Power group (r = 0.499, and r = 0.522; respectively, p < 0.05), and lower, and nonsignificant, for the Low-Power group. The best predictor of strength/power performance was the lean body mass of the lower extremities (r = 0.389-0.645, p < 0.05). These results suggest that in females with minimal exposure to systematic training, fascicle length may be weakly linked with type II fiber areas, only in females with high-power profiles.
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Affiliation(s)
- Thomas Mpampoulis
- Sports Performance Laboratory, School of Physical Education & Sports Science, National and Kapodistrian University of Athens, 17237 Athens, Greece; (S.M.); (P.S.); (A.-N.S.); (G.C.B.); (G.K.); (G.T.)
| | - Spyridon Methenitis
- Sports Performance Laboratory, School of Physical Education & Sports Science, National and Kapodistrian University of Athens, 17237 Athens, Greece; (S.M.); (P.S.); (A.-N.S.); (G.C.B.); (G.K.); (G.T.)
| | - Constantinos Papadopoulos
- A’ Neurology Clinic, Aiginition Hospital, Medical School, National and Kapodistrian University of Athens, 11528 Athens, Greece; (C.P.); (G.P.)
| | - Giorgos Papadimas
- A’ Neurology Clinic, Aiginition Hospital, Medical School, National and Kapodistrian University of Athens, 11528 Athens, Greece; (C.P.); (G.P.)
| | - Polyxeni Spiliopoulou
- Sports Performance Laboratory, School of Physical Education & Sports Science, National and Kapodistrian University of Athens, 17237 Athens, Greece; (S.M.); (P.S.); (A.-N.S.); (G.C.B.); (G.K.); (G.T.)
| | - Angeliki-Nikoletta Stasinaki
- Sports Performance Laboratory, School of Physical Education & Sports Science, National and Kapodistrian University of Athens, 17237 Athens, Greece; (S.M.); (P.S.); (A.-N.S.); (G.C.B.); (G.K.); (G.T.)
| | - Gregory C. Bogdanis
- Sports Performance Laboratory, School of Physical Education & Sports Science, National and Kapodistrian University of Athens, 17237 Athens, Greece; (S.M.); (P.S.); (A.-N.S.); (G.C.B.); (G.K.); (G.T.)
| | - Giorgos Karampatsos
- Sports Performance Laboratory, School of Physical Education & Sports Science, National and Kapodistrian University of Athens, 17237 Athens, Greece; (S.M.); (P.S.); (A.-N.S.); (G.C.B.); (G.K.); (G.T.)
| | - Gerasimos Terzis
- Sports Performance Laboratory, School of Physical Education & Sports Science, National and Kapodistrian University of Athens, 17237 Athens, Greece; (S.M.); (P.S.); (A.-N.S.); (G.C.B.); (G.K.); (G.T.)
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3
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Kelly NA, Hammond KG, Stec MJ, Bickel CS, Windham ST, Tuggle SC, Bamman MM. Quantification and characterization of grouped type I myofibers in human aging. Muscle Nerve 2017; 57:E52-E59. [PMID: 28561923 DOI: 10.1002/mus.25711] [Citation(s) in RCA: 42] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2016] [Revised: 05/02/2017] [Accepted: 05/28/2017] [Indexed: 11/06/2022]
Abstract
INTRODUCTION Myofiber type grouping is a histological hallmark of age-related motor unit remodeling. Despite the accepted concept that denervation-reinnervation events lead to myofiber type grouping, the completeness of those conversions remains unknown. METHODS Type I myofiber grouping was assessed in vastus lateralis biopsies from Young (26 ± 4 years; n = 27) and Older (66 ± 4 years; n = 91) adults. Grouped and ungrouped type I myofibers were evaluated for phenotypic differences. RESULTS Higher type I grouping in Older versus Young was driven by more myofibers per group (i.e., larger group size) (P < 0.05). In Older only, grouped type I myofibers displayed larger cross-sectional area, more myonuclei, lower capillary supply, and more sarco(endo)plasmic reticulum calcium ATPase I (SERCA I) expression (P < 0.05) than ungrouped type I myofibers. DISCUSSION Grouped type I myofibers retain type II characteristics suggesting that conversion during denervation-reinnervation events is either progressive or incomplete. Muscle Nerve 57: E52-E59, 2018.
