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Topic:Spine

The equine spine is a complex structure composed of numerous vertebrae that provide support, facilitate movement, and protect the spinal cord. It is divided into several regions: cervical, thoracic, lumbar, sacral, and coccygeal, each contributing to the overall biomechanics and flexibility of the horse. The spine plays a significant role in the horse's locomotion, posture, and ability to perform various tasks. Research on the equine spine encompasses studies on its anatomy, function, and the impact of various conditions such as injuries, deformities, and age-related changes. This page compiles peer-reviewed research studies and scholarly articles that explore the structural and functional aspects of the equine spine, as well as its role in equine health and performance.
Heterogeneity among traumatic spinal cord injuries at the thoracolumbar junction: helping select patients for clinical trials.
Spinal cord    June 25, 2019   Volume 57, Issue 11 972-978 doi: 10.1038/s41393-019-0317-x
Liu SJ, Wang Q, Tang HH, Bai JZ, Wang FY, Lv Z, Chen SZ, Liu JS, Hong Y, Zhang JW.Retrospective analysis. Methods: China Rehabilitation Research Center, Beijing, China. Objective: A retrospective study that documents the modalities and clarifies the heterogeneity among spinal cord injuries (SCIs) caused by trauma to the thoracolumbar vertebral junction. Methods: X-ray and MRI imaging, neurological records, and the urodynamics results of 190 patients were reviewed and used to categorize different SCI modalities. First, injuries were divided into complete and incomplete injuries using the International Standard for Neurological Classification of Spinal Cord Injury. Next, the ...
Ex Vivo Assessment of an Ultrasound-Guided Injection Technique of the Lumbosacral Disc in the Horse.
Veterinary and comparative orthopaedics and traumatology : V.C.O.T    June 11, 2019   Volume 32, Issue 5 383-388 doi: 10.1055/s-0039-1691793
Robert M, Manet H, Manneveau G, Geffroy O. The aim of this study was to describe an ultrasound-guided injection technique of the lumbosacral disc in horses through the cranial vertebral notch of the sacrum and to evaluate both accuracy and potential complications of the technique on equine cadavers. Methods:  Twenty-four injections of the lumbosacral area were performed on 12 equine cadavers shortly after euthanasia under ultrasound guidance with the horse in recumbency using two different dyes (one colour for each side). The lumbosacral area was dissected in each horse and the accuracy of the technique, as well as its potential c...
Update on Surgical Treatment of Wobblers.
The Veterinary clinics of North America. Equine practice    May 27, 2019   Volume 35, Issue 2 299-309 doi: 10.1016/j.cveq.2019.04.002
Pezzanite L, Easley J.Cervical vertebral compressive myelopathy (CVCM) represents the most significant disease of the spinal cord in horses for which surgical treatment is described. Current surgical methods used include ventral interbody fusion with kerf cut cylinders and dorsal laminectomy. Polyaxial pedicle screw and rod constructs and ventral locking compression plating have been introduced in the treatment of equine CVCM and present promising alternative approaches to achieve ventral interbody fusion. Advancements in diagnostic imaging and endoscopy of the cervical vertebral canal may improve reliable preopera...
Performance comparison of 159 Thoroughbred racehorses and matched cohorts before and after desmotomy of the interspinous ligament.
Veterinary journal (London, England : 1997)    May 11, 2019   Volume 249 16-23 doi: 10.1016/j.tvjl.2019.05.004
Derham AM, O'Leary JM, Connolly SE, Schumacher J, Kelly G.Racehorses may perform poorly because of impinging dorsal spinous processes (DSPs) of the thoracolumbar vertebrae. No study has looked objectively at the long-term outcome of racehorses undergoing desmotomy of the interspinous ligament as a treatment for horses with poor performance caused by impinging DSPs. The aim of this study was to examine objectively, by using pre-operative and post-operative racing records, the effectiveness of desmotomy of the interspinous ligament (DISL) in improving the performance of racehorses with impinging DSPs. Medical records of all horses undergoing desmotomy ...
Clinical investigation of back disorders in horses: A retrospective study (2002-2017).
