Tetralogy of Fallot(TOF)with total anomalous pulmonary vein connections(TAPVC)is a rare type of complex congenital heart disease among all TOF cases.Co-presentation of major aortopulmonary collateral arteries(MAPCAs)c...Tetralogy of Fallot(TOF)with total anomalous pulmonary vein connections(TAPVC)is a rare type of complex congenital heart disease among all TOF cases.Co-presentation of major aortopulmonary collateral arteries(MAPCAs)compensates for the lack of central pulmonary bloodflow and decreases the severity of right-to-left shunting in TOF.We present a case of a 2-year-old child with complex diagnoses of TOF,TAPVC,a large secun-dum atrial septal defect(ASD),and intraoperatively identified MAPCAs.She underwent surgery to repair the TAPVC,valve-sparing reconstruction of the right ventricular outflow tract,interventricular defect closure,and the creation of patent foramen ovale(PFO).After the operation,hemodynamic instability happened along with sudden blood pressure drop,desaturation,and increased central venous pressure,which subsided after adminis-tering inhalational nitric oxide(NO).A postoperative pulmonary hypertension crisis was suggested when the patient experienced recurrent symptoms after the termination of NO.Echocardiographicfindings of a D-shaped left ventricle(LV),right-to-left PFO shunt and high tricuspid valve gradientfirmly established the diagnosis.It was subsequently managed with continuous NO inhalation and sildenafil,which rendered a satisfactory outcome.Repaired TOF and TAPVC could be at particular risk of developing pulmonary hypertension crisis,especially in the presence of MAPCAs due to possible remodeling of the pulmonary vasculature.Furthermore,a relatively non-compliant LV function and small left atrial size may exacerbate the risk of developing postcapillary pulmonary hypertension after TAPVC repair.A successful postoperative outcome calls for a meticulous preoperative analysis of the anatomical lesions,as well as careful monitoring.展开更多
Objective.To assess the feature of pulmonary blood flow distribution after total cavopulmonary connection(TCPC)of different types,and to provide the selection of the best type.Methods. Thirty-two consecutive survival ...Objective.To assess the feature of pulmonary blood flow distribution after total cavopulmonary connection(TCPC)of different types,and to provide the selection of the best type.Methods. Thirty-two consecutive survival patients after TCPC underwent radionuclide lung perfusion imaging. According to the radionuclide counts in the left and right lungs,analyses of the distribution of blood flow from superior venous cava(SVC) and inferior venous cava(IVC)and the whole pulmonary blood flow in both lungs were made. All patients were divided into 4 groups by the the anastomosis between IVC and pulmonary artery.Results. GroupⅠ:The flow ratio of the IVC to left lung was greater than that to the right lung,P≤0.01;the flow ratio of the SVC to right lung was greater than that to the left lung,P≤0.01;and the whole pulmonary blood flow went dominantly to the left lung,P≤0.05,which is not in line with physiological distribution. GroupⅡ:the flows from the SVC and IVC were mixed in the middle of the junction and ran evenly into the right and left lungs,the whole pulmonary blood flow went to both lungs,P≥0.05. Group Ⅲ:the flow ratio of the SVC to both lungs were the same,P≥0.05,and major part from IVC went to the right lung,P≤0.01;the pulmonary blood flow go dominantly to the right lung,P≤0.05,which is in accord with physiological distribution. Group Ⅳ:the flows from the right SVC went to right lung by 100%,P≤0.01,and that from the left SVC went to left lung by 100% too,P≤0.01;the flows from IVC went dominantly to the left lung,with little part to the right lung ,P≤0.05.Conclusions. Different types of TCPC can result in different pulmonary blood distributions. The best flow distribution between the left and right lungs can be obtained by an offset of the IVC anastomosis toward the RPA with widening anastomosis for the patients without persist left superior venous cava(PLSVC).展开更多
Objective To compare the postoperative outcomes of patients with the diagnostic univentricular heart undergoing lateral tunnel (LT) operation with extracardiac conduit (EC) operation. Methods- From June 1996 to Ju...Objective To compare the postoperative outcomes of patients with the diagnostic univentricular heart undergoing lateral tunnel (LT) operation with extracardiac conduit (EC) operation. Methods- From June 1996 to July 2007, 114 consecutive patients with a single ventricle underwent total cavopulmonary connection (TCPC) in Children's Heart Center, lAniversity Hospital Giessen and Marburg GmbH, Germany. A LT was performed in 19 (16.7%) patients, and an EC in 95 (83.3%) patients. The mean age of EC group was 50.8±31.6 (ranging from 22 to 212) months, and that of LT group was 61.5±41.2 (ranging from 30 to 168) months. Early and midterm outcomes of two groups were analyzed.Results One died in LT group (5.3%) and three in EC group (3.2%). The overall mortality was 3.5%. There was no significant difference in mortality between EC-and-LT groups (P〉0.05). The postoperative pulmonary arterial pressure, oxygen saturation, and effusion time of two groups had no significant difference (all P〉0.05). No significant difference in the occurrences of complications (arrhythmias, enteropathy, and thrombosis) was found between two groups after operation (P〉0.05). Conclusions There seems no difference between LT and EC in the clinical results in the early and middle postoperative stage. Glenn anastomosis followed by an EC seems to have some advantages.展开更多
