Histopathological and Ultrasound Correlation in Women Presenting with Breast Lumps in Yaoundé, Cameroon

Context: Breast cancer is very deadly among women with higher rates in the developing world. Imaging tools such as ultrasound, can be used to differentiate between the types of breast lumps. This study aimed to determine the value of ultrasound as a first-line examination in the diagnosis of breast masses. Methods: This was a retrospective cross-sectional study of women presenting with breast lumps from November 2022 to June 2023 at the Yaounde General Hospital, which lasted seven months, from November 2022 to June 2023. The sampling was exhaustive and consecutive. Association between variables was studied using the x2 test and concordance between ultrasound and histopathological findings was assessed using the Kappa correlation coefficient. Results: 234 women were included in the study. Their mean age was 46.3 ± 11.4 years. Overall, 15 (6.4%) lumps were benign while 219 (93.6%) were malignant. Triple negative (5.6%) was the most recurrent genomic classification. The correlation between the ultrasound and histopathological findings was significant, with an observed concordance rate at 85.1%, kappa = 0.322 and a p-value Conclusion: The performance of ultrasound in differentiating benign and malignant lesion was high. However, the discordant cases highlight the need for a diagnosis system which blends histopathological and radiological findings for an improved management of patients with breast lumps.

Collisions Between Lumps/Rogue Waves and Solitons for A(3+1)-Dimensional Generalized Variable-Coefficient Shallow Water Wave Equation

In this paper,we investigate a(3+1)-dimensional generalized variable-coefficient shallow water wave equation,which can be used to describe the flow below a pressure surface in oceanography and atmospheric science.Employing the Kadomtsev−Petviashvili hierarchy reduction,we obtain the semi-rational solutions which describe the lumps and rogue waves interacting with the kink solitons.We find that the lump appears from one kink soliton and fuses into the other on the x−y and x−t planes.However,on the x−z plane,the localized waves in the middle of the parallel kink solitons are in two forms:lumps and line rogue waves.The effects of the variable coefficients on the two forms are discussed.The dispersion coefficient influences the speed of solitons,while the background coefficient influences the background’s height.

Analysis of High-Frequency Ultrasound in the differential Diagnosis of Lumps in Foot and Hand

Objective:To investigate the ultrasonogram characteristics of common lumps in hand and foot,pursuing for greater understanding of hand and foot lumps.Methods:65 cases of ultrasonographic characteristics of lumps in hand and foot were retrospectively analyzed,including the location,size,shape,boundary,internal echo and posterior echo,surrounding relationship and blood flow.Results:Among 65 cases,there were 26 cases of tendon sheath cyst,16 cases of tenosynovitis giant cell tumor,10 cases of hemangioma,4 cases of tendon sheath fibroma,3 cases of epidermoid cyst,2 cases of Schwannoma,2 cases of fibrolipoma,1 case of angiolipoma and 1 case of neurofibroma.The preoperative and postoperative pathological diagnoses of 45 cases,accounting for 69.23%,were consistent,3 cases(4.62%)were misdiagnosed,which included that 2 cases of tenosynovitis giant cell tumor were misdiagnosed as tendon sheath cyst,1 case of neurofibroma as epidermoid cyst,and the preoperative diagnosis of the rest 17 cases(26.15%)were indefinite.Conclusion:The high-frequency ultrasound can diagnose properties of lumps in foot and hand well,providing diagnosis basis for further treatment in clinic.