Veterinary world    March 12, 2019   Volume 12, Issue 3 377-381 doi: 10.14202/vetworld.2019.377-381
Mayaki AM, Intan-Shameha AR, Noraniza MA, Mazlina M, Adamu L, Abdullah R.Back disorder is an ailment that often affects athletic and riding horses. Despite the rapidly growing equine athletic and equestrian activities, there is no documentation on the nature of equine back disorder (EBD) in Malaysian horses. The purpose of this study was to characterize EBD cases presented to University Veterinary Hospital, Universiti Putra Malaysia, between 2002 and 2017. Methods: The compilation of data was based on signalment, case history, duration of clinical signs, anatomical location of the pain, method of diagnosis, type of EBD, treatment, and outcome. The diagnosis of EBD ...
The Translation of Movement From the Equine to Rider With Relevance for Hippotherapy.
Journal of equine veterinary science    February 28, 2019   Volume 77 125-131 doi: 10.1016/j.jevs.2019.02.017
Donaldson MC, Holter AM, Neuhoff S, Arnosky JA, Simpson BW, Vernon K, Blob RW, DesJardins JD.Although horseback riding is a well-established means of rehabilitation therapy for a variety of human patients, there are few data on the biomechanical relationships between horse and rider during such hippotherapy. We simultaneously tracked the movements of a horse with several different novice riders, under conditions similar to hippotherapy, to evaluate whether horses pass the same motion to different riders while being lead at a walk. Riders were outfitted with a goniometric data collection system that recorded the angles of flexion and extension and lateral bending of the thoracic and lu...
Investigation of the Reliability of Saddle Fitters to Determine the Position of the Last Thoracic Vertebra of Horses Using Palpation Techniques: A Pilot Study.
Journal of equine veterinary science    February 11, 2019   Volume 77 1-7 doi: 10.1016/j.jevs.2019.02.003
Nankervis KJ, Bradley F, Kosek K, Dyson SJ.Published guidelines indicate an English saddle tree should not extend beyond the 18th thoracic vertebra (T18). The study aimed to assess reliability of saddle fitters (SFs) to identify the T18 spinous process (SP). Part 1 investigated agreement between T18 (T18SF) as identified by three SFs using palpation and a veterinary surgeon (VS) using radiography (T18VS) in seven horses. Saddle fitter 1 and SF2 palpated the lumbosacral joint and counted cranially six SPs, whereas SF3 followed the rib curvature toward the dorsal midline. In part 2, SF1 and SF2 identified T18 by counting cranially five S...
Characterization of Dmrt3-Derived Neurons Suggest a Role within Locomotor Circuits.
The Journal of neuroscience : the official journal of the Society for Neuroscience    December 21, 2018   Volume 39, Issue 10 1771-1782 doi: 10.1523/JNEUROSCI.0326-18.2018
Perry S, Larhammar M, Vieillard J, Nagaraja C, Hilscher MM, Tafreshiha A, Rofo F, Caixeta FV, Kullander K.Neuronal networks within the spinal cord, collectively known as the central pattern generator (CPG), coordinate rhythmic movements underlying locomotion. The transcription factor doublesex and mab-3-related transcription factor 3 (DMRT3) is involved in the differentiation of the dorsal interneuron 6 class of spinal cord interneurons. In horses, a non-sense mutation in the gene has major effects on gaiting ability, whereas mice lacking the gene display impaired locomotor activity. Although the gene is necessary for normal spinal network formation and function in mice, a direct role for -deri...
Histological examination of the interspinous ligament in horses with overriding spinous processes.
Veterinary journal (London, England : 1997)    December 12, 2018   Volume 244 69-74 doi: 10.1016/j.tvjl.2018.12.012
Ehrle A, Ressel L, Ricci E, Merle R, Singer ER.The equine interspinous ligament (ISL) consists of an oblique crossing arrangement of collagenous bundles which are thought to counteract the tensile and rotational forces of distraction between the spinous processes (SPs) in the caudal thoracic and cranial lumbar spine. The aim of this controlled histological study was to assess the structural anatomy and innervation of the ISL in horses with clinically significant overriding (dorsal) SPs (ORSPs) and to compare the findings with the ISL of normal horses. Samples of the ISL were obtained from 10 horses that underwent subtotal ostectomy for tre...
