Implementation of a practical Markov chain Monte Carlo sampling algorithm in PyBioNetFit.

SUMMARY: Bayesian inference in biological modeling commonly relies on Markov chain Monte Carlo (MCMC) sampling of a multidimensional and non-Gaussian posterior distribution that is not analytically tractable. Here, we present the implementation of a practical MCMC method in the open-source software package PyBioNetFit (PyBNF), which is designed to support parameterization of mathematical models for biological systems. The new MCMC method, am, incorporates an adaptive move proposal distribution. For warm starts, sampling can be initiated at a specified location in parameter space and with a multivariate Gaussian proposal distribution defined initially by a specified covariance matrix. Multiple chains can be generated in parallel using a computer cluster. We demonstrate that am can be used to successfully solve real-world Bayesian inference problems, including forecasting of new Coronavirus Disease 2019 case detection with Bayesian quantification of forecast uncertainty. AVAILABILITY AND IMPLEMENTATION: PyBNF version 1.1.9, the first stable release with am, is available at PyPI and can be installed using the pip package-management system on platforms that have a working installation of Python 3. PyBNF relies on libRoadRunner and BioNetGen for simulations (e.g. numerical integration of ordinary differential equations defined in SBML or BNGL files) and Dask.Distributed for task scheduling on Linux computer clusters. The Python source code can be freely downloaded/cloned from GitHub and used and modified under terms of the BSD-3 license (https://github.com/lanl/pybnf). Online documentation covering installation/usage is available (https://pybnf.readthedocs.io/en/latest/). A tutorial video is available on YouTube (https://www.youtube.com/watch?v=2aRqpqFOiS4&t=63s). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Patient Expectation and Satisfaction with Different Prosthetic Treatment Modalities.

PURPOSE: To investigate the relationships between gender, age, patients' perceptions about the dentists' conduct, number of adjustments, treatment type, and expectation prior to prosthetic treatment and patient satisfaction with their treatments. MATERIALS AND METHODS: Data were integrated from four studies that measured patient expectations before treatment and satisfaction after treatment using a visual analog scale (VAS) from 0 to 10. These scores were given for each of four aspects of the therapeutic outcomes: chewing, esthetics, phonetics, and comfort. Patients' perceptions about the dentists' conduct was also assessed using a Likert-scale questionnaire. The total sample size, after combining the data from all four studies, was 223 subjects. Bivariate and multivariable analyses were performed. The covariates entertained were gender, age, treatment type, patients' perceptions about the dentists' conduct, number of adjustments, and expectation prior to denture fabrication. RESULTS: In the entire sample, 115 (51.57%) patients were females and 108 (48.43%) were males. They ranged in age from 28 to 81 years old; the mean age was 53.2 years (SD = 11.5). Combining four treatments together, there was no significant difference between patients' expectation and satisfaction scores for all four items. There were no significant differences between expectation and satisfaction for different genders. Multivariable analysis showed that patient expectation, satisfaction and the difference (satisfaction score-expectation score) scores for all four aspects were associated with treatment type (implant treatments were favored), and expectation prior to prosthetic treatment (the higher the expectation, the higher the satisfaction) was associated with satisfaction and difference scores. Satisfaction and difference scores for chewing were associated with number of adjustments and satisfaction, and satisfaction and difference scores for phonetics and comfort were associated with how well the dentist explained the intended treatment before performing it. CONCLUSIONS: Patient satisfaction was associated with treatment type (implant treatments were favored), expectations prior to prosthetic treatment (the higher the expectation, the higher the satisfaction), and how well the dentist explained the intended treatment before performing it.

BioNetFit: a fitting tool compatible with BioNetGen, NFsim and distributed computing environments.

UNLABELLED: Rule-based models are analyzed with specialized simulators, such as those provided by the BioNetGen and NFsim open-source software packages. Here, we present BioNetFit, a general-purpose fitting tool that is compatible with BioNetGen and NFsim. BioNetFit is designed to take advantage of distributed computing resources. This feature facilitates fitting (i.e. optimization of parameter values for consistency with data) when simulations are computationally expensive. AVAILABILITY AND IMPLEMENTATION: BioNetFit can be used on stand-alone Mac, Windows/Cygwin, and Linux platforms and on Linux-based clusters running SLURM, Torque/PBS, or SGE. The BioNetFit source code (Perl) is freely available (http://bionetfit.nau.edu). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online. CONTACT: bionetgen.help@gmail.com.

