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Background Cross-sectional tumor measures are traditional clinical trial endpoints; however volumetric measures may better assess tumor growth. We determined the correlation and compared the prognostic impact of cross-sectional and volumetric measures of progressive disease (PD) among patients with DIPG. Methods Imaging and clinical data were abstracted from the International DIPG Registry. Tumor volume and cross-sectional product (CP) were measured with mint Lesion™ software using manual contouring. Correlation between CP and volume (segmented and mathematical [ellipsoid] model) thresholds of PD were assessed by linear regression. Landmark analyses determined differences in survival (via log-rank) between patients classified as PD versus non-PD by CP and volumetric measurements at 1, 3, 5, 7, and 9 months postradiotherapy (RT). Hazard ratios (HR) for survival after these time points were calculated by Cox regression. Results A total of 312 MRIs (46 patients) were analyzed. Comparing change from the previous smallest measure, CP increase of 25% (PD) correlated with a segmented volume increase of 30% (R2 = 0.710), rather than 40% (spherical model extrapolation). CP-determined PD predicted survival at 1 month post-RT (HR = 2.77), but not other time points. Segmented volumetric-determined PD (40% threshold) predicted survival at all imaging timepoints (HRs = 2.57, 2.62, 3.35, 2.71, 16.29), and 30% volumetric PD threshold predicted survival at 1, 3, 5, and 9 month timepoints (HRs = 2.57, 2.62, 4.65, 5.54). Compared to ellipsoid volume, segmented volume demonstrated superior survival associations. Conclusions Segmented volumetric assessments of PD correlated better with survival than CP or ellipsoid volume at most time points. Semiautomated tumor volume likely represents a more accurate, prognostically-relevant measure of disease burden in DIPG.

Background Diffuse intrinsic pontine glioma (DIPG) remains a clinico-radiologic diagnosis without routine tissue acquisition. Reliable imaging distinction between DIPG and other pontine tumors with potentially more favorable prognoses and treatment considerations is essential. Methods Cases submitted to the International DIPG registry (IDIPGR) with histopathologic and/or radiologic data were analyzed. Central imaging review was performed on diagnostic brain MRIs (if available) by two neuro-radiologists. Imaging features suggestive of alternative diagnoses included nonpontine origin, Results Among 286 patients with pathology from biopsy and/or autopsy, 23 (8%) had histologic diagnoses inconsistent with DIPG, most commonly nondiffuse low-grade gliomas and embryonal tumors. Among 569 patients with centrally-reviewed diagnostic MRIs, 40 (7%) were classified as non-DIPG, alternative diagnosis suspected. The combined analysis included 151 patients with both histopathology and centrally-reviewed MRI. Of 77 patients with imaging classified as characteristic of DIPG, 76 (99%) had histopathologic diagnoses consistent with DIPG (infiltrating grade II-IV gliomas). Of 57 patients classified as likely DIPG with some unusual imaging features, 55 (96%) had histopathologic diagnoses consistent with DIPG. Of 17 patients with imaging features suggestive of an alternative diagnosis, eight (47%) had histopathologic diagnoses inconsistent with DIPG (remaining patients were excluded due to nonpontine tumor origin). Association between central neuro-imaging review impression and histopathology was significant (p < 0.001), and central neuro-imaging impression was prognostic of overall survival. Conclusions The accuracy and important role of central neuro-imaging review in confirming the diagnosis of DIPG is demonstrated.

We aimed to objectively compare the effects of wearing newer, higher-ranked football helmets (HRank) vs. wearing older, lower-ranked helmets (LRank) on pre- to post-season alterations to neuroimaging-derived metrics of athletes' white matter. Fifty-four high-school athletes wore an HRank helmet, and 62 athletes wore an LRank helmet during their competitive football season and completed pre- and post-season diffusion tensor imaging (DTI). Longitudinal within- and between-group DTI metrics [fractional anisotropy (FA) and mean/axial/radial diffusivity (MD, AD, RD)] were analyzed using tract-based spatial statistics. The LRank helmet group exhibited significant pre- to post-season reductions in MD, AD, and RD, the HRank helmet group displayed significant pre- to post-season increases in FA, and both groups showed significant pre- to post-season increases in AD (p's < .05 [corrected]). Between-group analyses revealed the pre- to post-season increase in AD was significantly less for athletes wearing HRank compared to LRank (p < .05 [corrected]). These data provide in vivo evidence that wearing an HRank helmet may be efficacious for preserving white matter from head impact exposure during high school football. Future prospective longitudinal investigations with complimentary imaging and behavioral outcomes are warranted to corroborate these initial in vivo findings.