Thoracic processi spinosi findings agree among subjective, semiquantitative, and modified semiquantitative scintigraphic image evaluation methods and partially agree with clinical findings in horses with and without thoracolumbar pain. van Zadelhoff C, Ehrle A, Merle R, Jahn W, Lischer C.Impinging processi spinosi in the equine thoracic spine are a common cause of poor performance in the horse. A modified semiquantitative scintigraphic image analysis has been proposed for the evaluation of equine processi spinosi. This technique showed a high inter- and intraobserver agreement when compared to subjective and semiquantitative image analysis. The aim of this retrospective, method comparison study was to evaluate the agreement of the modified semiquantitative scintigraphic image assessment with previous methods of interpretation and to compare these scintigraphic evaluation techn...
Extradural spinal hydatid cyst causing hindlimb ataxia in a horse.
Schweizer Archiv fur Tierheilkunde    November 1, 2018   Volume 160, Issue 11 659-664 doi: 10.17236/sat00183
Peter V, Marr C, Foote A, Auer H, Head M.This case report describes a 13-year-old cob-cross gelding presented for evaluation of recent onset hindlimb ataxia. The gelding had undergone general anaesthesia and tenoscopy of the right hindlimb digital flexor tendon sheath at a nearby clinic three months earlier and had appeared normal at routine post-operative assessments until the sudden onset of neurological deficits. Spinal trauma was suspected initially but radiography and scintigraphy were unremarkable. Due to the severity and progressive nature of the clinical signs the -gelding was subjected to euthanasia. Post mortem examinations...
A possible mechanism of horseback riding on dynamic trunk alignment.
Heliyon    September 11, 2018   Volume 4, Issue 9 e00777 doi: 10.1016/j.heliyon.2018.e00777
Funakoshi R, Masuda K, Uchiyama H, Ohta M.The study aimed to clarify the regularity of the motions of horse's back, rider's pelvis and spine associated with improvement of rider's dynamic trunk alignment. The study used a crossover design, with exercise using the horseback riding simulator (simulator hereafter) as the control condition. The experiments were conducted at Tokyo University of Agriculture Bio-therapy Center. The sample consisted of 20 healthy volunteers age 20-23 years. Participants performed 15-min sessions of horseback riding with a Hokkaido Pony and exercise using the simulator in experiments separated by ≥2 weeks. S...
Cervical stabilization with polyaxial pedicle screw and rod construct in horses: A proof of concept study.
Veterinary surgery : VS    September 10, 2018   Volume 47, Issue 7 932-941 doi: 10.1111/vsu.12938
Aldrich E, Nout-Lomas Y, Seim HB, Easley JT.To evaluate safety and efficacy of a novel technique for cervical stabilization. Methods: In vivo experimental. Methods: Four normal adult quarterhorse crossbreed horses (2-4 years of age, > 250 kg). Methods: One mid-cervical spinal unit (C3-C4) was distracted with a porous metal interbody fusion device (IFD) and stabilized with a polyaxial pedicle screw and rod construct. Neurologic examinations were performed preoperatively and postoperatively. Radiographs of the fusion site and adjoining vertebrae were obtained preoperatively and monthly. Horses were euthanized at 8 months and spin...
Outcome of Ventral Fusion of Two or Three Cervical Vertebrae with a Locking Compression Plate for the Treatment of Cervical Stenotic Myelopathy in Eight Horses.
Veterinary and comparative orthopaedics and traumatology : V.C.O.T    August 23, 2018   Volume 31, Issue 5 356-363 doi: 10.1055/s-0038-1666979
Kühnle C, Fürst AE, Ranninger E, Suárez Sánchez-Andrade J, Kümmerle JM. It was recently shown that biomechanical stability achieved with a locking compression plate (LCP) for ventral cervical fusion in horses is similar to the commonly used Kerf cut cylinder. The advantages of the LCP system render it an interesting implant for this indication. The goal of this report was to describe surgical technique, complications and outcome of horses that underwent ventral fusion of two or three cervical vertebrae with an LCP. Methods:  Medical records of eight horses were reviewed for patient data, history, preoperative grade of ataxia, diagnostic imaging, surgical tech...
Current dorsal myelographic column and dural diameter reduction rules do not apply at the cervicothoracic junction in horses. Estell K, Spriet M, Phillips KL, Aleman M, Finno CJ.Previously published myelographic studies do not report findings at the junction between the seventh cervical (C7) and first thoracic vertebrae (T1). Modern digital radiographic equipment allows improved visualization of C7-T1. Based on clinical experience, we hypothesized that 50% reduction of the dorsal myelographic column or 20% reduction of the dural diameter, criteria commonly used as a supportive finding for spinal cord compression in the cervical vertebral column, do not apply at C7-T1. A myelographic study was performed on 12 healthy, neurologically normal horses. Our hypothesis was co...