Histologic Analysis of 'Distraction Vaginogenesis' in a Rat Model.

Vaginal agenesis (VA) is frequently associated with mullerian agenesis. VA treatments include mechanical dilation and surgical vaginoplasty. We created a vaginal expansion sleeve (VES) as a novel device to progressively lengthen the vaginal canal. This study evaluated the histologic effects of the VES on rat vaginal tissue. The VES is a spring-like device made of proprietary woven cylindrical material and flat resin caps. The VESs were constructed as 25-30 mm, pre-contracted springs, which were secured into the vaginas of six Sprague Dawley rats and allowed to re-expand post-surgically. After one week, the VESs were removed, and the vaginas were harvested and measured in length. Test (n = 6) and control (n = 4) formalin-fixed paraffin-embedded tissues were stained with hematoxylin and eosin (H&E), Masson's trichrome, and anti-Desmin antibodies. The VESs achieved significant vaginal lengthening. The mean vaginal canal length increased from 20.0 ± 2.4 mm to 23.8 ± 1.2 mm after removal of the VESs (n = 6, p < 0.001), a 19% increase. There was a positive correlation between the expander/tension generated in the vagina and the amount of acute and chronic inflammation. H&E staining revealed increased submucosal eosinophilia in five of the six test tissues. One VES sample that was lengthened to 30 mm long showed evidence of lymphocytic and neutrophilic inflammation. Desmin immunostaining and Masson's trichrome stain revealed a thinner muscularis with more infiltrative fibrous tissue between muscle fibers in the test tissue compared to the control tissue. Although effective, the VES may provoke at least a transient increase in eosinophils consistent with a localized immune reaction during muscularis remodeling.

Next-generation sequencing of Coccidioides immitis isolated during cluster investigation.

Next-generation sequencing enables use of whole-genome sequence typing (WGST) as a viable and discriminatory tool for genotyping and molecular epidemiologic analysis. We used WGST to confirm the linkage of a cluster of Coccidioides immitis isolates from 3 patients who received organ transplants from a single donor who later had positive test results for coccidioidomycosis. Isolates from the 3 patients were nearly genetically identical (a total of 3 single-nucleotide polymorphisms identified among them), thereby demonstrating direct descent of the 3 isolates from an original isolate. We used WGST to demonstrate the genotypic relatedness of C. immitis isolates that were also epidemiologically linked. Thus, WGST offers unique benefits to public health for investigation of clusters considered to be linked to a single source.

RuleMonkey: software for stochastic simulation of rule-based models.

BACKGROUND: The system-level dynamics of many molecular interactions, particularly protein-protein interactions, can be conveniently represented using reaction rules, which can be specified using model-specification languages, such as the BioNetGen language (BNGL). A set of rules implicitly defines a (bio)chemical reaction network. The reaction network implied by a set of rules is often very large, and as a result, generation of the network implied by rules tends to be computationally expensive. Moreover, the cost of many commonly used methods for simulating network dynamics is a function of network size. Together these factors have limited application of the rule-based modeling approach. Recently, several methods for simulating rule-based models have been developed that avoid the expensive step of network generation. The cost of these "network-free" simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is now needed for the simulation and analysis of rule-based models of biochemical systems. RESULTS: Here, we present a software tool called RuleMonkey, which implements a network-free method for simulation of rule-based models that is similar to Gillespie's method. The method is suitable for rule-based models that can be encoded in BNGL, including models with rules that have global application conditions, such as rules for intramolecular association reactions. In addition, the method is rejection free, unlike other network-free methods that introduce null events, i.e., steps in the simulation procedure that do not change the state of the reaction system being simulated. We verify that RuleMonkey produces correct simulation results, and we compare its performance against DYNSTOC, another BNGL-compliant tool for network-free simulation of rule-based models. We also compare RuleMonkey against problem-specific codes implementing network-free simulation methods. CONCLUSIONS: RuleMonkey enables the simulation of rule-based models for which the underlying reaction networks are large. It is typically faster than DYNSTOC for benchmark problems that we have examined. RuleMonkey is freely available as a stand-alone application http://public.tgen.org/rulemonkey. It is also available as a simulation engine within GetBonNie, a web-based environment for building, analyzing and sharing rule-based models.