Our study evaluated the hemodynamic performance of an axial flow blood pump surgically implanted in idealized total cavopulmonary connection(TCPC)models.This blood pump was designed to augment pressure from the inferi...Our study evaluated the hemodynamic performance of an axial flow blood pump surgically implanted in idealized total cavopulmonary connection(TCPC)models.This blood pump was designed to augment pressure from the inferior vena cava(IVC)to the pulmonary circulation.Two Fontan procedures with single and bilateral superior vena cava(SVC)were compared to fit the mechanical supported TCPC physiologies.Computational fluid dynamics(CFD)analyses of two Pump-TCPC models were performed in the analyses.Pressure-flow characteristics,energy efficiency,fluid streamlines,hemolysis and thrombosis analyses were implemented.Numerical simulations indicate that the pump produces pressure generations of 1 mm to 24 mm Hg for rotational speeds ranging from 2000 RPM to 5000 RPM and flow rates of 2 LPM to 4 LPM.Two surgical models incorporated with the pump were found to be insignificant in pressure augmentation and energy boost.The risk assessment of blood trauma and thrombosis generation was evaluated representatively through blood damage index(BDI),particle resident time(PRT)and relative resistant time(RRT).The hemolysis and thrombosis analyses declare the advantage of the pump supported bilateral SVC surgical scheme in balancing flow distribution and reducing the risk of endothelial cell destruction and trauma generation.展开更多
From Aug. 1999 to Feb. 2001, 8 patients with complex congenital heart diseases, including 5 cases accompanied by hypoplastic left ventricle and 3 by hypoplastic right ventricle, were subjected to total cavopulmonary c...From Aug. 1999 to Feb. 2001, 8 patients with complex congenital heart diseases, including 5 cases accompanied by hypoplastic left ventricle and 3 by hypoplastic right ventricle, were subjected to total cavopulmonary connection . Eight cases underwent the operation under cardiopulmonary bypass and 7 of whom under no cardiac clamp. Seven cases received cavopulmoanry anastomosis by flaring method and one case by end side anastomosis. All the patients underwent the intracardiac tunnels to drain inferior vena cava and plus 4 mm fenestration except one. The results showed that 6 patients had postoperative oxygen saturation more than 90 %, sinus rhythm, no anastomostic stoma obstruction, no flow reguigitation and CVP<16 cmH 2O. Two patients died postoperatively from high venous pressure of 18—20 cmH 2O, finally from cardiac failure and anoxima. It was concluded that TCPC was an effective treatment for complex congenital cardiac diseases, especially with ventricular maldevelopment. Intracardiac tunnel plus 4 mm fenestration and flaring cavopulmonary anastomosis could prevent the postoperative complications. Larger anastomotic stoma, venous pressure less than 16 cmH 2O and artery saturation more than 90 % might indicate excellent TCPC procedures in our experience.展开更多
To investigate the value of echocardiography in the diagnosis of total anomalous pulmonary venous connection ( TAPVC ), 16 patients in our hospital were diagnosed to have TAPVC by echocardiography from year 1994 to 2...To investigate the value of echocardiography in the diagnosis of total anomalous pulmonary venous connection ( TAPVC ), 16 patients in our hospital were diagnosed to have TAPVC by echocardiography from year 1994 to 2001. In 11 cases the results of echocardiography were compared to those of surgery. Each patient was examined by using a combination of precordial, suprasternal and subcostal windows to visualize all the pulmonary veins and their drainage sites, common pulmonary venous trunk, and other associated abnormalities. Of the 16 cases, the drainage sites were as follow: supracardiac in 10, via vertical vein in 9, directly to superior vena cava in 1; cardiac in 5, via coronary sinus in 2, directly to right atrium in 3. Diagnoses were correctly made in all the 11 cases as confirmed by surgery. Echocardiography can also assess pulmonary arterial pressure and detect other associated abnormalities. It is concluded that echocardiography is the preferred examination method in the diagnosis of TAPVC before surgery. With careful examination using multiple windows and sections, TAPVC can be accurately diagnosed by echocardiography.展开更多
