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Relationship between lumbar spinal stenosis and cauda equina movement during the Valsalva maneuver. Skeletal Radiol 2023; 52:1349-1358. [PMID: 36609720 DOI: 10.1007/s00256-022-04274-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Revised: 12/23/2022] [Accepted: 12/29/2022] [Indexed: 01/09/2023]
Abstract
OBJECTIVE To confirm the relationship between lumbar spinal stenosis (LSS) and cauda equina movement during the Valsalva maneuver. MATERIALS AND METHODS Two radiologists at our institution independently evaluated cauda equina movement on pelvic cine MRI, which was performed for urethrorrhea after prostatectomy or pelvic prolapse in 105 patients (99 males; mean age: 69.0 [range: 50-78] years), who also underwent abdominopelvic CT within 2 years before or after the MRI. The qualitative assessment of the cine MRI involved subjective determination of the cauda equina movement type (non-movement, flutter, and inchworm-manner). The severity of LSS on abdominopelvic CT was quantified using our LSS scoring system and performed between L1/2 and L5/S1. We calculated the average LSS scores of two analysts and extracted the worst scores among all levels. RESULTS Cauda equina movement was observed in 15 patients (14%), inchworm-manner in 10 patients, and flutter in five patients. Participants with cauda equina movement demonstrated significantly higher LSS scores than those without movement (P < 0.001, Wilcoxon's rank-sum test). A significant difference was observed in the worst LSS scores between participants without movement and those with inchworm-manner movement (P < 0.001, Bonferroni's corrected). There were no significant differences between participants without movement and those with flutter movement (P = 0.3156) and between participants with flutter movement and those with inchworm-manner movement (P = 0.4843). CONCLUSION Cauda equina movement in cine MRI during the Valsalva maneuver is occasionally observed in patients with severe LSS, and may be associated with pathogenesis of redundant nerve roots.
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Gutiérrez-Montes C, Coenen W, Vidorreta M, Sincomb S, Martínez-Bazán C, Sánchez AL, Haughton V. Effect of Normal Breathing on the Movement of CSF in the Spinal Subarachnoid Space. AJNR Am J Neuroradiol 2022; 43:1369-1374. [PMID: 35981761 PMCID: PMC9451622 DOI: 10.3174/ajnr.a7603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2022] [Accepted: 06/24/2022] [Indexed: 01/26/2023]
Abstract
BACKGROUND AND PURPOSE Forced respirations reportedly have an effect on CSF movement in the spinal canal. We studied respiratory-related CSF motion during normal respiration. MATERIALS AND METHODS Six healthy subjects breathed at their normal rate with a visual guide to ensure an unchanging rhythm. Respiratory-gated phase-contrast MR flow images were acquired at 5 selected axial planes along the spine. At each spinal level, we computed the flow rate voxelwise in the spinal canal, together with the associated stroke volume. From these data, we computed the periodic volume changes of spinal segments. A phantom was used to quantify the effect of respiration-related magnetic susceptibility changes on the velocity data measured. RESULTS At each level, CSF moved cephalad during inhalation and caudad during expiration. While the general pattern of fluid movement was the same in the 6 subjects, the flow rates, stroke volumes, and spine segment volume changes varied among subjects. Peak flow rates ranged from 0.60 to 1.59 mL/s in the cervical region, 0.46 to 3.17 mL/s in the thoracic region, and 0.75 to 3.64 mL/s in the lumbar region. The differences in flow rates along the canal yielded cyclic volume variations of spine segments that were largest in the lumbar spine, ranging from 0.76 to 3.07 mL among subjects. In the phantom study, flow velocities oscillated periodically during the respiratory cycle by up to 0.02 cm/s or 0.5%. CONCLUSIONS Respiratory-gated measurements of the CSF motion in the spinal canal showed cyclic oscillatory movements of spinal fluid correlated to the breathing pattern.
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Affiliation(s)
- C Gutiérrez-Montes
- From the Department of Mechanical and Mining Engineering (C.G.-M.), University of Jaén, Jaén, Andalucía, Spain
| | - W Coenen
- Grupo de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos (W.C.), Universidad Carlos III de Madrid, Madrid, Spain
| | | | - S Sincomb
- Department of Mechanical and Aerospace Engineering (S.S., A.L.S.), University of California San Diego, San Diego, California
| | - C Martínez-Bazán
- Department of Structural Mechanics and Hydraulic Engineering (C.M.-B.), University of Granada, Granada, Spain
| | - A L Sánchez
- Department of Mechanical and Aerospace Engineering (S.S., A.L.S.), University of California San Diego, San Diego, California
| | - V Haughton
- Department of Radiology (V.H.), School of Medicine and Public Health, University of Wisconsin-Madison, Madison, Wisconsin
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De Andres J, Hayek S, Perruchoud C, Lawrence MM, Reina MA, De Andres-Serrano C, Rubio-Haro R, Hunt M, Yaksh TL. Intrathecal Drug Delivery: Advances and Applications in the Management of Chronic Pain Patient. FRONTIERS IN PAIN RESEARCH 2022; 3:900566. [PMID: 35782225 PMCID: PMC9246706 DOI: 10.3389/fpain.2022.900566] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2022] [Accepted: 05/02/2022] [Indexed: 11/19/2022] Open
Abstract
Advances in our understanding of the biology of spinal systems in organizing and defining the content of exteroceptive information upon which higher centers define the state of the organism and its role in the regulation of somatic and automatic output, defining the motor response of the organism, along with the unique biology and spatial organization of this space, have resulted in an increased focus on therapeutics targeted at this extracranial neuraxial space. Intrathecal (IT) drug delivery systems (IDDS) are well-established as an effective therapeutic approach to patients with chronic non-malignant or malignant pain and as a tool for management of patients with severe spasticity and to deliver therapeutics that address a myriad of spinal pathologies. The risk to benefit ratio of IDD makes it a useful interventional approach. While not without risks, this approach has a significant therapeutic safety margin when employed using drugs with a validated safety profile and by skilled practioners. The present review addresses current advances in our understanding of the biology and dynamics of the intrathecal space, therapeutic platforms, novel therapeutics, delivery technology, issues of safety and rational implementation of its therapy, with a particular emphasis upon the management of pain.