Simulation of large-scale rule-based models.

MOTIVATION: Interactions of molecules, such as signaling proteins, with multiple binding sites and/or multiple sites of post-translational covalent modification can be modeled using reaction rules. Rules comprehensively, but implicitly, define the individual chemical species and reactions that molecular interactions can potentially generate. Although rules can be automatically processed to define a biochemical reaction network, the network implied by a set of rules is often too large to generate completely or to simulate using conventional procedures. To address this problem, we present DYNSTOC, a general-purpose tool for simulating rule-based models. RESULTS: DYNSTOC implements a null-event algorithm for simulating chemical reactions in a homogenous reaction compartment. The simulation method does not require that a reaction network be specified explicitly in advance, but rather takes advantage of the availability of the reaction rules in a rule-based specification of a network to determine if a randomly selected set of molecular components participates in a reaction during a time step. DYNSTOC reads reaction rules written in the BioNetGen language which is useful for modeling protein-protein interactions involved in signal transduction. The method of DYNSTOC is closely related to that of StochSim. DYNSTOC differs from StochSim by allowing for model specification in terms of BNGL, which extends the range of protein complexes that can be considered in a model. DYNSTOC enables the simulation of rule-based models that cannot be simulated by conventional methods. We demonstrate the ability of DYNSTOC to simulate models accounting for multisite phosphorylation and multivalent binding processes that are characterized by large numbers of reactions. AVAILABILITY: DYNSTOC is free for non-commercial use. The C source code, supporting documentation and example input files are available at http://public.tgen.org/dynstoc/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

PyBioNetFit and the Biological Property Specification Language.

In systems biology modeling, important steps include model parameterization, uncertainty quantification, and evaluation of agreement with experimental observations. To help modelers perform these steps, we developed the software PyBioNetFit, which in addition supports checking models against known system properties and solving design problems. PyBioNetFit introduces Biological Property Specification Language (BPSL) for the formal declaration of system properties. BPSL allows qualitative data to be used alone or in combination with quantitative data. PyBioNetFit performs parameterization with parallelized metaheuristic optimization algorithms that work directly with existing model definition standards: BioNetGen Language (BNGL) and Systems Biology Markup Language (SBML). We demonstrate PyBioNetFit's capabilities by solving various example problems, including the challenging problem of parameterizing a 153-parameter model of cell cycle control in yeast based on both quantitative and qualitative data. We demonstrate the model checking and design applications of PyBioNetFit and BPSL by analyzing a model of targeted drug interventions in autophagy signaling.

A Step-by-Step Guide to Using BioNetFit.

BioNetFit is a software tool designed for solving parameter identification problems that arise in the development of rule-based models. It solves these problems through curve fitting (i.e., nonlinear regression). BioNetFit is compatible with deterministic and stochastic simulators that accept BioNetGen language (BNGL)-formatted files as inputs, such as those available within the BioNetGen framework. BioNetFit can be used on a laptop or stand-alone multicore workstation as well as on many Linux clusters, such as those that use the Slurm Workload Manager to schedule jobs. BioNetFit implements a metaheuristic population-based global optimization procedure, an evolutionary algorithm (EA), to minimize a user-defined objective function, such as a residual sum of squares (RSS) function. BioNetFit also implements a bootstrapping procedure for determining confidence intervals for parameter estimates. Here, we provide step-by-step instructions for using BioNetFit to estimate the values of parameters of a BNGL-encoded model and to define bootstrap confidence intervals. The process entails the use of several plain-text files, which are processed by BioNetFit and BioNetGen. In general, these files include (1) one or more EXP files, which each contains (experimental) data to be used in parameter identification/bootstrapping; (2) a BNGL file containing a model section, which defines a (rule-based) model, and an actions section, which defines simulation protocols that generate GDAT and/or SCAN files with model predictions corresponding to the data in the EXP file(s); and (3) a CONF file that configures the fitting/bootstrapping job and that defines algorithmic parameter settings.

Lumbar plexus and psoas major muscle: not always as expected.

