Left and Right Inverse Eigenpairs Problem of Orthogonal Matrices

In this paper, the left and right inverse eigenpairs problem of orthogonal matrices and its optimal approximation solution are considered. Based on the special properties of eigenvalue and the special relations of left and right eigenpairs for orthogonal matrices, we find the equivalent problem, and derive the necessary and sufficient conditions for the solvability of the problem and its general solutions. With the properties of continuous function in bounded closed set, the optimal approximate solution is obtained. In addition, an algorithm to obtain the optimal approximation and numerical example are provided.

Outcomes of right-lobe and left-lobe living-donor liver transplantations using small-for-size grafts

AIM To analyze the outcomes of living-donor liver transplantation(LDLT) using left-lobe(LL) or right-lobe(RL) small-for-size(SFS) grafts.METHODS Prospectively collected data of adult patients who underwent LDLT at our hospital in the period from January 2003 to December 2013 were reviewed. The patients were divided into the RL-LDLT group and the LL-LDLT group. The two groups were compared in terms of short-and long-term outcomes, including incidence of postoperative complication, graft function, graft survival, and patient survival. A SFS graft was defined as a graft with a ratio of graft weight(GW) to recipient standard liver volume(RSLV)(GW/RSLV) of < 50%. The Urata formula was used to estimate RSLV.RESULTS Totally 218 patients were included for analysis, with 199 patients in the RL-LDLT group and 19 patients in the LL-LDLT group. The two groups were similar in terms of age(median, 53 years in the RL-LDLT group and 52 years in the LL-LDLT group, P = 0.997) but had significantly different ratios of men to women(165:34 in the RL-LDLT group and 8:11 in the LL-LDLT group, P < 0.0001). The two groups were also significantly different in GW(P < 0.0001), GW/RSLV(P < 0.0001), and graft cold ischemic time(P = 0.007). When it comes to postoperative complication, the groups were comparable(P = 0.105). Five patients died in hospital,4(2%) in the RL-LDLT group and 1(5.3%) in the LLLDLT group(P = 0.918). There were 38 graft losses, 33(16.6%) in the RL-LDLT group and 5(26.3%) in the LL-LDLT group(P = 0.452). The 5-year graft survival rate was significantly better in the RL-LDLT group(95.2% vs 89.5%, P = 0.049). The two groups had similar 5-year patient survival rates(RL-LDLT: 86.8%, LL-LDLT: 89.5%, P = 0.476).CONCLUSION The use of SFS graft in LDLT requires careful tailormade surgical planning and meticulous operation. LLLDLT can be a good alternative to RL-LDLT with similar recipient outcomes but a lower donor risk. Further research into different patient conditions is needed in order to validate the use of LL graft.

Influence of High-Velocity Blood Flow on Right-to-Left Shunt in Patients with Patent Foramen Ovale during the Valsalva Maneuver

In this study, we investigated the changes in the right-to-left shunt (RLS) of the patent foramen ovale (PFO) at different phases of the Valsalva maneuver and analyzed the possible mechanisms. The study population consisted of 57 patients with symptoms highly suggestive of a PFO. These patients had been diagnosed with apsychia, migraine with aura, cerebral infarction, transient ischemic attack (TIA), and cerebral ischemia with unknown cause. Routine echocardiography was performed in all patients to rule out a cardiac malformation. Contrast-transcranial Doppler (c-TCD) and contrast-enhanced transthoracic echocardiography (c-TTE) were used to visualize and quantify the RLS. The standard apical four chamber view was used to observe the changes of E peak, A peak, and velocity-time integral (VTI) ratio of tricuspid blood flow during the strain phase and release phase of the Valsalva maneuver. Paired t-test was used to compare E peak, A peak, and VTI ratio of tricuspid blood flow during the different phases. The right-to-left shunt across the PFO (PFO-RLS) was graded in the two phases and compared by Kruskal-Wallis test. Compared with the strain phase of the Valsalva maneuver, the parameters of E, A, and VTI in diastolic period in patients with PFO-RLS at the release phase were significantly increased [54.30 ± 13.65 cm/s vs 100.35 ± 21.11 cm/s, 42.21 ± 12.32 cm/s vs 57.30 ± 18.88 cm/s, 10.34 ± 3.27 cm/s vs 19.58 ± 4.56 cm/s, respectively], and the difference was statistically significant. The positive consequence of PFO-RLS, as diagnosed by c-TTE with the Valsalva maneuver at the release phase of the Valsalva maneuver, was significantly higher than that at the strain phase of the Valsalva maneuver. At the beginning of release phase of the Valsalva maneuver, decreased intrathoracic pressure led to increased venous backflow into the right atrium. Thus, high-velocity blood flow rapidly pushed the PFO open, which resulted in a significant increase in the PFO-RLS. Therefore, the increase of the PFO-RLS during the Valsalva maneuver is caused by the impact of high-velocity blood flow the PFO.