Symmetry analysis of coupled higher-dimensional forced Burgers’ equation is investigated for various cases. The Lie algebra for the various cases of forcing terms is investigated. Interestingly, for a linear forcing term, the symmetry analysis leads to the Ermakov–Pinney equation and time-dependent oscillator equation.

Patellofemoral pain (PFP) is defined as retro- or peri-patellar knee pain without a clear structural abnormality. Unfortunately, many current treatment approaches fail to provide long-term pain relief, potentially due to an incomplete understanding of pain-disrupted sensorimotor dysfunction within the central nervous system. The purposes of this study were to evaluate brain functional connectivity in participants with and without PFP, and to determine the relationship between altered brain functional connectivity in association with patient-reported outcomes. Young female patients with PFP (n = 15; 14.3 ± 3.2 years) completed resting-state functional magnetic resonance imaging (rs-fMRI) and patient-reported outcome measures. Each patient with PFP was matched with two controls (n = 30, 15.5 ± 1.4 years) who also completed identical rs-fMRI testing. Six bilateral seeds important for pain and sensorimotor control were created, and seed-to-voxel analyses were conducted to compare functional connectivity between the two groups, as well as to determine the relationship between connectivity alterations and patient-reported outcomes. Relative to controls, patients with PFP exhibited altered functional connectivity between regions important for pain, psychological functioning, and sensorimotor control, and the connectivity alterations were related to perceived disability, dysfunction, and kinesiophobia. The present results support emergent evidence that PFP is not localized to structural knee dysfunction, but may actually be resultant to altered central neural processes. Clinical significance: These data provide potential neuro-therapeutic targets for novel therapies aimed to reorganize neural processes, improve neuromuscular function, and restore an active pain-free lifestyle in young females with PFP.

In this work, we emphasize the use of singularity analysis in obtaining analytic solutions for equations for which standard Lie point symmetry analysis fails to make any lucid decision. We study the higher-dimensional Kadomtsev–Petviashvili, Boussinesq, and Kaup–Kupershmidt equations in a more general sense. With higher-order equations, there can be a commensurate number of resonances and when consistency for the full equation is examined at each resonance the constant of integration is supposed to vanish from the expression so that it remains arbitrary, but if there is an instance of this not happening, the consistency can be partially established by giving the offending constant the value from the defining equation. If consistency is otherwise not compromised, the equation can be said to be partially integrable, i.e., integrable on a surface of the complex space. Furthermore, we propose an approach that is meant to magnify the scope of singularity analysis for equations admitting higher values for resonances or positive leading-order exponent.

Extraneural metastases are rare in pediatric high-grade gliomas and little is known about the genomic profiles of tumors that disseminate beyond the central nervous system. We describe a pediatric patient with H3 K27M-mutant diffuse midline glioma of the brain and spine with biopsy-confirmed osseous metastases present at diagnosis and suspected metastatic parenchymal pulmonary disease. Several potentially clinically and/or therapeutically relevant genomic alterations were identified, including H3F3A and TP53 mutations as well as MET, CDK6, EMSY, and PIK3CG amplifications. Sequencing is critical to improve our understanding of the molecular drivers of distant metastases and discover therapeutic targets that penetrate all disease sites.