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Affiliation(s)
- Neil A Kelly
- Departments of Cell, Developmental, and Integrative Biology, University of Alabama at Birmingham, Birmingham, Alabama, USA.,UAB Center for Exercise Medicine, 1313 13th Street South, OSB Room 300, University of Alabama at Birmingham, Birmingham, Alabama, 35205-5327, USA
| | - Kelley G Hammond
- UAB Center for Exercise Medicine, 1313 13th Street South, OSB Room 300, University of Alabama at Birmingham, Birmingham, Alabama, 35205-5327, USA.,Department of Physical Therapy, University of Alabama at Birmingham, Birmingham, Alabama, USA
| | - Michael J Stec
- Departments of Cell, Developmental, and Integrative Biology, University of Alabama at Birmingham, Birmingham, Alabama, USA.,UAB Center for Exercise Medicine, 1313 13th Street South, OSB Room 300, University of Alabama at Birmingham, Birmingham, Alabama, 35205-5327, USA
| | - C Scott Bickel
- UAB Center for Exercise Medicine, 1313 13th Street South, OSB Room 300, University of Alabama at Birmingham, Birmingham, Alabama, 35205-5327, USA.,Department of Physical Therapy, University of Alabama at Birmingham, Birmingham, Alabama, USA
| | - Samuel T Windham
- UAB Center for Exercise Medicine, 1313 13th Street South, OSB Room 300, University of Alabama at Birmingham, Birmingham, Alabama, 35205-5327, USA.,Department of Surgery, University of Alabama at Birmingham, Birmingham, Alabama, USA
| | - S Craig Tuggle
- Departments of Cell, Developmental, and Integrative Biology, University of Alabama at Birmingham, Birmingham, Alabama, USA.,UAB Center for Exercise Medicine, 1313 13th Street South, OSB Room 300, University of Alabama at Birmingham, Birmingham, Alabama, 35205-5327, USA
| | - Marcas M Bamman
- Departments of Cell, Developmental, and Integrative Biology, University of Alabama at Birmingham, Birmingham, Alabama, USA.,UAB Center for Exercise Medicine, 1313 13th Street South, OSB Room 300, University of Alabama at Birmingham, Birmingham, Alabama, 35205-5327, USA.,Geriatric Research, Education, and Clinical Center, VA Medical Center, Birmingham, Alabama, USA
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Bütikofer L, Zurlinden A, Bolliger MF, Kunz B, Sonderegger P. Destabilization of the neuromuscular junction by proteolytic cleavage of agrin results in precocious sarcopenia. FASEB J 2011; 25:4378-93. [PMID: 21885656 DOI: 10.1096/fj.11-191262] [Citation(s) in RCA: 100] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Abstract
Etiology and pathogenesis of sarcopenia, the progressive decline in skeletal muscle mass and strength that occurs with aging, are still poorly understood. We recently found that overexpression of the neural serine protease neurotrypsin in motoneurons resulted in the degeneration of their neuromuscular junctions (NMJ) within days. Therefore, we wondered whether neurotrypsin-dependent NMJ degeneration also affected the structure and function of the skeletal muscles. Using histological and functional analyses of neurotrypsin-overexpressing and neurotrypsin-deficient mice, we found that overexpression of neurotrypsin in motoneurons installed the full sarcopenia phenotype in young adult mice. Characteristic muscular alterations included a reduced number of muscle fibers, increased heterogeneity of fiber thickness, more centralized nuclei, fiber-type grouping, and an increased proportion of type I fibers. As in age-dependent sarcopenia, excessive fragmentation of the NMJ accompanied the muscular alterations. These results suggested the destabilization of the NMJ through proteolytic cleavage of agrin at the onset of a pathogenic pathway ending in sarcopenia. Studies of neurotrypsin-deficient and agrin-overexpressing mice revealed that old-age sarcopenia also develops without neurotrypsin and is not prevented by elevated levels of agrin. Our results define neurotrypsin- and age-dependent sarcopenia as the common final outcome of 2 etiologically distinct entities.