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Affiliation(s)
- Jose De Andres
- Surgical Specialties Department, Valencia University Medical School, Valencia, Spain
- Anesthesia Critical Care and Pain Management Department, Valencia, Spain
- *Correspondence: Jose De Andres
| | - Salim Hayek
- Department of Anesthesiology, University Hospitals Cleveland Medical Center, Cleveland, OH, United States
| | - Christophe Perruchoud
- Pain Center and Department of Anesthesia, La Tour Hospital, Geneva, Switzerland
- Lausanne University Hospital and University of Lausanne, Lausanne, Switzerland
| | - Melinda M. Lawrence
- Department of Anesthesiology, University Hospitals Cleveland Medical Center, Cleveland, OH, United States
| | - Miguel Angel Reina
- Department of Anesthesiology, Montepríncipe University Hospital, Madrid, Spain
- CEU-San-Pablo University School of Medicine, Madrid, Spain
- Department of Anesthesiology, University of Florida College of Medicine, Gainesville, FL, United States
- Facultad de Ciencias de la Salud Universidad Francisco de Vitoria, Madrid, Spain
| | | | - Ruben Rubio-Haro
- Anesthesia and Pain Management Department, Provincial Hospital, Castellon, Spain
- Multidisciplinary Pain Clinic, Vithas Virgen del Consuelo Hospital, Valencia, Spain
| | - Mathew Hunt
- Department of Physiology, Karolinska Institute, Stockholm, Sweden
| | - Tony L. Yaksh
- Departments of Anesthesiology and Pharmacology, University of California, San Diego, San Diego, CA, United States
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4
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Zhang ZX, Gong J, Yu SB, Li C, Sun JX, Ding SW, Ma GJ, Sun SZ, Zhou L, Hack GD, Zheng N, Sui HJ. A specialized myodural bridge named occipital-dural muscle in the narrow-ridged finless porpoise (Neophocaena asiaeorientalis). Sci Rep 2021; 11:15485. [PMID: 34326428 PMCID: PMC8322066 DOI: 10.1038/s41598-021-95070-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 07/19/2021] [Indexed: 11/25/2022] Open
Abstract
A dense bridge-like tissue named the myodural bridge (MDB) connecting the suboccipital muscles to the spinal dura mater was originally discovered in humans. However, recent animal studies have revealed that the MDB appears to be an evolutionarily conserved anatomic structure which may have significant physiological functions. Our previous investigations have confirmed the existence of the MDB in finless porpoises. The present authors conducted research to expound on the specificity of the MDB in the porpoise Neophocana asiaeorientalis (N.asiaeorientalis). Five carcasses of N.asiaeorientalis, with formalin fixation, were used for the present study. Two of the carcasses were used for head and neck CT scanning, three-dimensional reconstructions, and gross dissection of the suboccipital region. Another carcass was used for a P45 plastination study. Also, a carcass was used for a histological analysis of the suboccipital region and also one was used for a Scanning Electron Microscopy study. The results revealed that the MDB of the N.asiaeorientalis is actually an independent muscle originating from the caudal border of the occiput, passing through the posterior atlanto-occipital interspace, and then attaches to the cervical spinal dura mater. Thus the so called MDB of the N.asiaeorientalis is actually an independent and uniquely specialized muscle. Based on the origin and insertion of this muscle, the present authors name it the ‘Occipital-Dural Muscle’. It appears that the direct pull of this muscle on the cervical spinal dura mater may affect the circulation of the cerebrospinal fluid by altering the volume of the subarachnoid space via a pumping action.
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Affiliation(s)
- Zhao-Xi Zhang
- Department of Anatomy, College of Basic Medicine, Dalian Medical University, Dalian, China
| | - Jin Gong
- Department of Anatomy, College of Basic Medicine, Dalian Medical University, Dalian, China
| | - Sheng-Bo Yu
- Department of Anatomy, College of Basic Medicine, Dalian Medical University, Dalian, China
| | - Chan Li
- Department of Anatomy, College of Basic Medicine, Dalian Medical University, Dalian, China
| | - Jing-Xian Sun
- College of Fisheries and Life Science, Dalian Ocean University, Dalian, China
| | - Shuai-Wen Ding
- Department of Engineering Mechanics, Dalian University of Technology, Dalian, China
| | - Guo-Jun Ma
- Department of Engineering Mechanics, Dalian University of Technology, Dalian, China
| | - Shi-Zhu Sun
- Department of Anatomy, College of Basic Medicine, Dalian Medical University, Dalian, China
| | - Lin Zhou
- Department of Anatomy, College of Basic Medicine, Dalian Medical University, Dalian, China
| | - Gary D Hack
- Department of Advanced Oral Sciences and Therapeutics, University of Maryland School of Dentistry, Baltimore, MD, USA
| | - Nan Zheng
- Department of Anatomy, College of Basic Medicine, Dalian Medical University, Dalian, China.
| | - Hong-Jin Sui
- Department of Anatomy, College of Basic Medicine, Dalian Medical University, Dalian, China. .,Dalian Hoffen Preservation Technique Institution, Dalian, China.