BACKGROUND AND OBJECTIVES: Conflicting definitions concerning the exact location of the lumbar plexus have been proposed. The present study was carried out to detect anatomical variants regarding the topographical relation between the lumbar plexus and the psoas major muscle as well as lumbar plexus anatomy at the L4-L5 level. METHODS: Sixty-three lumbar plexuses from 32 embalmed cadavers were dissected to determine the topographical relation between lumbar plexus and psoas major muscle. At the L4-L5 levels variability in the course of the femoral as well as obturator nerve were described. RESULTS: The lumbar plexus was situated within the psoas major muscle in 61 of 63 cases. In 2 of 63 cases the entire plexus was localized posterior to the psoas major muscle. In the 61 of 63 cases in which the lumbar plexus was situated within the psoas major muscle, emergence of the individual nerves most often occurred on the posterior or posterolateral surface. CONCLUSIONS: Our results synthesize contrasting assumptions in previous literature, by demonstrating that both locations of the lumbar plexus may be encountered in clinical practice: within and posterior to the psoas major muscle. However, the latter situation represents a minor variant. At the level of L4-L5 the femoral nerve, showing a remarkable degree of branching, as well as the obturator nerve, were found within the psoas major muscle in the vast majority of specimens.

Mechanoradical-induced degradation in a pharmaceutical blend during high-shear processing.

Mechanically generated radicals were shown to affect short-term stability of a model pharmaceutical formulation during high-shear processing. A formulation containing an oxidatively sensitive drug, either amorphous or crystalline, and a polymeric excipient was high-shear mixed and the resulting short-term degradation was determined with HPLC. High-shear mixing of the excipients was also carried out before drug addition to isolate effects on excipients versus those directly on the drug. Short-term drug stability was found to be strongly dependent on the amount of shear added to excipients prior to drug addition, regardless of morphology. A mechanism for the observed degradation based on mechanically generated radicals from microcrystalline cellulose is proposed. These results indicate that excipient high-shear exposure needs to be considered in regards to drug stability.

How Bispectral Index Compares to Spectral Entropy of the EEG and A-line ARX Index in the Same Patient.

BACKGROUND: Bispectral index (BIS) monitoring of depth of anesthesia has pioneered the field for more recent monitoring devices like the A-line ARX Index (AAI) or the state (SE) and response entropy (RE) monitoring devices. Following an observational design the present study aimed to simultaneously compare in the same patient recorded BIS, AAI and entropy values. METHODS: Data from patients (n = 32) undergoing minor gynecological operations were analyzed. For all patients, standardized anesthesia was used. Before induction of anesthesia AEP electrodes, BIS and entropy sensors were simultaneously placed on the forehead and recordings were started at 3 minutes before induction and continued until patient transfer to the postanesthesia care unit. Markers were set at defined landmarks. RESULTS: Anesthesia reduced mean BIS, AAI and entropy values. During uneventful, and even more pronounced, during eventful anesthesia BIS/ entropy and BIS/ AAI values showed better correlation than did AAI and entropy values. The prediction probability (Pk) of AAI (0.824 ± 0.036) and RE (0.786 ± 0.040) or SE (0.781 ± 0.040) for preanesthesia awake, postanesthesia awake or anesthesia was comparable and significantly greater than that of BIS (0.705 ± 0.047). However, only 20% of BIS, AAI and entropy values simultaneously categorized the state of the patient as awake, inadequate anesthesia, optimal anesthesia or deep anesthesia. CONCLUSION: The prediction probability (Pk) of entropy and AAI was comparable and better than that of BIS. However, agreement between BIS, AAI and entropy measurements on patient state was poor.

The presentation of appendicitis in preadolescent children.