Unroofed coronary sinus,left-sided superior vena cava and mitral insufficiency:A case report and review of the literature

BACKGROUND Unroofed coronary sinus(UCS)is a rare subtype of atrial septal defect.It is frequently associated with a persistent left superior vena cava and is often part of a more intricate cardiac malformation.CASE SUMMARY This report describes a rare case of an adolescent patient with UCS featuring atrial situs solitus,absence of the right superior vena cava and a persistent left superior vena cava draining into the left atrium consistent with total unroofing of the coronary sinus.This was associated with concurrent severe mitral insufficiency secondary to redundant and prolapsing leaflets,and a substantial left-to-right shunt across the coronary sinus orifice.A comprehensive examination of the existing literature is included,shedding light on the diagnostic challenges of UCS and describing the available surgical options within the context of mitral valve surgery.CONCLUSION UCS is a complex condition requiring careful consideration of associated anomalies and a tailored surgical approach.

Does Right Coronary Artery Stenosis Increase Morbi-Mortality in Patients Undergoing Coronary Artery Bypass Graft for Left Main Coronary Artery Disease?

Background: The association of right coronary artery (RCA) stenosis in patients undergoing myocardial revascularization for left main coronary artery (LMCA) stenosis affects the prognosis. This study aimed to compare immediate results of patients with isolated LMCA stenosis and those with combined RCA stenosis. Patients and methods: We retrospectively evaluated 107 consecutive patients with LMCA disease who underwent coronary artery bypass grafts. The patients were divided into two groups: isolated LMCA stenosis (n = 36) and LMCA stenosis + RCA stenosis (n = 71). Different variables (preoperative, intra operative and post operative) were compared. Results: Patients with LMCA stenosis + RCA stenosis experienced higher prevalence of diabetes mellitus (p = 0.024) and smoker (p = 0.032). Also left ventricular EF was reduced (p = 0.004). Myocardial revascularization was more complete in patients with LMCA stenosis + RCA stenosis (p = 0.033), but in-hospital mortality rate was higher (12.6% vs 5.5%) in isolated LLMCA stenosis, but it did not reach statistical significance (p = 0.32). Except low output syndrome (LOS) that was frequent in presence of RCA stenosis (p = 0.026), no significant difference was found between groups for other complications. Conclusion: The presence of RCA stenosis in patients undergoing CABG for LMCA disease increases 30 day mortality but without significant impact on overall morbidities.

Left to Right Extracardial Shunt to Control Hemorrhage of Ascending Aorta and Left Ventricle: A Report of 3 Cases

Presented in this paper are 3 cases of hemorrhage of ascending aorta and left ventricle after open heart surgery treated by extracardial bypass in our hospital from Oct. 1994 to Dec. 1995. Remained aneurysmal wall enclosing conduit graft was used as a sac bypassed to right atrium to form a extracardial left-toright shunt in order to control bleeding and the results turned out to be satisfactory. The bypass and hemodynamically ignorable shunt can close spontaneously without complications with recovery of coagulation system. The technique may find wide application in clinical practice.