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Affiliation(s)
- Lukas Bütikofer
- University of Zurich, Department of Biochemistry, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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5
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Sorarù G, D'Ascenzo C, Nicolao P, Volpe M, Martignago S, Palmieri A, Romeo V, Koutsikos K, Piccione F, Cima V, Pegoraro E, Angelini C. Muscle histopathology in upper motor neuron-dominant amyotrophic lateral sclerosis. ACTA ACUST UNITED AC 2009; 9:287-93. [DOI: 10.1080/17482960802206801] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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6
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Martignago S, Fanin M, Albertini E, Pegoraro E, Angelini C. Muscle histopathology in myasthenia gravis with antibodies against MuSK and AChR. Neuropathol Appl Neurobiol 2009; 35:103-10. [PMID: 19187062 DOI: 10.1111/j.1365-2990.2008.00965.x] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
AIMS We compared myopathological features in myasthenia gravis (MG) patients with antibodies against AChR (seropositive) and muscle-specific tyrosin-kinase (MuSK). While the immunopathogenesis of seropositive MG is well known, there is a lack of pathological studies in anti-MuSK antibody-positive (MuSK+) MG. METHODS We analysed skeletal muscle biopsy features of 13 MG patients: 6 MuSK+ (all women) and 7 anti-AchR antibody-positive (AChR+) (2 women and 5 men). In our histopathological examination, we quantified the atrophy factor of both fibre types, and the extent of minicores, myofibrillar disarray, cytochrome c oxidase (COX)-negative fibres, mitochondrial aggregates and fibre type grouping. RESULTS Mean muscle fibre atrophy factor was higher in AChR+ MG than MuSK+ MG, both in type I fibres (494 vs. 210) and particularly in type II fibres (1023 vs. 300). Fibre type grouping was observed in AChR+ MG whereas COX-negative fibres were common in MuSK+ MG. Bulbar muscles were more severely affected in MuSK+ MG and the disease was more severe: the onset was usually earlier (39 years) with Myasthenia Gravis Foundation of America score III in MuSK+ MG, and score II was found in AChR+ MG (62 years). CONCLUSIONS Muscle biopsies of MuSK+ MG show myopathic signs with prominent mitochondrial abnormalities, whereas neurogenic features and atrophy are more frequently found in AChR+ MG. The mitochondrial impairment could explain the oculo-bulbar involvement in MuSK+ MG.
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Affiliation(s)
- S Martignago
- Department of Neurosciences, University of Padova, Padova, Italy
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7
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STRÖM D, HOLM S. Fibre type grouping in porcine masseter and soleus muscles assessed by the enclosed fibre type concept. A statistical and computational analysis. J Oral Rehabil 2008. [DOI: 10.1111/j.1365-2842.1997.tb00345.x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Abstract
Human skeletal muscle undergoes major structural and functional changes with advancing age. A progressive degeneration of the nervous system is now considered a major factor underlying these alterations. This review will briefly describe the changes that occur in the human motor unit with increasing age and focus specifically on the changes that relate to a degeneration of the nervous system.
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Affiliation(s)
- J Lexell
- Lund University Hospital, Orupssjukhuset, Sweden
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9
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Phoenix J, Betal D, Roberts N, Helliwell TR, Edwards RH. Objective quantification of muscle and fat in human dystrophic muscle by magnetic resonance image analysis. Muscle Nerve 1996; 19:302-10. [PMID: 8606693 DOI: 10.1002/(sici)1097-4598(199603)19:3<302::aid-mus4>3.0.co;2-h] [Citation(s) in RCA: 67] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
Information about changes in muscle composition has to date been primarily restricted to histological examination of biopsy samples or qualitative assessment of images obtained using a variety of techniques (e.g., ultrasound, CT, and MRI). We describe the development of a quantitative method for the analysis of muscle composition using MR T2 relaxation time mapping and image analysis. This approach provides an objective means of studying muscle and, when used in conjunction with force production measurements, may provide an accurate measure of response to muscle therapy.