PURPOSE: We describe the clinical presentation of appendicitis in preadolescent children and differences in symptoms among age-stratified subgroups. METHODS: This is a retrospective analysis of a prospectively collected de-identified data set of patients 3 years or older and patients younger than 12 years presenting to a pediatric emergency department during a 21-month period with symptoms suspicious for appendicitis. The rates of appendicitis, perforation, negative appendectomy, as well as sensitivities, specificities, and positive likelihood ratios for historical and clinical variables associated with appendicitis were calculated for the entire cohort and for 3 age-stratified subgroups. RESULTS: Of 379 children, 121 (32%) had appendicitis, 75 (62%) were male, 24 (20%) had a perforated appendix, and 16 (12%) had a negative appendectomy. The perforation rate was highest (53%) in the youngest subset of patients (3-5.99 years). Patients with appendicitis presented with inability to walk (82%), maximal right lower quadrant tenderness (82%), nausea (79%), pain with percussion, hopping, coughing (79%), and anorexia (75%). Fewer patients with appendicitis presented with a history of vomiting (66%), fever (47%), or diarrhea (16%), and these findings were not associated with the diagnosis. The youngest subset of patients (3-5.99 years) presented to the emergency department with fever; however, within this age subset, there was no significant difference in temperatures between patients with and without appendicitis. Fever was an indicator for perforation. Psoas, Rovsing, and obturator signs were infrequent but very specific for appendicitis (0.86-0.98 depending on age). CONCLUSIONS: Nausea, right lower quadrant tenderness, inability to walk, and elevated white blood cell and neutrophil counts are sensitive indicators of appendicitis in preadolescent children. Although peritoneal signs are infrequently elicited, when present, they substantially increase the likelihood of appendicitis. Fever, vomiting, and diarrhea are not associated with appendicitis in preadolescent children.

Quantification of recent smoking behaviour using proton transfer reaction-mass spectrometry (PTR-MS).

Smoking is the most important single risk factor in current public health. Surveillance of exposure to tobacco smoke may be accomplished using environmental monitoring or in-vivo tests for smoking biomarkers. Acetonitrile exhaled in human breath has been described as a potential marker mirroring recent smoking behavior. The aim of this study was to determine exhaled acetonitrile levels in a sample of 268 volunteers (48 smokers, 220 non-smokers) attending a local health fair. Breath specimens were collected into inert sample bags, with parallel collection of ambient air. Subsequently, all samples were analysed using proton transfer reaction-mass spectrometry (PTR-MS). Smokers had elevated levels of exhaled acetonitrile compared with non-smokers (p<0.001). Analysis using the receiver-operating-characteristic curve demonstrated that smoking can be predicted with a sensitivity of 79% and a specificity of 91%, using a cut-off concentration of 20.31 parts per billion of acetonitrile. This first field survey of exhaled acetonitrile in a large group of test persons demonstrates the feasibility of a rapid and non-invasive test for recent exposure to tobacco. We conclude that analysis of exhaled-breath acetonitrile may serve as a method of determining recent active smoking behaviour.

Special problems of pacing in children.

The number of children suffering from congenital or acquired rhythm disorders, and therefore being pacemaker dependent, is very small. This is one of the reasons why a special hardware has never been developed for this cohort. Pacemaker implantation into children does not differ substantially from operations in adults. But there are several important points which have to be fulfilled in these small patients in order to guarantee a complication free function. As most of these children remain pacemaker dependent a lifetime, it is of tremendous importance to minimize all revisions regarding the implanted systems and to enable our small patients a high and therefore nearly normal quality of life. Pros and cons of different surgical approaches, implantation sites and the problem of growth after pacemaker implantation in children are considered.

Evaluation of the precision of emergency department diagnoses in young children with fever.

OBJECTIVE. To characterize causes of fever in children presenting to a pediatric emergency department (ED). METHODS. One-year retrospective review of ED records. Inclusion criteria were 2 to 36 months of age with a documented temperature ≥ 39°C. Exclusion criteria were elopement, repeat visit, and underlying diagnosis with a predisposition to infection. Medical records were reviewed using a predefined, study-specific, data abstraction tool. Based on diagnosis and pathogen detection, visits were assigned to 3 groups, laboratory confirmed pathogen and focal or nonfocal diagnosis without confirmed pathogen. RESULTS. A total of 1091 visits met inclusion criteria. Fourteen percent had a pathogen detected, 56% had a focal diagnosis without a confirmed pathogen, and 30% had a nonfocal diagnosis without confirmed pathogen. CONCLUSIONS. In a cohort of febrile children 2 to 36 months of age, only 14% had a confirmed pathogen. New rapid viral diagnostic techniques may provide an opportunity to improve diagnostic certainty in young children presenting with fever.

Detection of viruses in young children with fever without an apparent source.