Intertwined leukocyte balances in tumours and peripheral blood as robust predictors of right and left colorectal cancer survival

BACKGROUND Colorectal cancer(CRC)accounts for 9.4%of overall cancer deaths,ranking second after lung cancer.Despite the large number of factors tested to predict their outcome,most patients with similar variables show big differences in survival.Moreover,right-sided CRC(RCRC)and left-sided CRC(LCRC)patients exhibit large differences in outcome after surgical intervention as assessed by preoperative blood leukocyte status.We hypothesised that stronger indexes than circulating(blood)leukocyte ratios to predict RCRC and LCRC patient outcomes will result from combining both circulating and infiltrated(tumour/peritumour fixed tissues)concentrations of leukocytes.AIM To seek variables involving leukocyte balances in peripheral blood and tumour tissues and to predict the outcome of CRC patients.METHODS Sixty-five patients diagnosed with colon adenocarcinoma by the Digestive Surgery Service of the La Paz University Hospital(Madrid,Spain)were enrolled in this study:43 with RCRC and 22 with LCRC.Patients were followed-up from January 2017 to March 2021 to record overall survival(OS)and recurrence-free survival(RFS)after surgical interventions.Leukocyte concentrations in peripheral blood were determined by routine laboratory protocols.Paraffin-fixed samples of tumour and peritumoural tissues were assessed for leukocyte concentrations by immunohistochemical detection of CD4,CD8,and CD14 marker expression.Ratios of leukocyte concentration in blood and tissues were calculated and evaluated for their predictor values for OS and RFS with Spearman correlations and Cox univariate and multivariate proportional hazards regression,followed by the calculation of the receiver-operating characteristic and area under the curve(AUC)and the determination of Youden’s optimal cutoff values for those variables that significantly correlated with either RCRC or LCRC patient outcomes.RCRC patients from the cohort were randomly assigned to modelling and validation sets,and clinician-friendly nomograms were developed to predict OS and RFS from the respective significant indexes.The accuracy of the model was evaluated using calibration and validation plots.RESULTS The relationship of leukocyte ratios in blood and peritumour resulted in six robust predictors of worse OS in RCRC:CD8+lymphocyte content in peritumour(CD8pt,AUC=0.585,cutoff<8.250,P=0.0077);total lymphocyte content in peritumour(CD4CD8pt,AUC=0.550,cutoff<10.160,P=0.0188);lymphocyte-to-monocyte ratio in peritumour(LMRpt,AUC=0.807,cutoff<3.185,P=0.0028);CD8+LMR in peritumour(CD8MRpt,AUC=0.757,cutoff<1.650,P=0.0007);the ratio of blood LMR to LMR in peritumour(LMRb/LMRpt,AUC=0.672,cutoff>0.985,P=0.0244);and the ratio of blood LMR to CD8+LMR in peritumour(LMRb/CD8MRpt,AUC=0.601,cutoff>1.485,P=0.0101).In addition,three robust predictors of worse RFS in RCRC were found:LMRpt(AUC=0.737,cutoff<3.185,P=0.0046);LMRb/LMRpt(AUC=0.678,cutoff>0.985,P=0.0155)and LMRb/CD8MRpt(AUC=0.615,cutoff>1.485,P=0.0141).Furthermore,the ratio of blood LMR to CD4+LMR in peritumour(LMRb/CD4MRpt,AUC=0.786,cutoff>10.570,P=0.0416)was found to robustly predict poorer OS in LCRC patients.The nomograms showed moderate accuracy in predicting OS and RFS in RCRC patients,with concordance index of 0.600 and 0.605,respectively.CONCLUSION Easily obtainable variables at preoperative consultation,defining the status of leukocyte balances between peripheral blood and peritumoural tissues,are robust predictors for OS and RFS of both RCRC and LCRC patients.

Left Radial Approach versus Right Radial Approach of Coronary Angiography in the Diagnosis of Coronary Heart Disease