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5
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Xu Q, Shao CX, Zhang Y, Zhang Y, Liu C, Chen YX, Wang XM, Chi YY, Yu SB, Sui HJ. Head-nodding: a driving force for the circulation of cerebrospinal fluid. Sci Rep 2021; 11:14233. [PMID: 34244586 PMCID: PMC8270937 DOI: 10.1038/s41598-021-93767-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2020] [Accepted: 06/24/2021] [Indexed: 11/28/2022] Open
Abstract
The myodural bridge (MDB) is a dense connective tissue bridge connecting the suboccipital muscles to the spinal dura mater, and it has been proven to be a normal common existing structure in humans and mammals. Some scholars believe that the suboccipital muscles can serve as a dynamic cerebrospinal fluid (CSF) pump via the MDB, and they found head rotations promote the CSF flow in human body, which provided evidence for this hypothesis. Head movement is a complex motion, but the effects of other forms of head movement on CSF circulation are less known. The present study explored the effects of head-nodding on CSF circulation. The CSF flow of 60 healthy volunteers was analyzed via cine phase-contrast magnetic resonance imaging at the level of the occipitocervical junction before and after one-minute-head-nodding period. Furthermore, the CSF pressures of 100 volunteers were measured via lumbar puncture before and after 5 times head-nodding during their anesthetizing for surgical preparation. As a result, it was found that the maximum and average CSF flow rates at the level of the upper border of atlas during ventricular diastole were significantly decreased from 1.965 ± 0.531 to 1.839 ± 0.460 ml/s and from 0.702 ± 0.253 to 0.606 ± 0.228 ml/s respectively. In the meantime, the changes in the ratio of cranial and caudal orientation of the net flow volume were found differed significantly after the one-minute-head-nodding period (p = 0.017). And on the other hand, the CSF pressures at the L3–L4 level were markedly increased 116.03 ± 26.13 to 124.64 ± 26.18 mmH2O. In conclusion, the head-nodding has obvious effects on CSF circulation and head movement is one of the important drivers of cerebrospinal fluid circulation. We propose that the suboccipital muscles, participating in various head movements, might pull the dura sac via the myodural bridge, and thus, head movement provides power for the CSF circulation.
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Affiliation(s)
- Qiang Xu
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China.,Department of Radiology, The 967 Hospital of the Joint Logistics Support Force of PLA, Dalian, 116021, China
| | - Chang-Xi Shao
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China.,Department of Anesthesiology, Baishan Municipal Central Hospital, Baishan, 134300, China
| | - Ying Zhang
- Graduate School, Dalian Medical University, Dalian, 116044, China
| | - Yu Zhang
- Graduate School, Dalian Medical University, Dalian, 116044, China
| | - Cong Liu
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China.,Department of Radiology, The 967 Hospital of the Joint Logistics Support Force of PLA, Dalian, 116021, China
| | - Yu-Xiao Chen
- Graduate School, Dalian Medical University, Dalian, 116044, China
| | - Xue-Mei Wang
- Department of Radiology, Dalian Municipal Central Hospital, Dalian, 116033, China
| | - Yan-Yan Chi
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China
| | - Sheng-Bo Yu
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China.
| | - Hong-Jin Sui
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China.
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6
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Ferrante E, Pontrelli G, Rubino F, Trimboli M. Spontaneous intracranial hypotension with brain sagging causing "prayer headache". Rev Neurol (Paris) 2020; 177:321-323. [PMID: 32736813 DOI: 10.1016/j.neurol.2020.06.003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2020] [Accepted: 06/02/2020] [Indexed: 01/25/2023]
Affiliation(s)
- E Ferrante
- AOR San Carlo, Neurology Department, Potenza, Italy; Alto Vicentino Hospital - AULSS, Neurology Department, 7, Pedemontana, Santorso, Italy
| | - G Pontrelli
- AOR San Carlo, Neurology Department, Potenza, Italy; SS. Annunziata Hospital, Complex Structure of Neurology, Taranto, Italy
| | - F Rubino
- Palliative care and Pain management Department, ASST Valtellina, Sondrio, Italy
| | - M Trimboli
- AOR San Carlo, Neurology Department, Potenza, Italy; Magna Græcia University, Institute of Neurology Department of Medical and Surgical Sciences, Catanzaro, Italy.
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7
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Kurucz P, Meszaros C, Ganslandt O, Buchfelder M, Barany L. The "Valva Cerebri": Morphometry, Topographic Anatomy and Histology of the Rhomboid Membrane at the Craniocervical Junction. Clin Anat 2019; 33:56-65. [PMID: 31444925 DOI: 10.1002/ca.23460] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2019] [Accepted: 08/19/2019] [Indexed: 11/09/2022]
Abstract
The arachnoid membranes' anatomy is a controversial topic in the literature, and the rhomboid membrane at the craniovertebral junction is an element of this system that has been described poorly. Hence, the objective of our study was to examine this membrane's anatomy and histology. A total of 45 fresh formalin-fixed human cadaveric heads were examined, and anatomic dissections and histologic examinations using standard staining methods were performed. The membrane was found to be a constant structure. It has a rhomboid shape and is located on the medulla oblongata and upper cervical spine's ventral surface within the subarachnoid space. Its average craniocaudal length is 49 mm and the short axis is 26 mm. The cranial apex is attached to the vertebral arteries' junction, and the caudal apex reaches the level of C4. The lateral apices are attached to the dura mater at the level of the denticulate ligament's second insertion. The C1 spinal nerves perforate the membrane, while the C2 roots are located dorsal to it. The membrane is attached strongly to the underlying pia mater. Histologically, it has a typical arachnoid structure, in which its adhesions to the vertebral arteries as well as to the pia mater could be verified histologically. This is the first detailed examination of the rhomboid membrane. Our results suggest that the membrane serves a valve-like function between the spinal and cranial subarachnoid spaces. Based on our findings, further hydrodynamic studies should clarify the membrane's physiological role. Clin. Anat. 32:56-65, 2019. © 2019 Wiley Periodicals, Inc.