In order to improve the surgical treatment of the congenital heart disease patient with single ventricle defect,two axial flow blood pumps,one with diffuser and the other without diffuser,were designed and virtually i...In order to improve the surgical treatment of the congenital heart disease patient with single ventricle defect,two axial flow blood pumps,one with diffuser and the other without diffuser,were designed and virtually implanted into an idealized total cavopulmonary connection(TCPC)model to form two types of Pump-TCPC physiological structure.Computational fluid dynamics(CFD)simulationswere performed to analyze the variations of the hemodynamic characteristics,such as flow field,wall shear stress(WSS),oscillatory shear index(OSI),relative residence time(RRT),between the two Pump-TCPC models.Numerical results indicate that the Pump-TCPC with diffuser has better flow field stability,less damage on endothelial cell of vessel wall,and lower risk of vascular injury and thrombosis formation than that without diffuser.展开更多
BACKGROUND Alagille syndrome(ALGS)is an autosomal dominant genetic disorder caused by mutations in the JAG1 or NOTCH2 gene.It is characterized by decreased intrahepatic bile ducts associated with a variety of abnormal...BACKGROUND Alagille syndrome(ALGS)is an autosomal dominant genetic disorder caused by mutations in the JAG1 or NOTCH2 gene.It is characterized by decreased intrahepatic bile ducts associated with a variety of abnormalities in many other organ systems,such as the cardiovascular,skeletal,and urinary systems.CASE SUMMARY We report a rare case of ALGS.A 1-month-old male infant presented with sustained jaundice and had a rare congenital heart disease:Total anomalous pulmonary venous connection(TAPVC).Sustained jaundice,particularly with cardiac murmur,caught our attention.Laboratory tests revealed elevated levels of alanine aminotransferase,aspartate aminotransferase,gamma-glutamyl transpeptidase,total bilirubin,and total bile acids,indicating serious intrahepatic cholestasis.Imaging confirmed the presence of butterfly vertebra at the seventh thoracic vertebra.This suggested ALGS,which was confirmed by genetic testing with a c.3197dupC mutation in the JAG1 gene.Ursodiol was administered immediately after confirmation of the diagnosis,and cardiac surgery was performed when the patient was 1.5 month old.He recovered well after treatment and was discharged at the age of 3 mo.At the age of two years,the patient returned to our clinic because multiple cutaneous nodules with xanthomas appeared,and their size and number increased over time.CONCLUSION We report a unique case of ALGS associated with TAPVC and severe xanthomas.This study has enriched the clinical manifestations of ALGS and emphasized the association between JAG1 gene and TAPVC.展开更多
Introduction: To present a rare occurrence of coronary sinus atrial septal defect (ASD) associated with total anomalous pulmonary venous connection (TAPVC). Case Report: A 16-year-old girl was diagnosed with features ...Introduction: To present a rare occurrence of coronary sinus atrial septal defect (ASD) associated with total anomalous pulmonary venous connection (TAPVC). Case Report: A 16-year-old girl was diagnosed with features of an atrial septal defect (ASD) by transthoracic echocardiography and the absence of PLSVC (persistent left superior vena cava) connection to coronary sinus was confirmed by saline contrast echocardiography (“bubble study”). Discussion: The cause of the dilated coronary sinus was due to total anomalous pulmonary venous connection. Conclusion: Coronary sinus atrial septal defect (ASD) is a rare interatrial shunt that is commonly associated with a persistent left superior vena cava (PLSVC) and occurs in less than 1% of cases of ASDs. It is characterized by the absence of at least a portion of the common wall that separates the coronary sinus and left atrium. Isolated defects are associated with low rate of morbidity and mortality.展开更多
The question associated with total domination on the queen’s graph has a long and rich history, first having been posed by Ahrens in 1910 [1]. The question is this: What is the minimum number of queens needed so that...The question associated with total domination on the queen’s graph has a long and rich history, first having been posed by Ahrens in 1910 [1]. The question is this: What is the minimum number of queens needed so that every square of an n × n board is attacked? Beginning in 2005 with Amirabadi, Burchett, and Hedetniemi [2] [3], work on this problem, and two other related problems, has seen progress. Bounds have been given for the values of all three domination parameters on the queen’s graph. In this paper, formations of queens are given that provide new bounds for the values of total, paired, and connected domination on the queen’s graph, denoted , , and respectively. For any n × n board size, the new bound of is arrived at, along with the separate bounds of , for with , and , for with .展开更多
The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path...The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of length k-1 in G,and their union forms either a cycle or a path of length k+1.Let Ek={(v,p),p E V(P_(k)(G)),v is an end vertex of p in G},we define total P_(k)-graphs T_(k)(G)as Yk(G)=(V(G)UV(P_(k)(G)),E(G)U E(PI(G))U Ek).In this note,we introduce total P,-graphs Th(G)and study their edge connectivity,as the generaliza-tion of total graphs.展开更多
基金The report was conducted in accordance with the Nuremberg Code and Declaration of Helsinki,and the protocol was approved by the Institutional Review Board of National Cardiovascular Center Harapan Kita(No.LB.02.01/VII/037/KEP037/2022).