OBJECTIVE: Fever without an apparent source is common in young children. Currently in the United States, serious bacterial infection is unusual. Our objective was to determine specific viruses that might be responsible. METHODS: We enrolled children aged 2 to 36 months with temperature of 38°C or greater without an apparent source or with definite or probable bacterial infection being evaluated in the St Louis Children's Hospital Emergency Department and afebrile children having ambulatory surgery. Blood and nasopharyngeal swab samples were tested with an extensive battery of virus-specific polymerase chain reaction assays. RESULTS: One or more viruses were detected in 76% of 75 children with fever without an apparent source, 40% of 15 children with fever and a definite or probable bacterial infection, and 35% of 116 afebrile children (P < .001). Four viruses (adenovirus, human herpesvirus 6, enterovirus, and parechovirus) were predominant, being detected in 57% of children with fever without a source, 13% of children with fever and definite or probable bacterial infection, and 7% of afebrile children (P < .001). Thirty-four percent of 146 viral infections were detected only by polymerase chain reaction performed on blood. Fifty-one percent of children with viral infections and no evidence of bacterial infection were treated with antibiotics. CONCLUSIONS: Viral infections are frequent in children with fever without an apparent source. Testing of blood in addition to nasopharyngeal secretions expanded the range of viruses detected. Future studies should explore the utility of testing for the implicated viruses. Better recognition of viruses that cause undifferentiated fever in young children may help limit unnecessary antibiotic use.

The incidence of lumbar ligamentum flavum midline gaps.

UNLABELLED: Lumbar epidural anesthesia and analgesia has gained increasing importance in perioperative pain therapy for abdominal and lower limb surgery. The loss-of-resistance technique, used to identify the epidural space, is thought to rely on the penetration of the ligamentum flavum. However, the exact morphology of the ligamentum flavum at different vertebral levels remains controversial. Therefore, in this study, we directly investigated the incidence of lumbar ligamentum flavum midline gaps in embalmed cadavers. Vertebral column specimens were obtained from 45 human cadavers. On each dissected level, ligamentum flavum midline gaps were recorded. The incidence of midline gaps per number of viable specimens at the following levels was: L1-2 = 10 of 45 (22.2%), L2-3 = 5 of 44 (11.4%), L3-4 = 5 of 45 (11.1%), L4-5 = 4 of 43 (9.3%), L5/S1 = 0 of 33 (0%). In conclusion, the present study determined the frequency of lumbar ligamentum flavum midline gaps. Gaps in the lumbar ligamentum flavum are most frequent between L1 and L2 but are more rare below this level. When using the midline approach, the ligamentum flavum may not impede entering the epidural space in all patients. IMPLICATIONS: The ligamentum flavum is a crucial anatomical landmark for the safe performance of epidural anesthesia. However, the present study demonstrates some failure of the lumbar ligamentum flavum as a landmark. This may mean that, using a midline approach, one cannot always rely on the ligamentum flavum as a perceptible barrier to epidural needle advancement.

Cervical and high thoracic ligamentum flavum frequently fails to fuse in the midline.

BACKGROUND: Cervical and high thoracic epidural anesthesia and analgesia have gained increasing importance in the treatment of painful conditions and as components of anesthetics for cardiac and breast surgery. In contrast to the hanging-drop technique, the loss-of-resistance technique is thought to rely on the penetration of the ligamentum flavum. However, the exact morphology of the ligamentum flavum at different vertebral levels remains controversial. Therefore, the aim of this study was to investigate the incidence and morphology of cervical and high thoracic ligamentum flavum mid-line gaps in embalmed cadavers. METHODS: Vertebral column specimens were obtained from 52 human cadavers. On each dissected level, ligamentum flavum mid-line gaps were recorded and evaluated with respect to shape and size. RESULTS: The following variations were encountered: complete fusion in the mid-line, mid-line fusion with a gap in the caudal part, mid-line gap, and mid-line gap with widened caudal end. The incidence of mid-line gaps at the following levels was: C3-C4: 66%, C4-C5: 58%, C5-C6: 74%, C6-C7: 64%, C7-T1: 51%, Th1-Th2: 21%, Th2-Th3: 11%, Th3-Th4: 4%, Th4-Th5: 2%, and Th5-Th6: 2%. The mean width of mid-line gaps was 1.0 +/- 0.3 mm. CONCLUSIONS: In conclusion, the present study shows that gaps in the ligamenta flava are frequent at cervical and high thoracic levels but become rare at the T3/T4 level and below, such that one cannot always rely on the ligamentum flavum as a perceptible barrier to epidural needle placement at these levels.