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Affiliation(s)
- Peter Kurucz
- Department of Neurosurgery, Katharinenhospital, Klinikum Stuttgart, Stuttgart, Germany.,Department of Neurosurgery, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany
| | - Cintia Meszaros
- Laboratory for Applied and Clinical Anatomy, Department of Anatomy, Histology and Embryology, Semmelweis University, Budapest, Hungary
| | - Oliver Ganslandt
- Department of Neurosurgery, Katharinenhospital, Klinikum Stuttgart, Stuttgart, Germany
| | - Michael Buchfelder
- Department of Neurosurgery, Friedrich-Alexander-University Erlangen-Nuremberg, Erlangen, Germany
| | - Laszlo Barany
- Laboratory for Applied and Clinical Anatomy, Department of Anatomy, Histology and Embryology, Semmelweis University, Budapest, Hungary
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8
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Bock HC, Dreha-Kulaczewski SF, Alaid A, Gärtner J, Ludwig HC. Upward movement of cerebrospinal fluid in obstructive hydrocephalus-revision of an old concept. Childs Nerv Syst 2019; 35:833-841. [PMID: 30919042 DOI: 10.1007/s00381-019-04119-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/25/2019] [Accepted: 03/08/2019] [Indexed: 12/26/2022]
Abstract
PURPOSE The specific pathophysiological processes in many forms of obstructive hydrocephalus (HC) are still unclear. Current concepts of cerebrospinal fluid (CSF) dynamics presume a constant downward flow from the lateral ventricles towards subarachnoid spaces, which are in contrast to neurosurgical observations and findings of MRI flow studies. The aim of our study was to analyze CSF movements in patients with obstructive HC by neuroendoscopic video recordings, X-ray studies, and MRI. METHODS One hundred seventeen pediatric patients with obstructive HC who underwent neuroendoscopy in our center were included. Video recordings were analyzed in 85 patients. Contrast-enhanced X-rays were conducted during surgery prior to intervention in 75 patients, and flow void signals on pre-operative MRI could be evaluated in 110 patients. RESULTS In 83.5% of the video recordings, CSF moved upwards synchronous to inspiration superimposed by cardiac pulsation. Application of contrast medium revealed a flow delay in 52% of the X-ray studies prior to neurosurgery, indicating hindered CSF circulation. The appearances and shapes of flow void signals in 88.2% of the pre-operative MRI studies suggested valve-like mechanisms and entrapment of CSF. CONCLUSIONS Neuroendoscopic observations in patients with obstructive HC revealed upward CSF movements and the corresponding MRI signs of trapped CSF in brain cavities. These observations are in contrast to the current pathophysiological concept of obstructive HC. However, recent real-time flow MRI studies demonstrated upward movement of CSF, hence support our clinical findings. The knowledge of cranial-directed CSF flow expands our understanding of pathophysiological mechanisms in HC and is the key to effective treatment.
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Affiliation(s)
- Hans C Bock
- Department of Neurosurgery, Section Pediatric Neurosurgery, University Medical Center Göttingen, Robert-Koch-Str. 40, 37075, Göttingen, Germany
| | - Steffi F Dreha-Kulaczewski
- Department of Pediatrics and Adolescent Medicine, Division of Pediatric Neurology, University Medical Center Göttingen, Robert-Koch-Str. 40, 37075, Göttingen, Germany
| | - Awad Alaid
- Department of Neurosurgery, Section Pediatric Neurosurgery, University Medical Center Göttingen, Robert-Koch-Str. 40, 37075, Göttingen, Germany
| | - Jutta Gärtner
- Department of Pediatrics and Adolescent Medicine, Division of Pediatric Neurology, University Medical Center Göttingen, Robert-Koch-Str. 40, 37075, Göttingen, Germany
| | - Hans C Ludwig
- Department of Neurosurgery, Section Pediatric Neurosurgery, University Medical Center Göttingen, Robert-Koch-Str. 40, 37075, Göttingen, Germany.
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9
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Bezuidenhout AF, Khatami D, Heilman CB, Kasper EM, Patz S, Madan N, Zhao Y, Bhadelia RA. Relationship between Cough-Associated Changes in CSF Flow and Disease Severity in Chiari I Malformation: An Exploratory Study Using Real-Time MRI. AJNR Am J Neuroradiol 2018; 39:1267-1272. [PMID: 29748208 DOI: 10.3174/ajnr.a5670] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2018] [Accepted: 03/21/2018] [Indexed: 11/07/2022]
Abstract
BACKGROUND AND PURPOSE Currently no quantitative objective test exists to determine disease severity in a patient with Chiari I malformation. Our aim was to correlate disease severity in symptomatic patients with Chiari I malformation with cough-associated changes in CSF flow as measured with real-time MR imaging. MATERIALS AND METHODS Thirteen symptomatic patients with Chiari I malformation (tonsillar herniation of ≥5 mm) were prospectively studied. A real-time, flow-sensitized pencil-beam MR imaging scan was used to measure CSF stroke volume during rest and immediately following coughing and relaxation periods (total scan time, 90 seconds). Multiple posterior fossa and craniocervical anatomic measurements were also obtained. Patients were classified into 2 groups by neurosurgeons blinded to MR imaging measurements: 1) nonspecific Chiari I malformation (5/13)-Chiari I malformation with nonspecific symptoms like non-cough-related or mild occasional cough-related headache, neck pain, dizziness, paresthesias, and/or trouble swallowing; 2) specific Chiari I malformation (8/13)-patients with Chiari I malformation with specific symptoms and/or objective findings like severe cough-related headache, myelopathy, syringomyelia, and muscle atrophy. The Spearman correlation was used to determine correlations between MR imaging measurements and disease severity, and both groups were also compared using a Mann-Whitney U test. RESULTS There was a significant negative correlation between the percentage change in CSF stroke volume (resting to postcoughing) and Chiari I malformation disease severity (R = 0.59; P = .03). Mann-Whitney comparisons showed the percentage change in CSF stroke volume (resting to postcoughing) to be significantly different between patient groups (P = .04). No other CSF flow measurement or anatomic measure was significantly different between the groups. CONCLUSIONS Our exploratory study suggests that assessment of CSF flow response to a coughing challenge has the potential to become a valuable objective noninvasive test for clinical assessment of disease severity in patients with Chiari I malformation.