Male Flat Jockeys Do Not Display Deteriorations in Bone Density or Resting Metabolic Rate in Accordance With Race Riding Experience: Implications for RED-S.
International journal of sport nutrition and exercise metabolism    June 22, 2018   Volume 28, Issue 4 434-439 doi: 10.1123/ijsnem.2017-0371
Wilson G, Martin D, Morton JP, Close GL.Despite consistent reports of poor bone health in male jockeys, it is not yet known if this is a consequence of low energy availability or lack of an osteogenic stimulus. Given the rationale that low energy availability is a contributing factor in low bone health, we tested the hypothesis that both hip and lumbar bone mineral density (BMD) should progressively worsen in accordance with the years of riding. In a cross-sectional design, male apprentice (n = 17) and senior (n = 14) jockeys (matched for body mass and fat-free mass) were assessed for hip and lumbar spine BMD, as well as bot...
Biochemical and biomechanical characterisation of equine cervical facet joint cartilage.
Equine veterinary journal    May 17, 2018   Volume 50, Issue 6 800-808 doi: 10.1111/evj.12845
O'Leary SA, White JL, Hu JC, Athanasiou KA.The equine cervical facet joint is a site of significant pathology. Located bilaterally on the dorsal spine, these diarthrodial joints work in conjunction with the intervertebral disc to facilitate appropriate spinal motion. Despite the high prevalence of pathology in this joint, the facet joint is understudied and thus lacking in viable treatment options. Objective: The goal of this study was to characterise equine facet joint cartilage and provide a comprehensive database describing the morphological, histological, biochemical and biomechanical properties of this tissue. Methods: Descriptive...
Semi-quantitative methods yield greater inter- and intraobserver agreement than subjective methods for interpreting 99m technetium-hydroxymethylene-diphosphonate uptake in equine thoracic processi spinosi. van Zadelhoff C, Ehrle A, Merle R, Jahn W, Lischer C.Scintigraphy is a standard diagnostic method for evaluating horses with back pain due to suspected thoracic processus spinosus pathology. Lesion detection is based on subjective or semi-quantitative assessments of increased uptake. This retrospective, analytical study is aimed to compare semi-quantitative and subjective methods in the evaluation of scintigraphic images of the processi spinosi in the equine thoracic spine. Scintigraphic images of 20 Warmblood horses, presented for assessment of orthopedic conditions between 2014 and 2016, were included in the study. Randomized, blinded image ev...
Parameters and functional analysis of the deep epaxial muscles in the thoracic, lumbar and sacral regions of the equine spine.
Journal of anatomy    April 30, 2018   Volume 233, Issue 1 55-63 doi: 10.1111/joa.12818
García Liñeiro JA, Graziotti GH, Rodríguez Menéndez JM, Ríos CM, Affricano NO, Victorica CL.The epaxial muscles produce intervertebral rotation in the transverse, vertical and axial axes. These muscles also counteract the movements induced by gravitational and inertial forces and movements produced by antagonistic muscles and the intrinsic muscles of the pelvic limb. Their fascicles are innervated by the dorsal branch of the spinal nerve, which corresponds to the metamere of its cranial insertion in the spinous process. The structure allows the function of the muscles to be predicted: those with long and parallel fibres have a shortening function, whereas the muscles with short and o...
Multipulse transcranial electrical stimulation (TES): normative data for motor evoked potentials in healthy horses.
BMC veterinary research    April 3, 2018   Volume 14, Issue 1 121 doi: 10.1186/s12917-018-1447-7
Journée SL, Journée HL, de Bruijn CM, Delesalle CJG.There are indications that transcranial electrical stimulation (TES) assesses the motor function of the spinal cord in horses in a more sensitive and reproducible fashion than transcranial magnetic stimulation (TMS). However, no normative data of TES evoked motor potentials (MEP) is available. Results: In this prospective study normative data of TES induced MEP wave characteristics (motor latency times (MLT); amplitude and waveform) was obtained from the extensor carpi radialis (ECR) and tibial cranialis (TC) muscles in a group of healthy horses to create a reference frame for functional diagn...