Aims Atrial fibrillation (AF) is a complex heritable disease whose genetic underpinnings remain largely unexplained, though recent work has suggested that the arrhythmia may develop secondary to an underlying atrial cardiomyopathy. We sought to evaluate for enrichment of loss-of-function (LOF) and copy number variants (CNVs) in genes implicated in ventricular cardiomyopathy in ‘lone’ AF. Methods and results Whole-exome sequencing was performed in 255 early onset ‘lone’ AF cases, defined as arrhythmia onset prior to 60 years of age in the absence of known clinical risk factors. Subsequent evaluations were restricted to 195 cases of European genetic ancestry, as defined by principal component analysis, and focused on a pre-defined set of 43 genes previously implicated in ventricular cardiomyopathy. Bioinformatic analysis identified 6 LOF variants (3.1%), including 3 within the TTN gene, among cases in comparison with 4 of 503 (0.80%) controls [odds ratio: 3.96; 95% confidence interval (CI): 1.11–14.2; P = 0.033]. Further, two AF cases possessed a novel heterozygous 8521 base pair TTN deletion, confirmed with Sanger sequencing and breakpoint validation, which was absent from 4958 controls (P = 0.0014). Subsequent cascade screening in two families revealed evidence of co-segregation of a LOF variant with ‘lone’ AF. Conclusion ‘Lone’ AF cases are enriched in rare LOF variants from cardiomyopathy genes, findings primarily driven by TTN, and a novel TTN deletion, providing additional evidence to implicate atrial cardiomyopathy as an AF genetic sub-phenotype. Our results also highlight that AF may develop in the context of these variants in the absence of a discernable ventricular cardiomyopathy.

OBJECTIVE Patients with tuberous sclerosis complex (TSC) epilepsy present with unique clinical challenges such as early seizure onset and high rates of intractability and multifocality. Although there are numerous studies about the safety and efficacy of stereoelectroencephalography (SEEG), this topic has not been studied in TSC patients who have distinct epilepsy profiles. The authors investigated subdural grid (SDG) and SEEG monitoring to determine whether these procedures lead to similar seizure and safety outcomes and to identify features unique to this pediatric population. METHODS TSC patients who underwent SDG or SEEG placement and a second epilepsy surgery during the period from 2007 to 2021 were included in this single-center retrospective cohort analysis. Various patient, hospitalization, and epilepsy characteristics were collected. RESULTS A total of 50 TSC patients were included in this study: 30 were included in the SDG cohort and 20 in the SEEG cohort. Baseline weekly seizure count did not significantly differ between the 2 groups (p = 0.412). The SEEG group had a greater mean baseline number of antiepileptic drugs (AEDs) (3.0 vs 2.0, p = 0.003), higher rate of previous surgical interventions (25% vs 0%, p = 0.007), and larger proportion of patients who underwent bilateral monitoring (50% vs 13.3%, p = 0.005). Despite this, there was no significant difference in seizure freedom between the SDG and SEEG cohorts. The mean reduction in seizure count was 84.9% and 47.8% of patients were seizure free at last follow-up (mean 79.4 months). SEEG trended toward being a safer procedure than SDG monitoring, with a shorter mean ICU stay (0.7 days vs 3.9 days, p < 0.001), lower blood transfusion rate (0% vs 13.3%, p = 0.140), and lower surgical complication rate (0% vs 10%, p = 0.265). CONCLUSIONS In the comparison of the SDG and SEEG cohorts, the SEEG group included patients who appeared to receive more aggressive management and have a higher rate of multifocality, more prior surgical interventions, more AEDs at baseline, and a higher rate of bilateral invasive monitoring. Despite this, the SEEG cohort had similar seizure outcomes and a trend toward increased safety. Based on these findings, SEEG appears to allow for monitoring of a wider breadth of TSC patients given its minimally invasive nature and its relative simplicity for monitoring numerous regions of the brain.

To quantify the effects of an externally worn collar device for mitigating the influence of repetitive head impacts on alterations to diffusion tensor imaging (DTI) metrics of white matter. Fifteen female high-school soccer athletes (age: 14.00–16.98 yrs) completed pre- and post-season DTI over two consecutive years, including measures of diffusivity, changes in which may be associated with brain dysfunction. The collar was worn during year 1 (Yr1) but not during year 2 (Yr2). Athlete exposures (AEs) and head impact exposure were recorded over the competitive seasons. There were no significant differences in AEs or head impact exposures between Yr1 and Yr2 (P > 0.05). In Yr2, there was significant pre- to post-season mean diffusivity and/or axial diffusivity reduction in multiple WM regions (corrected P