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Affiliation(s)
- J Phoenix
- Magnetic Resonance Research Centre, Department of Medicine, University of Liverpool, United Kingdom
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10
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Abstract
The analysis of Gates and Betz (1993 Anat. Rec., 236:381-389) of the spatial distribution of two different populations of muscle fibers in the lumbrical muscle of the rat is discussed. The conclusion that muscle fibers belonging to a single motor unit are distributed at random in most muscles appears to need reconsideration. A new technique is applied to some examples to show that the amount of clustering of fiber types in a muscle cross section can be quantified.
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Affiliation(s)
- H W Venema
- Department of Diagnostic Radiology, University of Amsterdam, The Netherlands
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11
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Lester JM, Soule NW, Bradley WG, Brenner JF. An augmented computer model of motor unit reorganization in neurogenic diseases of skeletal muscle. Muscle Nerve 1993; 16:43-56. [PMID: 8423831 DOI: 10.1002/mus.880160109] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
A computer model of denervation and complete reinnervation in skeletal muscle was originally developed for the purpose of furthering an understanding of the underlying mechanisms of motor unit reorganization in neurogenic diseases. We now describe its successor, a computer model for investigating different rates of denervation and reinnervation, as well as incomplete reinnervation. The new model introduces the concept of permanent denervation and features enhanced interactive control over the distribution of motor unit centers and additional measures of dispersion and co-dispersion of muscle fibers. The use of this model for investigating pathophysiologically significant issues in denervating diseases is illustrated with five different sets of parameters. These simulate some of the processes that may be operational in chronic spinal muscular atrophy, amyotrophic lateral sclerosis, and progressive postpolio muscular dystrophy. The enhanced model will allow in-depth analysis of the influence of hypothesized pathophysiological processes on clinical, electrophysiological and pathological outcomes in human disease.
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Affiliation(s)
- J M Lester
- Image Analysis Laboratory, New England Medical Center Hospitals, Boston, Massachusetts 02111
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12
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Harrison GD, Duncan ID, Clayton MK. Determination of the early age of onset of equine recurrent laryngeal neuropathy. 1. Muscle pathology. Acta Neuropathol 1992; 84:307-15. [PMID: 1384268 DOI: 10.1007/bf00227824] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
The age of onset of equine recurrent laryngeal neuropathy has not been ascertained, although the clinical condition of left laryngeal hemiplegia ("roaring") has been recognized for centuries. The purpose of this study was to evaluate the laryngeal muscles of draft horse foals for the presence of fiber-type grouping, indicating denervation and reinnervation, and to determine if histological evidence of recurrent laryngeal neuropathy was present. Abductor and adductor laryngeal muscles from the left and right sides were collected immediately after euthanasia from male draft horse foals, six less than 2 weeks and four 6 months of age, and stained for myosin ATPase. A morphometric test was used to objectively evaluate several areas from each muscle for fiber-type grouping. Extensive fiber-type grouping which was characteristic of recurrent laryngeal neuropathy was found in one of the young foals and all of the older foals. Four of the young foals had some areas of fiber-type grouping suggestive of mild, early changes associated with recurrent laryngeal neuropathy. One of the young foals had no fiber-type grouping present in any of the laryngeal muscles evaluated. These findings suggest an early age of onset of recurrent laryngeal neuropathy.
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Affiliation(s)
- G D Harrison
- Department of Medical Sciences, School of Veterinary Medicine, University of Wisconsin, Madison 53706
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13
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Abstract
A new approach to the quantification of fiber type grouping is presented, in which the distribution of histochemical type in a muscle cross section is regarded as a realization of a binary Markov random field (BMRF). Methods for the estimation of the parameters of this model are discussed. The first order BMRF, which is used in this article, contains 2 parameters: alpha and beta. The parameter beta is of prime importance, as it is an interaction parameter which governs the degree of type grouping. The value of this parameter is estimated for 9 muscle biopsies. The interpretation of the results is discussed.