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Affiliation(s)
| | - D Khatami
- From the Departments of Radiology (A.F.B., D.K., R.A.B.)
| | | | - E M Kasper
- Neurosurgery (E.M.K.), Beth Israel Deaconess Medical Center, Boston, Massachusetts
| | - S Patz
- Department of Radiology (S.P.), Brigham and Woman's Hospital, Boston, Massachusetts
| | - N Madan
- Radiology (N.M.), Tufts Medical Center, Boston, Massachusetts
| | - Y Zhao
- Philips Healthcare (Y.Z.), Boston, Massachusetts
| | - R A Bhadelia
- From the Departments of Radiology (A.F.B., D.K., R.A.B.)
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10
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Cerebrospinal Fluid Dynamics and Intrathecal Delivery. Neuromodulation 2018. [DOI: 10.1016/b978-0-12-805353-9.00067-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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11
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Emami A, Tepper J, Short B, Yaksh TL, Bendele AM, Ramani T, Cisternas AF, Chang JH, Mellon RD. Toxicology Evaluation of Drugs Administered via Uncommon Routes: Intranasal, Intraocular, Intrathecal/Intraspinal, and Intra-Articular. Int J Toxicol 2017; 37:4-27. [PMID: 29264927 DOI: 10.1177/1091581817741840] [Citation(s) in RCA: 39] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
As the need for nasal, ocular, spinal, and articular therapeutic compounds increases, toxicology assessments of drugs administered via these routes play an important role in human safety. This symposium outlined the local and systemic evaluation to support safety during the development of these drugs in nonclinical models with some case studies. Discussions included selection of appropriate species for the intended route; conducting nonclinical studies that closely mimic the intended use with adequate duration; functional assessment, if deemed necessary; evaluation of local tissues with special histological staining procedure; and evaluations of safety margins based on local and systemic toxicity.
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Affiliation(s)
- Armaghan Emami
- 1 US Food and Drug Administration, Silver Spring, MD, USA
| | - Jeff Tepper
- 2 Tepper Nonclinical Consulting, San Carlos, CA, USA
| | - Brian Short
- 3 Brian Short Consulting, LLC, Trabuco Canyon, CA, USA
| | - Tony L Yaksh
- 4 Department of Anesthesiology, University of California, San Diego, La Jolla, CA, USA
| | | | | | | | - Jay H Chang
- 1 US Food and Drug Administration, Silver Spring, MD, USA
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12
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Thyagaraj S, Pahlavian SH, Sass LR, Loth F, Vatani M, Choi JW, Tubbs RS, Giese D, Kroger JR, Bunck AC, Martin BA. An MRI-Compatible Hydrodynamic Simulator of Cerebrospinal Fluid Motion in the Cervical Spine. IEEE Trans Biomed Eng 2017; 65:1516-1523. [PMID: 28961100 DOI: 10.1109/tbme.2017.2756995] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
GOAL Develop and test an MRI-compatible hydrodynamic simulator of cerebrospinal fluid (CSF) motion in the cervical spinal subarachnoid space. Four anatomically realistic subject-specific models were created based on a 22-year-old healthy volunteer and a five-year-old patient diagnosed with Chiari I malformation. METHODS The in vitro models were based on manual segmentation of high-resolution T2-weighted MRI of the cervical spine. Anatomically realistic dorsal and ventral spinal cord nerve rootlets (NR) were added. Models were three dimensional (3-D) printed by stereolithography with 50-μm layer thickness. A computer controlled pump system was used to replicate the shape of the subject specific in vivo CSF flow measured by phase-contrast MRI. Each model was then scanned by T2-weighted and 4-D phase contrast MRI (4D flow). RESULTS Cross-sectional area, wetted perimeter, and hydraulic diameter were quantified for each model. The oscillatory CSF velocity field (flow jets near NR, velocity profile shape, and magnitude) had similar characteristics to previously reported studies in the literature measured by in vivo MRI. CONCLUSION This study describes the first MRI-compatible hydrodynamic simulator of CSF motion in the cervical spine with anatomically realistic NR. NR were found to impact CSF velocity profiles to a great degree. SIGNIFICANCE CSF hydrodynamics are thought to be altered in craniospinal disorders such as Chiari I malformation. MRI scanning techniques and protocols can be used to quantify CSF flow alterations in disease states. The provided in vitro models can be used to test the reliability of these protocols across MRI scanner manufacturers and machines.
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Ichikawa S, Motosugi U, Okumura A, Shimizu T, Onishi H. Measurement of Cerebrospinal Fluid Flow Dynamics Using Phase Contrast MR Imaging with Bilateral Jugular Vein Compression: A Feasibility Study in Healthy Volunteers. Magn Reson Med Sci 2017; 17:265-268. [PMID: 28819086 PMCID: PMC6039778 DOI: 10.2463/mrms.tn.2017-0056] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022] Open
Abstract
We measured the changes in the cerebrospinal fluid (CSF) flow dynamics after compression of the bilateral jugular veins using phase contrast-magnetic resonance imaging (PC-MRI). PC-MRI was performed in 10 healthy male volunteers using a 3T clinical scanner with a two-dimensional gradient echo sequence. We successfully measured the changes in CSF flow velocity using PC-MRI with and without compression of the bilateral jugular veins. The relative velocity range decreased by about 30% when the bilateral jugular veins were compressed.