OBJECTIVEThe aim of this study was to investigate diffusion tensor imaging (DTI), an objective and noninvasive neuroimaging technique, for its potential as an imaging biomarker to predict the need and timing of CSF diversion surgery in patients after prenatal myelomeningocele (MMC) repair.METHODSThis was a retrospective analysis of data based on 35 pediatric patients after prenatal MMC repair (gestational age at birth 32.68 ± 3.42 weeks, range 24–38 weeks; 15 females and 20 males). A logistic regression analysis was used to classify patients to determine the need for CSF diversion surgery. The model performance was compared between using the frontooccipital horn ratio (FOHR) alone and using the FOHR combined with DTI values (the genu of the corpus callosum [gCC] and the posterior limb of the internal capsule [PLIC]). For patients who needed to be treated surgically, timing of the procedure was used as the clinical outcome to test the predictive value of DTI acquired prior to surgery based on a linear regression analysis.RESULTSSignificantly lower fractional anisotropy (FA) values in the gCC (p = 0.014) and PLIC (p = 0.037) and higher mean diffusivity (MD) values in the gCC (p = 0.013) were found in patients who required CSF diversion surgery compared with those who did not require surgery (all p values adjusted for age). Based on the logistic regression analysis, the FOHR alone showed an accuracy of performance of 0.69 and area under the receiver operating characteristic curve (AUC) of 0.60. The performance of the model was higher when DTI measures were used in the logistic regression model (accuracy = 0.77, AUC = 0.84 for using DTI values in gCC; accuracy = 0.75, AUC = 0.84 for using DTI values in PLIC). Combining the DTI values of the gCC or PLIC and FOHR did not improve the model performance when compared with using the DTI values alone. In patients who needed CSF diversion surgery, significant correlation was found between DTI values in the gCC and the time interval between imaging and surgery (FA: ρ = 0.625, p = 0.022; MD: ρ = −0.6830, p = 0.010; both adjusted for age and FOHR).CONCLUSIONSThe authors’ data demonstrated that DTI could potentially serve as an objective biomarker differentiating patients after prenatal MMC repair regarding those who may require surgery for MMC-associated hydrocephalus. The predictive value for the need and timing of CSF diversion surgery is highly clinically relevant for improving and optimizing decision-making for the treatment of hydrocephalus in this patient population.

While autopsy-repository programs with a variety of pediatric central nervous system (CNS) tumor types are a critical resource for preclinical neuro-oncology research, few exist and there is no published guidance on how to develop one. The goal of this prospective Pediatric Brain Tumor Repository (PBTR) study was to develop such a program at Cincinnati Children’s Hospital Medical Center (CCHMC) and then publish the quantitative and experiential data as a guide to support the development of similar programs. Protocols and infrastructure were established—to educate oncologists and families, establish eligibility, obtain consent, address pre- and post-autopsy logistics (e.g., patient and tissue transportation), process and authenticate tissue samples, and collect and analyze data. Of the 129 pediatric CNS tumor patients at CCHMC who died between 2013 and 2018, 109 were eligible for our study. Of these, 74% (81 of 109) were approached for PBTR donation, and 68% (55 of 81) consented. In the final year of the study, approach and consent rates were 93% and 85%, respectively. Median time from death to autopsy (postmortem interval, PMI) was 10 h (range, 1.5–30). In the outpatient setting, PMI increased with distance (from the hospice/home where the patient died to CCHMC). In all patients, PMI appeared to be lower, when consent was obtained more than 24 h before death. Procurement of autopsy specimens need not be a barrier in neuro-oncology research. Regional centers, strict timing-of-consent, patient education, and dedicated staff are all needed to minimize PMI and, thereby, increase the value of the procured tissue for an array of basic and translational research applications.

The Shalipayco Zn–Pb deposit, in central Peru, is composed of several stratabound orebodies, the largest of which are the Resurgidora and Intermedios, contained in carbonate rocks of the Upper Triassic Chambara Formation, Pucara group. Petrography suggests that a single ore-forming episode formed sphalerite and galena within vugs, open spaces, and fractures. Three-dimensional (3D) geological modeling has allowed division of the Chambara Formation into four members (Chambara I, II, III, and IV) that better define lithological controls on sulfide formation. Diagenetic replacement of evaporite minerals with the organic matter (OM) presence likely generated secondary porosity and H2S accumulation by bacterial sulfate reduction (BSR), providing ground preparation for the later Zn–Pb mineralizing event. The least-altered host rocks have C–O isotope compositions of 1.8 ± 0.1‰ (VPDB) and 29.9 ± 2.1‰ (VSMOW), respectively, within the Triassic marine carbonate ranges. Early dolomite contains lighter C–O composition (1.1 ± 0.9 and 23.8 ± 2.9‰, respectively) consistent with OM decomposition during burial diagenesis. Post-mineralization calcite has still lighter C–O composition (− 5.1 and 13.3‰, respectively), suggesting meteoric water that had migrated through organic-rich strata. The strontium isotopes of Mitu group basalts (0.709654–0.719669) indicate it as a possible, but not the unique source of strontium and probably of other metals. Highly negative sulfide sulfur isotope values (− 23.3 to − 6.2‰ (VCDT)) indicate a major component of the ore sulfur derived ultimately from BSR. However, multiple lines of evidence suggest that preexisting H2S underwent thermochemical redox cycling prior to ore formation. The influx of hot metalliferous brines to dolomitized zones containing trapped H2S is the preferred model for ore deposition at Shalipayco.