文摘Tetralogy of Fallot(TOF)with total anomalous pulmonary vein connections(TAPVC)is a rare type of complex congenital heart disease among all TOF cases.Co-presentation of major aortopulmonary collateral arteries(MAPCAs)compensates for the lack of central pulmonary bloodflow and decreases the severity of right-to-left shunting in TOF.We present a case of a 2-year-old child with complex diagnoses of TOF,TAPVC,a large secun-dum atrial septal defect(ASD),and intraoperatively identified MAPCAs.She underwent surgery to repair the TAPVC,valve-sparing reconstruction of the right ventricular outflow tract,interventricular defect closure,and the creation of patent foramen ovale(PFO).After the operation,hemodynamic instability happened along with sudden blood pressure drop,desaturation,and increased central venous pressure,which subsided after adminis-tering inhalational nitric oxide(NO).A postoperative pulmonary hypertension crisis was suggested when the patient experienced recurrent symptoms after the termination of NO.Echocardiographicfindings of a D-shaped left ventricle(LV),right-to-left PFO shunt and high tricuspid valve gradientfirmly established the diagnosis.It was subsequently managed with continuous NO inhalation and sildenafil,which rendered a satisfactory outcome.Repaired TOF and TAPVC could be at particular risk of developing pulmonary hypertension crisis,especially in the presence of MAPCAs due to possible remodeling of the pulmonary vasculature.Furthermore,a relatively non-compliant LV function and small left atrial size may exacerbate the risk of developing postcapillary pulmonary hypertension after TAPVC repair.A successful postoperative outcome calls for a meticulous preoperative analysis of the anatomical lesions,as well as careful monitoring.
文摘Objective.To assess the feature of pulmonary blood flow distribution after total cavopulmonary connection(TCPC)of different types,and to provide the selection of the best type.Methods. Thirty-two consecutive survival patients after TCPC underwent radionuclide lung perfusion imaging. According to the radionuclide counts in the left and right lungs,analyses of the distribution of blood flow from superior venous cava(SVC) and inferior venous cava(IVC)and the whole pulmonary blood flow in both lungs were made. All patients were divided into 4 groups by the the anastomosis between IVC and pulmonary artery.Results. GroupⅠ:The flow ratio of the IVC to left lung was greater than that to the right lung,P≤0.01;the flow ratio of the SVC to right lung was greater than that to the left lung,P≤0.01;and the whole pulmonary blood flow went dominantly to the left lung,P≤0.05,which is not in line with physiological distribution. GroupⅡ:the flows from the SVC and IVC were mixed in the middle of the junction and ran evenly into the right and left lungs,the whole pulmonary blood flow went to both lungs,P≥0.05. Group Ⅲ:the flow ratio of the SVC to both lungs were the same,P≥0.05,and major part from IVC went to the right lung,P≤0.01;the pulmonary blood flow go dominantly to the right lung,P≤0.05,which is in accord with physiological distribution. Group Ⅳ:the flows from the right SVC went to right lung by 100%,P≤0.01,and that from the left SVC went to left lung by 100% too,P≤0.01;the flows from IVC went dominantly to the left lung,with little part to the right lung ,P≤0.05.Conclusions. Different types of TCPC can result in different pulmonary blood distributions. The best flow distribution between the left and right lungs can be obtained by an offset of the IVC anastomosis toward the RPA with widening anastomosis for the patients without persist left superior venous cava(PLSVC).