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Affiliation(s)
- H W Venema
- Laboratory of Medical Physics and Informatics, University of Amsterdam, The Netherlands
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14
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Lexell J, Sjöström M, Nordlund AS, Taylor CC. Growth and development of human muscle: a quantitative morphological study of whole vastus lateralis from childhood to adult age. Muscle Nerve 1992; 15:404-9. [PMID: 1557091 DOI: 10.1002/mus.880150323] [Citation(s) in RCA: 127] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
The mechanisms underlying the increase in volume of muscle tissue, and the functional development of muscle fibers from childhood through adolescence to adult age, have been studied. Cross sections of autopsied whole vastus lateralis muscle from 22 previously physically healthy males, 5 to 37 years of age, were prepared enzyme histochemically (myofibrillar ATPase) and examined morphometrically. The data obtained on muscle cross-sectional area, size, total number, and proportion of type 1 (slow-twitch) and type 2 (fast-twitch) fibers were analyzed using linear regression techniques. The results show that the increase in muscle cross-sectional area from childhood to adult age is caused by an increase in mean fiber size. This is accompanied by a functional development of the fiber population: the proportion of type 2 fibers increases significantly from the age of 5 (approx. 35%) to the age of 20 (approx. 50%), which, in the absence of any discernible effect on the total number of fibers, is most likely caused by a transformation of type 1 to type 2 fibers.
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Affiliation(s)
- J Lexell
- Department of Neurology, University of Umeå, Sweden
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15
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Lexell J, Downham DY. The occurrence of fibre-type grouping in healthy human muscle: a quantitative study of cross-sections of whole vastus lateralis from men between 15 and 83 years. Acta Neuropathol 1991; 81:377-81. [PMID: 2028741 DOI: 10.1007/bf00293457] [Citation(s) in RCA: 129] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
Methods that objectively assess the muscle fibre-type arrangement may improve the detection of fibre-type grouping, a diagnostic sign of a denervation and reinnervation process. To distinguish between a diseased and a normal muscle, there is a need for quantitative data on the fibre-type arrangement in healthy human muscles at different ages. In this study, cross-sections were prepared of whole autopsied vastus lateralis muscle from 24 previously physically healthy men, aged 15 to 83 years. The arrangements of type 1 and type 2 fibers were assessed in terms of the number of enclosed fibres in individual fascicles throughout each muscle. Recent improvements to the enclosed fibre method were used to define measures of randomness which facilitated the combination of several sample areas and the quantification of the fibre-type arrangements. Segregation was typical for young muscles, randomness was most common between 30 and 50 years of age, while some fibre-type grouping was considered "normal" in old muscles. The arrangements of type 1 and type 2 fibres were quantitatively similar, irrespective of the age of the individual. The results imply that the fibre population changes considerably during a lifetime, and that it undergoes a continuous denervation and reinnervation process with normal ageing. Because of its importance, age should be accommodated in the analysis of a muscle sample, irrespective of the statistical model and method used.
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Affiliation(s)
- J Lexell
- Department of Neurology, University of Umeå, Sweden
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16
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Abstract
Algorithms are described for the calculation of spatial statistics. The statistics are the functions K(t), G(y), F(x), and K12(t). They can be used to determine (a) which type of spatial process ('random', 'clustered', 'regular', etc.) best fits a data set and whether the spatial pattern changes with distance, and (b) whether two types of events are correlated with each other, and if so, at which distances the correlation occurs. These functions provide a powerful tool for analysing the spatial distribution of biomedical and biological phenomena. An interactive, command-driven program that incorporates these algorithms is described.
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Affiliation(s)
- M Fisher
- Department of Biology, Sultan Qaboos University, Muscat, Sultanate of Oman
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17
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Lexell J, Wilson C, Downham D. Detection of fiber type grouping: further improvements to the enclosed fiber method. Muscle Nerve 1989; 12:1024-6. [PMID: 2622469 DOI: 10.1002/mus.880121211] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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