Background: Transradial coronary angiography has established itself as safe alternative to transfemoral approach. Today, the artery of approach lies completely on the operator’s choice. The Right Radial Approach (RRA) has been a favorite for most of the interventional cardiologists due to the convenience in operating from the right side. The Left Radial Approach (LRA) has always been a neglected route. LRA does have many advantages over the right, the vascular anatomy being one of them. The aim of our study was to compare the right radial approach of diagnostic coronary angiography with left radial approach. Method: A total of 70 cases of Coronary Angiography (CAG) with normal Allen test and satisfying the inclusion criteria were prospectively observed and studied after randomly assigning them into two equal groups, LRA (Left Radial Approach) n = 35 and RRA (Right Radial Approach) n = 35. Multipurpose TIG (Tiger) catheter was used in both the approaches to catheterize the right as well as left coronary artery. Results: The access time, catheter manipulation time, procedure time, amount of contrast used, hospital stay, intensity of pain experienced, cost of the procedure and quality of coronary angiogram observed were statistically insignificant while the fluoroscopy time was slightly statistically significant which was independent to catheter manipulation time. Conclusions: The neglected Left Radial Approach to coronary angiography is as efficacious, safe and cost effective with reduction in arterial spasm complications when compared to the Right Radial Approach performed by multipurpose Tiger catheter.

Right-and left-sided colorectal cancers respond differently to traditional Chinese medicine

AIM To explore the differences in the responses of left-sided colorectal cancer(LSCRC) and right-sided colon cancer(RSCC) to traditional Chinese medicine(TCM).METHODS Patients with postoperative stage I-III colorectal cancer(CRC) were enrolled and divided into the LSCRC with or without TCM and RSCC with or without TCM groups depending on the primary tumor side and TCM administration. Patients in the TCM group were given TCM for at least 6 mo. Our research adopted diseasefree survival(DFS) as the primary endpoint. We applied a Cox proportional hazards regression model for the multivariate factor analysis using Stata 12.0 and SPSS 22.0 software for data analysis.RESULTS Of the 817 patients included in our study, 617 had LSCRC(TCM group, n = 404; Non-TCM group, n = 213), and 200 had RSCC(TCM group, n = 132; NonTCM group, n = 68). The 6-year DFS for patients with LSCRC was 56.95% in the TCM group and 41.50% in the Non-TCM group(P = 0.000). For patients with RSCC, the 6-year DFS was 52.92% in the TCM group and 37.19% in the Non-TCM group(P = 0.003). Differences between LSCRC and RSCC were not statistically significant regardless of TCM ingestion.CONCLUSION Patients with either LSCRC or RSCC and who took TCM experienced longer DFS; furthermore, patients with RSCC benefited more from TCM in DFS.

“Taking the Left for the Upper” or “Taking the Right for the Upper”

Currently, there are two rituals coexist in the world:"taking the left for the upper"and"taking the right for the up?per". The former is usually taken in domestic affairs such as meetings, dinners, etc. while the latter enjoys an overwhelmingly fa?vor in the west and so that it becomes the international practice in every conceivable social activities. The paper intends to offer a deep explanation of the differences of two rituals with adequate evidence and examples in some specific situations, say different kinds of seat arrangement in various large and small meetings, respectively in China and the west. Then it follows to provide the underlying reasons for the differences from the perspective of cultural difference. It finds that different denotation of"left"and"right"in English and Chinese may shed some light on the understanding of the two different rituals.

MDCT of right aortic arch with aberrant left subclavian artery associated with kommerell diverticulum and calcified ligamentum arteriosum

We present a case of the right aortic arch with kommerell diverticulum (KD) and aberrant left subclavian artery in a symptomatic 50-year-old patient with a calcification in the presumed attachment site of the ligamentum arteriosum (LA) to the KD. In another 30-year-old male patient, the entire course of a calcified LA was demonstrated using multidetector row computed tomography.

Hypoxemia without persistent right-to-left pressure gradient across a patent foramen ovale:A clinical challenge

Patent foramen ovale (PFO) closure for systemic hypoxemia is controversial. The first systematic, albeit retrospective, study was recently presented which showed good procedural and clinical success for PFO closure for this indication. We present a case of acute right to left intra-cardiac shunt across PFO where the shunting is not persistent. Hence making a decision on PFO closure based on the aforementioned promising trial may not have been the right decision for the patient. This case highlights that the decision on PFO closure for such indication needs to be individualized. We also review the sparse literature on PFO closure for this indication and discuss how the decision making for such indication needs to be individualized.