Antidiastole Value of Three-dimensional Ultrasonography and Power Doppler between Uterine Parenchyma Lumps and Endometrial Cancer:A Retrospective Study

Sometimes endometrial polyps,submucosal myomas,and endometrial cancer show similar findings under ultrasonography.The aim of this study was to assess the antidiastole value of blood flow parameters using three-dimensional(3D)power Doppler ultrasonography angiography(PDA)between endometrial cancer and uterine parenchyma lumps.The data of the blood flow indices in 3D-PDA including the vascularization index(VI),flow index(FI),and vascularization flow index(VFI)in 40 patients with endometrial cancer and 41 patients with uterine parenchyma lumps(endometrial polyps and submucosal myomas)were retrospectively analysed and compared utilizing Virtual Organ Computer-aided AnaLysis(VOCAL)software.The results showed that all the blood flow parameters(VI,FI,VFI)were significantly higher in women with endometrial cancer than in those with uterine parenchyma lumps(P<0.001).The area under the curve of ROC of VI,FI,and VFI was 0.98,0.84,and 0.97,respectively.Thus,the best predictor of endometrial carcinoma was VI with a sensitivity of 97.0% and a specificity of 91.0%.The optimal cutoff value of VI was 4.06%.Our data demonstrated that all of the blood flow signal parameters(including VI,FI,and VFI)in 3D power Doppler ultrasonography had significant antidiastole values between endometrial cancer and uterine parenchyma lumps to assist clinicians in properly diagnosing patients.

Repeated lumps and infections: A case report on breast augmentation complications

BACKGROUND Polyacrylamide hydrogel(PAAG)injections were once common in breast augmentation and have been prohibited for augmentation mammaplasty in China since a large number of patients who underwent breast augmentation with PAAG injections have continued to seek medical advice as a result of related complications.Among all these complications,distant migration is relatively rare.CASE SUMMARY A 49-year-old female presented at the hospital with a one-year history of a vulvar lump.The sonography of the lump showed several subcutaneous fluid-filled regions from the left vulva to the pubic symphysis,which suggested possible fat liquefaction.An enhanced magnetic resonance imaging(MRI)revealed a cystic area,which was considered a benign lesion.Intraoperative observations showed that the mass did not have an obvious capsule,the subcutaneous tissue presented as a cavity,and some yellow material came out of this cavity.A culture of the drainage did not show bacterial contamination.Histopathology revealed a foreign body granuloma.After resection and closed drainage,lumps were successively observed in the left lower abdomen and the bilateral hypochondriac region with infections.Sonography found that the hypoechoic areas in the bilateral hypochondriac region seemed continuous with deep in the breasts.The patient reported that she had undergone surgery with PAAG injections 20 years ago after she was repeatedly asked about her past history.Finally,a diagnosis of distant migration of PAAG was made.CONCLUSION PAAG gel can migrate after long periods of time.A diagnosis should not be limited to the area where the symptom develops.

General M-lumps, T-breathers, and hybrid solutions to (2+1)-dimensional generalized KDKK equation

A special transformation is introduced and thereby leads to the N-soliton solution of the(2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt(KDKK) equation.Then,by employing the long wave limit and imposing complex conjugate constraints to the related solitons,various localized interaction solutions are constructed,including the general M-lumps,T-breathers,and hybrid wave solutions.Dynamical behaviors of these solutions are investigated analytically and graphically.The solutions obtained are very helpful in studying the interaction phenomena of nonlinear localized waves.Therefore,we hope these results can provide some theoretical guidance to the experts in oceanography,atmospheric science,and weather forecasting.

Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

Preliminary study on CT perfusion imaging in guiding biopsy of pulmonary lumps

Background CT perfusion imaging （CTP） has been proved to be a powerful functional imaging technique. This study aimed to evaluate the value of CTP in guiding biopsy of pulmonary lumps. Methods A total of 147 patients with pulmonary lumps who had CT guided biopsies were enrolled in this study from February 2005 to June 2007. The patients were assigned to 3 groups： 33 cases guided by CTP as group 1, 45 cases guided by contrast-enhanced scan of CT as group Ⅱ, and 69 cases guided by plain scan of CT as group Ⅲ. Each group was subdivided into central and peripheral types according to the location of the lumps. The achievement ratio of biopsy, the accuracy in grouping, and grading of lung cancer, and the incidence of complication were compared. Results The total achievement ratios of biopsy from group Ⅰ to Ⅲ were 100% （33/33）, 91% （41/45）, and 80% （55/69） respectively, and the difference was statistically significant between group Ⅰ and Ⅲ （P 〈0.05）. For the central type, they were 100% （18/18）, 88% （15/17）, and 79% （11/14） respectively, and the difference was also statistically significant between group Ⅰand Ⅲ （P 〈0.05）. For the peripheral type, they were 100% （15/15）, 93% （26/28）, and 80% （44/55） respectivelies, and the difference was not statistically significant among the three groups. The total accuracies in grouping and grading of lung cancer from group Ⅰ to Ⅲ were 100% （27/27）, 91% （31/34）, and 72% （33/46） respectively, and the difference was statistically significant between group Ⅰ and Ⅲ and between group Ⅱ and Ⅲ （P 〈0.05）. For the central type, they were 100% （16/16）, 94% （16/17）, and 70% （8/12） respectively, and the difference was statistically significant between group Ⅰ and Ⅲ （P〈0.05）. For the peripheral type, they were 100% （11/11）, 88% （15/17）, and 72% （26/36） respectively, and the difference was statistically significant between group Ⅰ and Ⅲ （P 〈0.05）. The total incidence of complication from group Ⅰ to Ⅲ were 15% （5/33）, 27% （12/45）, and 43% （30/69） respectively, and the difference was statistically significant between group Ⅰ and Ⅲ （P 〈0.01）. For the central type, they were 11% （2/18）, 24% （4/17）, and 57% （8/14） respectively, and the difference was statistically significant between group Ⅰ and Ⅲ （P 〈0.01）. For the peripheral type, they were 20% （3/15）, 29% （8/28）, and 40% （22/55） respectively, and no statistically significant difference was found among the three groups. Conclusions CTP guided biopsy of pulmonary lumps using multi-detector row CT has the potential to improve the accuracy of histopathological diagnosis with a lower risk and higher achievement ratio. More research and technical improvements are needed before it is widelv used.

广义(3+1)维KP方程的精确有理解

利用Hirota方法及Maple,得到了一类带9个二阶导数项的(3+1)维KP方程的精确有理解。在一定条件下,方程有lump型解,解中有八个自由参数,在特定参数下,通过定量与作图分析给出了解的数值模拟。

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

A large member of lump chain solutions of the(2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili(BKP)equation are constructed by means of theτ-function in the form of Grammian.The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities.An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains.The degenerate structures of parallel,superimposed,and molecular lump chains are presented.The interaction solutions between lump chains and kink-solitons are investigated,where the kink-solitons lie on the boundaries of dominant region determined by the constant term in theτ-function.Furthermore,the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated.The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

广义(3+1)维KdV方程的lump解、相互作用解和呼吸子解

基于广义(3+1)维KdV方程的双线性形式,得到了方程的lump解、相互作用解及呼吸子解.证明了lump解在空间各个方向上都是有理局域的,并在lump波与线孤子的相互作用过程中观察到了“聚变”和“裂变”现象,最后得到了方程的呼吸子解.

From breather solutions to lump solutions:A construction method for the Zakharov equation

Periodic solutions of the Zakharov equation are investigated.By performing the limit operationλ_(2l-1)→λ_(1)on the eigenvalues of the Lax pair obtained from the n-fold Darboux transformation,an order-n breather-positon solution is first obtained from a plane wave seed.It is then proven that an order-n lump solution can be further constructed by taking the limitλ_(1)→λ_(0)on the breather-positon solution,because the unique eigenvalueλ_(0)associated with the Lax pair eigenfunctionΨ(λ_(0))=0 corresponds to the limit of the infinite-periodic solutions.A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.

Different wave patterns for two-coupled Maccari's system with complex structure via truncated Painlevéapproach

We focused on the two-coupled Maccari's system.With the help of truncated Painlevéapproach(TPA),we express local solution in the form of arbitrary functions.From the solution obtained,using its appropriate arbitrary functions,we have generated the rogue wave pattern solutions,rogue wave solutions,and lump solutions.In addition,by controlling the values of the parameters in the solutions,we show the dynamic behaviors of the rogue wave pattern solutions,rogue wave solutions,and lump solutions with the aid of Maple tool.The results of this study will contribute to the understanding of nonlinear wave dynamics in higher dimensional Maccari's systems.