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Affiliation(s)
| | - Utaroh Motosugi
- Corresponding author, Phone: +81-55-273-1111, Fax: +81-55-273-6744, E-mail:
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Daouk J, Bouzerar R, Baledent O. Heart rate and respiration influence on macroscopic blood and CSF flows. Acta Radiol 2017; 58:977-982. [PMID: 28273732 DOI: 10.1177/0284185116676655] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Background Changes in blood volume in the intracranial arteries and the resulting oscillations of brain parenchyma have been presumed as main initiating factors of cerebrospinal fluid (CSF) pulsations. However, respiration has been recently supposed to influence CSF dynamics via thoracic pressure changes. Purpose To measure blood and CSF cervical flow and quantify the contribution of cardiac and respiratory cycles on the subsequent signal evolution. Material and Methods Sixteen volunteers were enrolled. All participant underwent two-dimensional fast field echo echo planar imaging (FFE-EPI). Regions of interest were placed on internal carotids, jugular veins, and rachidian canal to extract temporal profiles. Spectral analysis was performed to extract respiratory and cardiac frequencies. The contribution of respiration and cardiac activity was assessed to signal evolution by applying a multiple linear model. Results Mean respiratory frequency was 14.6 ± 3.9 cycles per min and mean heart rate was 66.8 ± 9 cycles per min. Cardiac contribution was higher than breathing for internal carotids, explaining 74.68% and 10.27% of the signal variance, respectively. For the jugular veins, respiratory component was higher than the cardiac one contributing 44.28% and 6.53% of the signal variance, respectively. For CSF, breathing and cardiac component contributed less than half of signal variance (12.61% and 23.23%, respectively). Conclusion Respiration and cardiac activity both influence fluid flow at the cervical level. Arterial inflow is driven by the cardiac pool whereas venous blood aspiration seems more due to thoracic pressure changes. CSF dynamics acts as a buffer between these two blood compartments.
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Affiliation(s)
- Joël Daouk
- Bioflow Image Unit, Jules Verne University of Picardie, Amiens, France
| | - Roger Bouzerar
- Bioflow Image Unit, Jules Verne University of Picardie, Amiens, France
- Medical Image Processing Unit, Amiens University Medical Center, Amiens, France
| | - Olivier Baledent
- Bioflow Image Unit, Jules Verne University of Picardie, Amiens, France
- Medical Image Processing Unit, Amiens University Medical Center, Amiens, France
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16
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Xu Q, Yu SB, Zheng N, Yuan XY, Chi YY, Liu C, Wang XM, Lin XT, Sui HJ. Head movement, an important contributor to human cerebrospinal fluid circulation. Sci Rep 2016; 6:31787. [PMID: 27538827 PMCID: PMC4990938 DOI: 10.1038/srep31787] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2016] [Accepted: 07/26/2016] [Indexed: 11/23/2022] Open
Abstract
The suboccipital muscles are connected to the upper cervical spinal dura mater via the myodural bridges (MDBs). Recently, it was suggested that they might work as a pump to provide power for cerebrospinal fluid (CSF) circulation. The purpose of this study was to investigate effects of the suboccipital muscles contractions on the CSF flow. Forty healthy adult volunteers were subjected to cine phase-contrast MR imaging. Each volunteer was scanned twice, once before and once after one-minute-head-rotation period. CSF flow waveform parameters at craniocervical junction were analyzed. The results showed that, after the head rotations, the maximum and average CSF flow rates during ventricular diastole were significantly increased, and the CSF stroke volumes during diastole and during entire cardiac cycle were significantly increased. This suggested that the CSF flow was significantly promoted by head movements. Among the muscles related with head movements, only three suboccipital muscles are connected to the upper cervical spinal dura mater via MDBs. It was believed that MDBs might transform powers of the muscles to CSF. The present results suggested that the head movements served as an important contributor to CSF dynamics and the MDBs might be involved in this mechanism.
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Affiliation(s)
- Qiang Xu
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China.,Department of Radiology, The 403 Affiliated Hospital of Chinese PLA General Hospital, Dalian, 116021, China
| | - Sheng-Bo Yu
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China
| | - Nan Zheng
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China
| | - Xiao-Ying Yuan
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China
| | - Yan-Yan Chi
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China
| | - Cong Liu
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China.,Department of Radiology, The 403 Affiliated Hospital of Chinese PLA General Hospital, Dalian, 116021, China
| | - Xue-Mei Wang
- Department of Radiology, Dalian Municipal Central Hospital, Dalian, 116033, China
| | - Xiang-Tao Lin
- Shandong Medical Imaging Research Institute, School of Medicine, Shandong University, Jinan, 250021, China
| | - Hong-Jin Sui
- Department of Anatomy, Dalian Medical University, Dalian, 116044, China
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17
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Holdsworth SJ, Rahimi MS, Ni WW, Zaharchuk G, Moseley ME. Amplified magnetic resonance imaging (aMRI). Magn Reson Med 2016; 75:2245-54. [PMID: 26888418 DOI: 10.1002/mrm.26142] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2015] [Revised: 12/31/2015] [Accepted: 12/31/2015] [Indexed: 01/03/2023]
Abstract
PURPOSE This work describes a new method called amplified MRI (aMRI), which uses Eulerian video magnification to amplify the subtle spatial variations in cardiac-gated brain MRI scans and enables better visualization of brain motion. METHODS The aMRI method takes retrospective cardiac-gated cine MRI data as input, applies a spatial decomposition, followed by temporal filtering and frequency-selective amplification of the MRI cardiac-gated frames before synthesizing a motion-amplified cine data set. RESULTS This approach reveals deformations of the brain parenchyma and displacements of arteries due to cardiac pulsatility, especially in the brainstem, cerebellum, and spinal cord. CONCLUSION aMRI has the potential for widespread neuro- and non-neuro clinical use because it can amplify and characterize small, often barely perceptible motion and can visualize the biomechanical response of tissues using the heartbeat as an endogenous mechanical driver. Magn Reson Med 75:2245-2254, 2016. © 2016 Wiley Periodicals, Inc.