Quantification of Equine Sacral and Iliac Motion During Application of Manual Forces and Comparison Between Motion Capture With Skin-Mounted and Bone-Fixated Sensors.
Journal of equine veterinary science    January 31, 2018   Volume 64 5-11 doi: 10.1016/j.jevs.2018.01.007
Goff LM, McGowan CM, Condie P, Jasiewicz J, van Weeren R.Diagnosis of sacroiliac dysfunction in horses includes manual motion palpation of the equine ilium and sacrum. Motion of the ilium and sacrum during manual force application to the equine pelvis has been measured previously in vitro. The aim of this study was to measure the amount and direction of motion in vivo, including comparison of bone-fixated and skin-mounted inertial sensors. Sensors were skin-mounted over tuber sacrale (TS) and third sacral spinous process of six Thoroughbred horses and later attached via Steinmann pins inserted into the same bony landmarks. Orientations of each TS ...
Intervertebral Disc Degeneration in Warmblood Horses: Morphology, Grading, and Distribution of Lesions.
Veterinary pathology    January 5, 2018   Volume 55, Issue 3 442-452 doi: 10.1177/0300985817747950
Bergmann W, Bergknut N, Veraa S, Gröne A, Vernooij H, Wijnberg ID, Back W, Grinwis GCM.Equine intervertebral disc degeneration is thought to be rare and of limited clinical relevance, although research is lacking. To objectively assess pathological changes of the equine intervertebral disc and their clinical relevance, description of the normal morphology and a practical, biologically credible grading scheme are needed. The objectives of this study are to describe the gross and histological appearance of the equine intervertebral discs and to propose a grading scheme for macroscopic degeneration. Spinal units from 33 warmblood horses were grossly analyzed and scored. Of the 286 ...
Spinal Cord Compression in a Horse due to a Granular Cell Variant of Neurofibroma.
Journal of comparative pathology    November 7, 2017   Volume 157, Issue 4 303-307 doi: 10.1016/j.jcpa.2017.10.002
Civello ANE, Dunkel B, Summers BA, Martineau HM.A neurofibroma of granular cell subtype is described in a 7-year-old horse. The horse had a 3-month history of ataxia affecting the forelimbs and hindlimbs, suggesting a C1-C6 neuroanatomical localization. Post-mortem examination revealed an intradural mass arising from the right sixth cervical spinal nerve and compressing the spinal cord. Histologically, the mass was composed largely of wavy spindle cells (a mixture of Schwann cells, perineurial cells and fibroblasts) intimately associated with ropy collagen fibres. Approximately 25% of the spindle cells were swollen and contained densely-pac...
Microglia and astrocyte activation in the spinal cord of lame horses.
Veterinary anaesthesia and analgesia    November 2, 2017   Volume 45, Issue 1 92-102 doi: 10.1016/j.vaa.2017.10.001
Meneses CS, Müller HY, Herzberg DE, Uberti B, Werner MP, Bustamante HA.To determine the microglial and astrocyte response to painful lameness in horses. Methods: Ionized calcium binding adaptor molecule 1 (Iba-1) and glial fibrillary acidic protein (GFAP) expression, cell density and morphology were determined through immunofluorescence within the dorsal horn of equine spinal cord. Methods: A total of five adult horses with acute or chronic unilateral lameness, previously scheduled for euthanasia. Methods: Musculoskeletal lameness was evaluated in five horses through visual evaluation according to clinical guidelines. Spinal cord samples were obtained immediately...
Development of a minimally invasive approach to equine cervical articular facet joints for placement of an ND:YAG LASER.
The Canadian veterinary journal = La revue veterinaire canadienne    November 2, 2017   Volume 58, Issue 11 1181-1186 
Shearer TR, Kinsley MA, Pease AP, Patterson JS.The purpose of this study was to develop a minimally invasive approach to equine cervical articular facet joints for application of an ND:YAG LASER and to evaluate the effects of the laser fiber on the surrounding tissue. Under general anesthesia, an ND:YAG LASER was used to apply 2000 J of energy to 5 cervical articular facet joints in 3 horses (15 joints total). Horses were euthanized and the cervical facets and spinal cords were examined grossly and histologically. Gross pathology of the articular facets revealed evidence of articular cartilage charring and diffuse roughening of the surface...