Left Ventricular Pseudoaneurysm Caused by a Left Ventricular Venting Catheter via the Right Superior Pulmonary Vein during Thoracic Aortic Surgery: A Case Report

A left ventricular (LV) pseudoaneurysm is one of the complications of acute myocardial infarction. It is also reported after chest trauma, cardiac surgery, and endocarditis. We report a rare case of an LV pseudoaneurysm induced by an LV venting catheter through the right superior pulmonary vein during thoracic aortic surgery. A 77-year-old man was referred for surgical repair of a distal aortic arch aneurysm. He underwent total aortic arch reconstruction with the frozen elephant trunk technique. The early postoperative period was uneventful. Postoperative contrast computed tomography and transthoracic echocardiography (TTE) revealed a pseudoaneurysm with a narrow neck at the apex of the LV that had sub-clinically progressed. Because of the risk of spontaneous rupture, an urgent aneurysmectomy was performed via a repeat sternotomy. Under cardioplegic arrest, the pseudoaneurysm was opened and the small orifice, which communicated with the LV, was confirmed. No myocardial ischemic changes were observed around the orifice. The pseudoaneurysm was thought to be induced by endocardial laceration by the tip of the venting catheter. The pseudoaneurysm was closed by linear repair reinforced with felt strips. The patient recovered well and was discharged 18 days after the second surgery. TTE showed no recurrence of LV aneurysm at the last follow-up.

Partial Orders on Right Inverse Semigroups

It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.

Consideration of the Necessity of Prophylactic Bypass Grafting for Anomalous Origin of the Right Coronary Artery—Based on a Case with Concomitant Left Main Trunk Disease Resuscitated from Cardiopulmonary Arrest

Anomalous origin of the right coronary artery is a rare congenital anomaly, but is associated with sudden death. Originating from the opposite sinus of Valsalva, an interarterial?course and an intramural course are especially considered as the risk factor for fatal cardiac events. Surgical indication remains controversial because many patients are asymptomatic. A 52-year-old man with anomalous origin of the right coronary artery with an interarterial?course concomitant with the left main trunk disease was resuscitated from cardiopulmonary arrest. It was likely to be attributed to the left main trunk disease, but anatomical structure of the right coronary artery suggests its possible involvement. Prophylactic bypass grafting for the right coronary artery was performed using saphenous vein graft without ligating native vessel to prevent future cardiac events, as well as revascularization of the left main trunk disease. All grafts were patent in one-year follow-up coronary angiography. Any cardiac event has not occurred.

CRT-D Upgrading in a Patient with Persistent Left Superior Vena Cava and Right Superior Vena Cava Atresia Using the Novel Active-Fixation Quadripolar Left Ventricular Lead

The persistence of left superior vena cava (PLSVC) is the most common congenital anomaly of the venous return system to the heart. Because of the increasing number of patients referred for cardiac resynchronization therapy (CRT) devices implantations, it is expected to encounter this venous anatomic variation. Left ventricular lead placement at an appropriate site is an integral and technically challenging part of successful CRT. In case of cardiac abnormalities could be difficult to achieve an optimal cardiac rhythm management devices implantation. Previous reports in patients with PLSVC highlighted the challenges to achieve an optimal cardiac rhythm device implantation. Recently, a new quadripolar active fixation left ventricular lead is available for CRT device implantation. Hereby we report a case of a device upgrading from dual-chamber pacemaker to CRT with defibrillator backup using the active fixation left ventricular quadripolar lead in a patient with PLSVC and right superior vena cava atresia.

A Case of Premature Ventricular Complexes from the Proximal Left Bundle Branch Successfully Ablated from the Right Coronary Cusp

Background:Premature ventricular complexes(PVCs)from the proximal left bundle branch(LBB)can be ablated in the left ventricular outflow tract but can easily damage normal conduction bundles.Here,we report a case of successful ablation of PVCs from the proximal LBB within the right coronary cusp(RCC).Case presentation:Our patient was a 70-year-old woman with PVCs from the proximal LBB that were successfully ablated via the RCC through radiofrequency catheter ablation with a 3D mapping system;she had a complication of incomplete right bundle branch block(RBBB)and remained asymptomatic during follow-up.Conclusion:The RCC provides an alternative approach for ablating PVCs originating from the proximal LBB,ow-ing to the close relationship between the RCC and proximal LBB.