An adequate understanding of the relationships between radiographic and genomic features in diffuse intrinsic pontine glioma (DIPG) is essential, especially in the absence of universal biopsy, to further characterize the molecular heterogeneity of this disease and determine which patients are most likely to respond to biologically-driven therapies. Here, a radiogenomics analytic approach was applied to a cohort of 28 patients with DIPG. Tumor size and imaging characteristics from all available serial MRIs were evaluated by a neuro-radiologist, and patients were divided into three radiographic response groups (partial response [PR], stable disease [SD], progressive disease [PD]) based on MRI within 2 months of radiotherapy (RT) completion. Whole genome and RNA sequencing were performed on autopsy tumor specimens. We report several key, therapeutically-relevant findings: (1) Certain radiologic features on first and subsequent post-RT MRIs are associated with worse overall survival, including PD following irradiation as well as present, new, and/or increasing peripheral ring enhancement, necrosis, and diffusion restriction. (2) Upregulation of EMT-related genes and distant tumor spread at autopsy are observed in a subset of DIPG patients who exhibit poorer radiographic response to irradiation and/or higher likelihood of harboring H3F3A mutations, suggesting possible benefit of upfront craniospinal irradiation. (3) Additional genetic aberrations were identified, including DYNC1LI1 mutations in a subgroup of patients with PR on post-RT MRI; further investigation into potential roles in DIPG tumorigenesis and/or treatment sensitivity is necessary. (4) Whereas most DIPG tumors have an immunologically “cold” microenvironment, there appears to be a subset which harbor a more inflammatory genomic profile and/or higher mutational burden, with a trend toward improved overall survival and more favorable radiographic response to irradiation, in whom immunotherapy should be considered. This study has begun elucidating relationships between post-RT radiographic response with DIPG molecular profiles, revealing radiogenomically distinct subgroups with unique clinical trajectories and therapeutic targets.

In this paper, we determine a recursion operator for the Kummer-Schwarz equation, which leads to a sequence with unacceptable singularity properties. A different sequence is devised based upon the relationship between the Kummer-Schwarz equation and the first-order Riccati equation for which a particular generator has been found to give interesting and excellent properties. We examine the elements of this sequence in terms of the usual properties to be investigated – symmetries, singularity properties, integrability, alternate sequence – and provide an explanation of the curious relationship between the results of the singularity analysis and a consideration of the solution of each element obtained by quadratures.

The boundary layer flow of an incompressible viscoelastic Jeffrey’s nanofluid from a vertical permeable flat plate is investigated. We consider the effects of heat generation, thermal radiation, and chemical reaction on the fluid flow. The nonlinear transformed coupled differential equations that describe the transport processes are solved numerically using a multidomain bivariate spectral quasilinearization method (MD-BSQLM). This innovative method involves blending the quasilinearization idea with the bivariate Lagrange interpolation. The solutions of the resulting system of equations are then obtained sequentially on multiple intervals using the Chebyshev spectral collocation method. The method is shown to give accurate solutions for boundary layer-type equations. The influence of various physical parameters on velocity, temperature, and nanoparticle concentration fields, as well as on the skin friction and heat and mass transfer coefficients, is shown and discussed in detail. The range of the values of the governing parameters considered in this study is between 0 , 4 . For qualitative validation of the results and the numerical method used, calculations were carried out to graphically obtain the velocity, temperature, and nanoparticle concentration fields for selected physical parameter values. The results obtained were found to correlate with the results from published literature. For quantitative verification of our findings, the MD-BSQLM numerical solutions were again confirmed against published results reported in the literature, and the results were observed to be in perfect agreement. This study’s findings indicate that the Deborah number and suction parameter have related effects on the velocity profile, which is to suppress both the flow velocity and the momentum boundary layer thickness. Increasing the heat generation and thermal radiation parameters enhances both the temperature and thermal boundary layer depths. In contrast, an increase in the chemical reaction parameter causes a decrease in the fluid concentration.