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Affiliation(s)
- Samantha J Holdsworth
- Lucas Center for Imaging, Department of Radiology, Stanford University Stanford, California, USA
| | - Mahdi Salmani Rahimi
- Lucas Center for Imaging, Department of Radiology, Stanford University Stanford, California, USA
| | - Wendy W Ni
- Lucas Center for Imaging, Department of Radiology, Stanford University Stanford, California, USA
| | - Greg Zaharchuk
- Lucas Center for Imaging, Department of Radiology, Stanford University Stanford, California, USA
| | - Michael E Moseley
- Lucas Center for Imaging, Department of Radiology, Stanford University Stanford, California, USA
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18
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Bhadelia RA, Patz S, Heilman C, Khatami D, Kasper E, Zhao Y, Madan N. Cough-Associated Changes in CSF Flow in Chiari I Malformation Evaluated by Real-Time MRI. AJNR Am J Neuroradiol 2015; 37:825-30. [PMID: 26705321 DOI: 10.3174/ajnr.a4629] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Accepted: 10/27/2015] [Indexed: 11/07/2022]
Abstract
BACKGROUND AND PURPOSE Invasive pressure studies have suggested that CSF flow across the foramen magnum may transiently decrease after coughing in patients with symptomatic Chiari I malformation. The purpose of this exploratory study was to demonstrate this phenomenon noninvasively by assessing CSF flow response to coughing in symptomatic patients with Chiari I malformation by using MR pencil beam imaging and to compare the response with that in healthy participants. MATERIALS AND METHODS Eight symptomatic patients with Chiari I malformation and 6 healthy participants were studied by using MR pencil beam imaging with a temporal resolution of ∼50 ms. Patients and healthy participants were scanned for 90 seconds (without cardiac gating) to continuously record cardiac cycle-related CSF flow waveforms in real-time during resting, coughing, and postcoughing periods. CSF flow waveform amplitude, CSF stroke volume, and CSF flow rate (CSF Flow Rate = CSF Stroke Volume × Heart Rate) in the resting and immediate postcoughing periods were determined and compared between patients and healthy participants. RESULTS There was no significant difference in CSF flow waveform amplitude, CSF stroke volume, and the CSF flow rate between patients with Chiari I malformation and healthy participants during rest. However, immediately after coughing, a significant decrease in CSF flow waveform amplitude (P < .001), CSF stroke volume (P = .001), and CSF flow rate (P = .001) was observed in patients with Chiari I malformation but not in the healthy participants. CONCLUSIONS Real-time MR imaging noninvasively showed a transient decrease in CSF flow across the foramen magnum after coughing in symptomatic patients with Chiari I malformation, a phenomenon not seen in healthy participants. Our results provide preliminary evidence that the physiology-based imaging method used here has the potential to be an objective clinical test to differentiate symptomatic from asymptomatic patients with Chiari I malformation.
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Affiliation(s)
- R A Bhadelia
- From the Department of Radiology (R.A.B., D.K.), Beth Israel Deaconess Medical Center, Boston, Massachusetts
| | - S Patz
- Department of Radiology (S.P.), Brigham and Women's Hospital, Boston, Massachusetts
| | | | - D Khatami
- From the Department of Radiology (R.A.B., D.K.), Beth Israel Deaconess Medical Center, Boston, Massachusetts
| | - E Kasper
- Department of Neurosurgery (E.K.), Beth Israel Deaconess Medical Center, Boston, Massachusetts
| | - Y Zhao
- Phillips Healthcare (Y.Z.), Boston, Massachusetts
| | - N Madan
- Radiology (N.M.), Tufts Medical Center, Boston, Massachusetts
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Dynamics of respiratory and cardiac CSF motion revealed with real-time simultaneous multi-slice EPI velocity phase contrast imaging. Neuroimage 2015; 122:281-7. [PMID: 26241682 DOI: 10.1016/j.neuroimage.2015.07.073] [Citation(s) in RCA: 67] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2015] [Revised: 06/22/2015] [Accepted: 07/24/2015] [Indexed: 11/20/2022] Open
Abstract
Cerebrospinal fluid (CSF) dynamics have been mostly studied with cardiac-gated phase contrast MRI combining signal from many cardiac cycles to create cine-phase sampling of one time-averaged cardiac cycle. The relative effects of cardiac and respiratory changes on CSF movement are not well understood. There is possible respiration-driven movement of CSF in ventricles, cisterns, and subarachnoid spaces which has not been characterized with velocity measurements. To date, commonly used cine-phase contrast techniques of velocity imaging inherently cannot detect respiratory velocity changes since cardiac-gated data acquired over several minutes randomizes respiratory phase contributions. We have developed an extremely fast, real-time, and quantitative MRI technique to image CSF velocity in simultaneous multi-slice (SMS) echo planar imaging (EPI) acquisitions of 3 or 6 slice levels simultaneously over 30s and observe 3D spatial distributions of CSF velocity. Measurements were made in 10 subjects utilizing a respiratory belt to record respiratory phases and visual cues to instruct subjects on breathing rates. A protocol is able to measure velocity within regions of brain and basal cisterns covered with 24 axial slices in 4 minutes, repeated for 3 velocity directions. These measurements were performed throughout the whole brain, rather than in selected line regions so that a global view of CSF dynamics could be visualized. Observations of cardiac and breathing-driven CSF dynamics show bidirectional respiratory motion occurs primarily along the central axis through the basal cisterns and intraventricular passageways and to a lesser extent in the peripheral Sylvian fissure with little CSF motion present in subarachnoid spaces. During inspiration phase, there is upward (inferior to superior) CSF movement into the cranial cavity and lateral ventricles and a reversal of direction in expiration phase.