The Hidden Value of Assessing Right Ventricular Performance with Exercise in Hypertensive Patients with Left Ventricular Diastolic Dysfunction

Background: Right ventricular (RV) dysfunction could develop during exercise in patients with both hypertension and left ventricular diastolic dysfunction and may contribute to the patient symptoms. The objective is to assess RV function, both at rest and during exercise in patients with hypertension and left ventricular diastolic dysfunction. Methods: We included 30 patients with hypertension and resting LV diastolic dysfunction. The systolic function of the right ventricle was assessed by TAPSE (Tricuspid Annular Plane Systolic Excursion) and S, while E/A ratio, annular lateral E’, E/E’ and E’/A’ were used to measure diastolic function. The global function of the right ventricle was assessed by measuring the right indexed myocardial performance. The dimensions and pulmonary pressures were also measured. Results: The following parameters of RV systolic function were increased significantly with exercise: TAPSE (P = 0.0054), S’ (P = 0.0045). Moreover, the following diastolic parameters of the RV increased significantly with exercise: E/E’ (P = 0.05), A’ (P = 0.04). The global RV function showed also a significant increase (P = 0.0011). The three RV dimensions as well as the pulmonary artery pressures also increased during exercise (P = 0.000004, 0.001, and 0.00000064 respectively). In addition, the presence of resting LV grade II DD predicted significantly higher pulmonary pressures during exercise (P = 0.006). The advanced resting grade of LVDD predicted significantly the presence of advanced grade of RVDD with exercise (P = 0.037). Conclusions: Some patients who have both hypertension and LV diastolic dysfunction showed structural and functional changes of the right ventricle at rest. However, all patients had RV functional changes during exercise.

Chest Pain on Exertion: Origin of the Right Coronary Artery from the Left Coronary Sinus, through the Aortic Pulmonary Sulcus with Squeezed, or Anterior Descending Branch Borderline Coronary Lesion?

The prognosis of patients in whom the right coronary artery (RCA) arises from the left coronary sinus (LCS) is unequal. An initial intramural course of the coronary artery within the aortic media is considered to cause myocardial ischemia in cases of coronary anomalies. In this case report, we present one patient admitted due to chest pain on exertion that suggested angina. Her only risk factor for coronary artery disease was hypertension. Clinical examination findings that the origin of the right coronary artery from the LCS, through the aortic pulmonary sulcus with atherosclerotic narrowing and squeezed of the RCA critical ostial, stenosis at the ostium of the RCA and the middle of left anterior descending (LAD) coronary, intravascular ultrasonography (IVUS) showed LAD and RCA minimal lumen area were 3.9 mm2, 5.9 mm2;plaque burden 66%, 65% respectively. We inserted EXCEL 3.0 × 18 mm stent in LAD stenosis. No complaints and adverse events were noticed during a 1-year follow-up.

Urgent Off-Pump Revascularisation in ACS and Cardiogenic Shock with Anomalous Origin of Right Coronary Artery from Left Anterior Descending Artery: A Case Report

A 55-year-old female known case of essential hypertension and diabetes was brought to the Emergency Department in a drowsy state with cardiogenic shock. At presentation systolic BP was 70 mm Hg, pulse rate was 44/min and random blood sugar was 239 mg/dl. Troponin I was 8.07. Electrocardiography showed junctional rhythm and bradycardia. Ejection Fraction (LVEF) was 15% - 20%. Coronary angiography was done which revealed single vessel disease in LAD with anomalous origin of RCA from midsegment of LAD. Patient was immediately taken up for Off-pump Coronary Artery Bypass Grafting (OPCAB). Right saphenous vein graft was harvested and anastomosed proximally to aorta and distally to LAD on beating heart using Medtronic Octopus heart stabilizer and coronary shunts. Wound closed in layers after achieving complete hemostasis. Patient was taken off ventilatory support on first post-operative day and discharged in a stable condition on fourth post-operative day. Post-operative Echocardiography showed LVEF increased from 15% - 20% at time of admission to 38% and 52% after 3 months and 12 months of surgery respectively.