We apply the theory of Lie symmetries in order to study a fourth-order 1+2 evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular ...

Cyclin-dependent kinase-retinoblastoma (CDK-RB) pathway is dysregulated in some diffuse intrinsic pontine gliomas (DIPG). We evaluated safety, feasibility, and early efficacy of the CDK4/6-inhibitor ribociclib, administered following radiotherapy in newly-diagnosed DIPG patients. Following radiotherapy, eligible patients received ribociclib in 28-day cycles (350 mg/m2; 21 days on/7 days off). Feasibility endpoints included tolerability for at least 6 courses, and a less than 2-week delay in restarting therapy after 1 dose reduction. Early efficacy was measured by 1-year and median overall survival (OS). Patient/parent-by-proxy reported outcomes measurement information system (PROMIS) assessments were completed prospectively. The study included 10 evaluable patients, 9 DIPG and 1 diffuse midline glioma (DMG)—all 3.7 to 19.8 years of age. The median number of courses was 8 (range 3–14). Three patients required dose reduction for grade-4 neutropenia, and 1 discontinued therapy for hematological toxicity following course 4. The most common grade-3/4 toxicity was myelosuppression. After 2 courses, MRI evaluations in 4 patients revealed increased necrotic volume, associated with new neurological symptoms in 3 patients. The 1-year and median OS for DIPG was 89% and 16.1 months (range 10–30), respectively; the DMG patient died at 6 months post-diagnosis. Five patients donated brain tissue and tumor; 3 were RB+ . Ribociclib administered following radiotherapy is feasible in DIPG and DMG. Increased tumor necrosis may represent a treatment effect. These data warrant further prospective volumetric analyses of tumors with necrosis. Feasibility and stabilization findings support further investigation of ribociclib in combination therapies. NCT02607124.

We evaluated stereo-EEG electrical stimulation mapping (ESM) for localization of anatomic sensorimotor parcels in pediatric patients with drug-resistant epilepsy. We also analyzed sensorimotor and after-discharge thresholds, and the somatotopy of sensorimotor responses.ESM was performed with 50 Hz, biphasic, 2-3 s trains, using 1-9 mA current. Pre- and post-implant neuroimaging was co-registered and intersected with Neurosynth reference, to classify each electrode contact as lying within/outside an anatomic sensorimotor parcel. Indices of diagnostic performance were computed. Sensorimotor and after-discharge thresholds were analyzed using multivariable linear mixed models.In 15 patients (6 females), aged 5.5-21.2 years, ESM showed high accuracy (0.80), high specificity (0.86), and diagnostic odds ratio (11.4, p 0.0001) for localization of sensorimotor parcels. Mean sensorimotor threshold (3.4 mA) was below mean after-discharge threshold (4.2 mA, p = 0.0004). Sensorimotor and after-discharge thresholds showed a significant decrease with increasing intelligence quotient. Somatotopy of sensorimotor responses was mapped to standardized brain parcels.We provide evidence for diagnostic validity and safety of stereo-EEG sensorimotor ESM.The somatotopy of sensorimotor responses elicited with electrical stimulation provide new insights into mechanisms of motor control and sensory perception.

We study the Jimbo – Miwa equation and two of its extended forms, as proposed by Wazwaz et al., using Lie’s group approach. Interestingly, the travelling – wave solutions for all the three equations are similar. Moreover, we obtain certain new reductions which are completely different for each of the three equations. For example, for one of the extended forms of the Jimbo – Miwa equation, the subsequent reductions leads to a second – order equation with Hypergeometric solutions. In certain reductions, we obtain simpler first – order and linearisable second – order equations, which helps us to construct the analytic solution as a closed – form function. The variation in the nonzero Lie brackets for each of the different forms of the Jimbo – Miwa also presents a different perspective. Finally, singularity analysis is applied in order to determine the integrability of the reduced equations and of the different forms of the Jimbo – Miwa equation.