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20
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Quon JL, Grant RA, DiLuna ML. Multimodal evaluation of CSF dynamics following extradural decompression for Chiari malformation Type I. J Neurosurg Spine 2015; 22:622-30. [DOI: 10.3171/2014.10.spine1433] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
OBJECT
Extradural decompression is a minimally invasive technique for treating Chiari malformation Type I (CM-I) that avoids the complications of dural opening. While there is no agreement on which surgical method is optimal, mounting evidence demonstrates that extradural decompression effectively treats clinical symptoms, with a minimal reoperation rate. Neurological symptoms such as headache may be related to obstructed flow of CSF, and one aspect of successful extradural decompression is improved CSF dynamics. In this series, the authors report on their use of phase-contrast cine flow MRI to assess CSF flow as well as satisfactory decompression.
METHODS
The authors describe their first surgical series of 18 patients with CM-I undergoing extradural decompression and correlate clinical improvement with radiological changes. Patients were categorized as having complete, partial, or no resolution of their symptoms. Posterior fossa area, cisterna magna area, and tonsillar herniation were assessed on T2-weighted MRI, whereas improvement of CSF flow was evaluated with phase-contrast cine flow MRI. All patients received standard pre- and postoperative MRI studies; 8 (44.4%) patients had pre- and postoperative phase-contrast cine, while the rest underwent cine studies only postoperatively.
RESULTS
All 18 patients presented with symptomatic CM-I, with imaging studies demonstrating tonsillar herniation ≥ 5 mm, and 2 patients had associated syringomelia. All patients underwent suboccipital decompression and C-1 laminectomy with splitting of the dura. Patients with complete resolution of their symptoms had a greater relative increase in cisterna magna area compared with those with only partial improvement (p = 0.022). In addition, in those with complete improvement the preoperative cisterna magna area was smaller than in those who had either partial (0.020) or no (0.025) improvement. Ten (91%) of the 11 patients with improved flow also had improvement in their symptoms. There was 1 postoperative complication of dysphagia and dysphonia. None of the patients have required a second operation.
CONCLUSIONS
Extradural decompression has the potential to be the first-line treatment for CM-I but has been lacking an objective measure by which to assess surgical success as well as the need for reoperation. An increase in the CSF spaces and improved CSF dynamics may be associated with resolution of clinical symptoms. Including cine imaging as part of routine pre- and postoperative evaluation can help identify which patients are most likely to benefit from surgery.
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Abstract
The mechanisms behind CSF flow in humans are still not fully known. CSF circulates from its primary production sites at the choroid plexus through the brain ventricles to reach the outer surface of the brain in the subarachnoid spaces from where it drains into venous bloodstream and cervical lymphatics. According to a recent concept of brain fluid transport, established in rodents, CSF from the brain surface also enters the brain tissue along para-arterial routes and exits through paravenous spaces again into subarachnoid compartments. This unidirectional flow is mainly driven by arterial pulsation. To investigate how CSF flow is regulated in humans, we applied a novel real-time magnetic resonance imaging technique at high spatial (0.75 mm) and temporal (50 ms) resolution in healthy human subjects. We observed significant CSF flow exclusively with inspiration. In particular, during forced breathing, high CSF flow was elicited during every inspiration, whereas breath holding suppressed it. Only a minor flow component could be ascribed to cardiac pulsation. The present results unambiguously identify inspiration as the most important driving force for CSF flow in humans. Inspiratory thoracic pressure reduction is expected to directly modulate the hydrostatic pressure conditions for the low-resistance paravenous, venous, and lymphatic clearance routes of CSF. Furthermore, the experimental approach opens new clinical opportunities to study the pathophysiology of various forms of hydrocephalus and to design therapeutic strategies in relation to CSF flow alterations.
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Haughton V, Mardal KA. Spinal fluid biomechanics and imaging: an update for neuroradiologists. AJNR Am J Neuroradiol 2014; 35:1864-9. [PMID: 25012674 DOI: 10.3174/ajnr.a4023] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Flow imaging with cardiac-gated phase-contrast MR has applications in the management of neurologic disorders. Together with computational fluid dynamics, phase-contrast MR has advanced our understanding of spinal CSF flow. Phase-contrast MR is used to evaluate patients with Chiari I malformation who are candidates for surgical treatment. In theory, abnormal CSF flow resulting from the abnormal tonsil position causes syringomyelia and other neurologic signs and symptoms in patients with Chiari I. CSF flow imaging also has research applications in syringomyelia and spinal stenosis. To optimize MR acquisition and interpretation, neuroradiologists must have familiarity with healthy and pathologic patterns of CSF flow. The purpose of this review is to update concepts of CSF flow that are important for the practice of flow imaging in the spine.
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Affiliation(s)
- V Haughton
- From the Department of Radiology (V.H.), University of Wisconsin, Madison, Wisconsin
| | - K-A Mardal
- Center for Biological Computing (K.-A.M.), Simula, Lysaker, Norway
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