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.

具有新四阶项的非线性微分方程的精确解

研究了一类具有新的四阶项D_(x)^(2)D_(T)^(2)非线性偏微分方程的问题,其中三个新的四阶导数项和一些二阶导数项增加了非线性方程求解的困难.构造非线性偏微分方程的Hirota双线性形式,利用Hirota双线性方法得到方程的Lump解.通过绘图分析了它们的动力学行为.

广义地球物理KdV方程的Lump波与扭结波相互作用解初值扰动行为

针对一类广义地球物理KdV方程进行研究,利用Painleve分析思想构造了一个包含初始常数解的双线性变换,并应用拟设函数法得到两类与初值有关的Lump波与周期波、扭结波相互作用的显式精确解.此外,根据包含初始常数解u 0扰动的解的结构得到u 0的两个分叉点.最后,在一定参数条件下,利用数学软件对所得Lump波与周期波相互作用模式、Lump波与扭结波相互作用模式进行了绘图展示.结果表明:方程初始常数解对广义地球物理KdV方程的发展性态具有明显的扰动特征.

(3+1)维Hirota双线性方程的lump解

非线性发展方程是现代数学的一重要分支,其精确解的计算一直都是非线性科学领域的主流与焦点问题.lump解是精确解析解的一种特殊形式,以(3+1)维Hirota双线性方程为例对此展开研究.首先,利用Hirota双线性方法研究其经典lump解.其次,以双线性神经网络方法为基础,借助符号计算方法,得到方程的高阶lump解,主要是4阶lump解的计算.最后,通过对参数赋予一些特殊值,借助Maple软件,绘制出相关的三维图、密度图、相图以及传播图等,得到一些新的现象,同时展示了所求出的解的动力学行为.

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.

Dynamics of Nonlinear Waves in(2+1)-Dimensional Extended Boiti-Leon-Manna-Pempinelli Equation

Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.

New Lump Solution and Their Interactions with N-Solitons for a Shallow Water Wave Equation

By employing the Hirota’s bilinear method and different test functions, the breather solutions of HSI equation with different structures are obtained based on symbolic calculation with perturbation parameters. Some new lump solitons are found in the process of studying the degradation behavior of breather solutions. The interaction between lump solution and soliton solution is constructed in the form of lump solution, and the motion trajectory of lump is obtained. In addition, the theorem of lump solitons and N-solitons superposition is given and proved. The superposition formula of lump is derived from the theorem, and its spatial evolution behavior is given.

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.

一类(2+1)-维非线性波方程的精确解

该文通过不同的方法得到了(2+1)-维非线性波方程的不同类型的精确解。首先运用同宿测试法,得到了方程的呼吸解和孤立波解。运用三波法,得到了单、双呼吸解,然后通过参数极限法,将这两种解退化得到lump解。其次,在N-孤子解的基础上,分别添加不同的约束条件,得到了Q-呼吸解和Y-型孤子解。最后,在Y-型孤子解的基础上增加了约束条件,得到了呼吸解与Y-型孤子解组成的相互作用解。

Characteristics and genesis of microbial lumps in the Maozhuang Stage(Cambrian Series 2),Shandong Province,China

Microbial lumps have been found in the Maozhuang Stage(Cambrian Series 2) in the Liangcheng section,Shandong Province,China.Their macro-and micro-scale features distinguish them from other carbonate particles such as intraclasts and oncoids.Most lumps have a coarse sand to pebble size.They were mostly rounded during sedimentation or combined to form irregular shapes.A distinct boundary is present between the lumps and the surrounding cement of sparry calcite.The lumps contain either no core at all or several irregular "cores",without a distinct inner texture.They are composed mainly of calcified(micritized) microbes,most likely cyanobacteria.The microbes drilled holes in carbonate grains,after which lumps formed by micritization,cementation,and agglutination by an extracellular polymeric substance(EPS) in a high-energy shallow-marine,subtidal environment.As the lumps are directly related to microbes,they should be considered as microbialites.

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.