Immunofluorescence characterization of spinal cord dorsal horn microglia and astrocytes in horses.
PeerJ    October 27, 2017   Volume 5 e3965 doi: 10.7717/peerj.3965
Meneses CS, Müller HY, Herzberg DE, Uberti B, Bustamante HA, Werner MP.The role of glial cells in pain modulation has recently gathered attention. The objective of this study was to determine healthy spinal microglia and astrocyte morphology and disposition in equine spinal cord dorsal horns using Iba-1 and GFAP/Cx-43 immunofluorescence labeling, respectively. Five adult horses without visible wounds or gait alterations were selected. Spinal cord segments were obtained post-mortem for immunohistochemical and immunocolocalization assays. Immunodetection of spinal cord dorsal horn astrocytes was done using a polyclonal goat antibody raised against Glial Fibrillary ...
Neurotoxicosis in horses associated with consumption of Trema micrantha.
Equine veterinary journal    September 7, 2017   Volume 50, Issue 2 192-195 doi: 10.1111/evj.12741
Lorenzett MP, Pereira PR, Bassuino DM, Konradt G, Panziera W, Bianchi MV, Argenta FF, Hammerschmitt ME, Caprioli RA, de Barros CSL, Pavarini SP....Trema micrantha is a tree widely distributed throughout the Americas. The tree produces highly palatable leaves that have been associated with natural poisoning in goats, sheep and horses, in which hepatic necrosis and hepatic encephalopathy have been observed. Objective: This study describes malacia and haemorrhage in the central nervous system (CNS) due to T. micrantha consumption, with minimal to absent hepatic lesions. Methods: Retrospective case series. Methods: A total of 14 horses with a history of neurological signs and spontaneous consumption of T. micrantha leaves were submitted to...
Effect of a 4-week elastic resistance band training regimen on back kinematics in horses trotting in-hand and on the lunge.
Equine veterinary journal    June 19, 2017   Volume 49, Issue 6 829-835 doi: 10.1111/evj.12690
Pfau T, Simons V, Rombach N, Stubbs N, Weller R.Training and rehabilitation techniques aiming at improving core muscle strength may result in increased dynamic stability of the equine vertebral column. A system of elastic resistance bands is suggested to provide proprioceptive feedback during motion to encourage recruitment of core abdominal and hindquarter musculature for improved dynamic stability. Objective: To quantify the effects of a specific resistance band system on back kinematics during trot in-hand and lungeing at beginning and end of a 4-week exercise programme. Methods: Quantitative analysis of back movement before/after a 4-we...
Complementary and alternative medicine for the management of orthopaedic problems in Swiss Warmblood horses.
Veterinary medicine and science    May 29, 2017   Volume 3, Issue 3 125-133 doi: 10.1002/vms3.64
Lange CD, Axiak Flammer S, Gerber V, Kindt D, Koch C.It appears that complementary and alternative medicine (CAM) is used increasingly often in horses for the assessment and treatment of suspected orthopaedic problems, especially back problems. The aim of this study was to determine the frequency of CAM use for the management of orthopaedic problems in a defined population of Swiss Warmblood horses. A total of 239 owners and caretakers of horses from a pre-defined database were called by a veterinarian to participate in the survey. A standardized questionnaire was designed to determine, for each orthopaedic case, where the localization of the pr...
Ultrasonographic assessment of the atlanto-occipital space in healthy Thoroughbred foals and Thoroughbred foals with neonatal maladjustment syndrome.
Veterinary journal (London, England : 1997)    May 2, 2017   Volume 223 55-59 doi: 10.1016/j.tvjl.2017.04.002
Mackenzie CJ, Haggett EF, Pinchbeck GL, Marr CM.Ultrasonography of the atlanto-occipital (AO) space may be useful as a non-invasive diagnostic tool in neonatal foals. The aims of the study were establish a range of values for ultrasonographic measurements of the AO space in healthy Thoroughbred foals and to compare these variables in healthy foals with foals diagnosed with neonatal maladjustment syndrome (NMS). Ultrasonography of the AO space was performed on 38 healthy Thoroughbred foals and 28 Thoroughbred foals with NMS≤4days of age. Transverse image spinal cord height (P=0.001), width (P<0.001) and spinal cord cross sectional area ...