Rheological and Morphological Characterization of Modified Bitumen with Cup Lump Rubber

Pure bitumen is not suitable for heavy traffic loads;hence modifiers are used to improve the bitumen performance.Recently,cup lump rubber(CLR)has become a preferred modifier due to its outstanding performance and less cost.However,little is known about the interactions between CLR and bitumen.Thus,this study investigates the behavior of bitumen with CLR.Four percentages of CLR(2.5%,5.0%,7.5%,and 10.0%by weight of bitumen)were used to modify conventional 60/70 penetration grade bitumen.The modified bitumen was evaluated through different laboratory testing such as dynamic shear rheometer,rotational viscosity,softening point,bending beam rheometer,ductility,and elastic recovery.The testing results show that the addition of CLR increased the bitumen’s rutting resistance by 3 PG grades at high temperatures.At low pavement temperatures,the cup lump rubber modified bitumen(CMB)can withstand up to−34℃.Fourier Transform Infrared(FTIR)analysis shows that the Aromaticity index at 1600 cm^(−1) rose as the CLR percentage increased,indicating the formation of a binder with a compact structure.This is expected to improve the elasticity of bitumen throughπ-πinteractions.Atomic Force Microscopy(AFM)results showed the Catana phase increased in size and quantity at 5.0%and 7.5%CLR content.While contact angle measurement revealed that the binders are hydrophobic and tend to repel the dropped water on the bitumen surface.

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation

The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.

Simulation of anchor chain based on lumped mass method

In order to develop a anchoring operation simulation system and improve safety during anchoring operations,a relatively accurate mathematical model of anchoring operations needs to be established.In this paper,the stress condition of anchor chain under environmental and subsea geological conditions is further studied and the stress condition of anchor chain is analyzed based on the previous research.In this paper,a quasi-static model based on catenary method is used as the basis of dynamic analysis,and the dynamic model of anchor chain is established based on the concentrated mass method,which fully considers the influence of anchor chain weight,hydrodynamic force,ocean current and interaction with the seabed.The fourth-order Runge Kutta method was used to solve the model numerically,and a calculation procedure was developed.The accuracy of the model was verified by comparing the calculated results with the experimental results,indicating that the constructed anchor chain dynamics model has a high accuracy.

Interaction solutions for the second extended(3+1)-dimensional Jimbo–Miwa equation

Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions.

Effect of lump ore ratio on the metallurgical properties of blast furnace charge

We conducted a series of experimental studies on the metallurgical properties of N-lump and F-lump ores used in Baosteel’s blast furnace, including thermal cracking, low-temperature reduction pulverization, reducibility, and droplet properties.The results show that the thermal burst properties of N-lump ore are better than those of F-lump ore.The low-temperature reduction degradation index(RDI) pulverization of the charge is the best when the ratios of N-lump ore and F-lump ore account for 35% each.The reduction performance of the charge is improved when F-lump and N-lump ores are mixed with sinter.In the softening-melting performance experiment, when the proportion of N-lump ore is 40%,the characteristic area value(S) as the charge permeability index is the smallest.When F-lump ore is mixed with sinter, its droplet performance improves compared with that of single F-lump ore.The proportion of F-lump ore should not exceed 15%.

Introduction to Mesh Based Generated Lumped Parameter Models for Electromagnetic Problems using Triangular Elements

This paper is an introduction to mesh based generated reluctance network modeling using triangular elements.Many contributions on mesh based generated reluctance networks using rectangular shaped elements have been published,but very few on those generated from a mesh using triangular elements.The use of triangular elements is aimed at extending the application of the approach to any shape of modeled devices.Basic concepts of the approach are presented in the case of electromagnetic devices.The procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB environment are also included.