文摘Objective To compare the postoperative outcomes of patients with the diagnostic univentricular heart undergoing lateral tunnel (LT) operation with extracardiac conduit (EC) operation. Methods- From June 1996 to July 2007, 114 consecutive patients with a single ventricle underwent total cavopulmonary connection (TCPC) in Children's Heart Center, lAniversity Hospital Giessen and Marburg GmbH, Germany. A LT was performed in 19 (16.7%) patients, and an EC in 95 (83.3%) patients. The mean age of EC group was 50.8±31.6 (ranging from 22 to 212) months, and that of LT group was 61.5±41.2 (ranging from 30 to 168) months. Early and midterm outcomes of two groups were analyzed.Results One died in LT group (5.3%) and three in EC group (3.2%). The overall mortality was 3.5%. There was no significant difference in mortality between EC-and-LT groups (P〉0.05). The postoperative pulmonary arterial pressure, oxygen saturation, and effusion time of two groups had no significant difference (all P〉0.05). No significant difference in the occurrences of complications (arrhythmias, enteropathy, and thrombosis) was found between two groups after operation (P〉0.05). Conclusions There seems no difference between LT and EC in the clinical results in the early and middle postoperative stage. Glenn anastomosis followed by an EC seems to have some advantages.
文摘Our study evaluated the hemodynamic performance of an axial flow blood pump surgically implanted in idealized total cavopulmonary connection(TCPC)models.This blood pump was designed to augment pressure from the inferior vena cava(IVC)to the pulmonary circulation.Two Fontan procedures with single and bilateral superior vena cava(SVC)were compared to fit the mechanical supported TCPC physiologies.Computational fluid dynamics(CFD)analyses of two Pump-TCPC models were performed in the analyses.Pressure-flow characteristics,energy efficiency,fluid streamlines,hemolysis and thrombosis analyses were implemented.Numerical simulations indicate that the pump produces pressure generations of 1 mm to 24 mm Hg for rotational speeds ranging from 2000 RPM to 5000 RPM and flow rates of 2 LPM to 4 LPM.Two surgical models incorporated with the pump were found to be insignificant in pressure augmentation and energy boost.The risk assessment of blood trauma and thrombosis generation was evaluated representatively through blood damage index(BDI),particle resident time(PRT)and relative resistant time(RRT).The hemolysis and thrombosis analyses declare the advantage of the pump supported bilateral SVC surgical scheme in balancing flow distribution and reducing the risk of endothelial cell destruction and trauma generation.
文摘From Aug. 1999 to Feb. 2001, 8 patients with complex congenital heart diseases, including 5 cases accompanied by hypoplastic left ventricle and 3 by hypoplastic right ventricle, were subjected to total cavopulmonary connection . Eight cases underwent the operation under cardiopulmonary bypass and 7 of whom under no cardiac clamp. Seven cases received cavopulmoanry anastomosis by flaring method and one case by end side anastomosis. All the patients underwent the intracardiac tunnels to drain inferior vena cava and plus 4 mm fenestration except one. The results showed that 6 patients had postoperative oxygen saturation more than 90 %, sinus rhythm, no anastomostic stoma obstruction, no flow reguigitation and CVP<16 cmH 2O. Two patients died postoperatively from high venous pressure of 18—20 cmH 2O, finally from cardiac failure and anoxima. It was concluded that TCPC was an effective treatment for complex congenital cardiac diseases, especially with ventricular maldevelopment. Intracardiac tunnel plus 4 mm fenestration and flaring cavopulmonary anastomosis could prevent the postoperative complications. Larger anastomotic stoma, venous pressure less than 16 cmH 2O and artery saturation more than 90 % might indicate excellent TCPC procedures in our experience.
文摘To investigate the value of echocardiography in the diagnosis of total anomalous pulmonary venous connection ( TAPVC ), 16 patients in our hospital were diagnosed to have TAPVC by echocardiography from year 1994 to 2001. In 11 cases the results of echocardiography were compared to those of surgery. Each patient was examined by using a combination of precordial, suprasternal and subcostal windows to visualize all the pulmonary veins and their drainage sites, common pulmonary venous trunk, and other associated abnormalities. Of the 16 cases, the drainage sites were as follow: supracardiac in 10, via vertical vein in 9, directly to superior vena cava in 1; cardiac in 5, via coronary sinus in 2, directly to right atrium in 3. Diagnoses were correctly made in all the 11 cases as confirmed by surgery. Echocardiography can also assess pulmonary arterial pressure and detect other associated abnormalities. It is concluded that echocardiography is the preferred examination method in the diagnosis of TAPVC before surgery. With careful examination using multiple windows and sections, TAPVC can be accurately diagnosed by echocardiography.
基金This work has been supported by the Natural Science Foundation of China(No.11872152).
文摘In order to improve the surgical treatment of the congenital heart disease patient with single ventricle defect,two axial flow blood pumps,one with diffuser and the other without diffuser,were designed and virtually implanted into an idealized total cavopulmonary connection(TCPC)model to form two types of Pump-TCPC physiological structure.Computational fluid dynamics(CFD)simulationswere performed to analyze the variations of the hemodynamic characteristics,such as flow field,wall shear stress(WSS),oscillatory shear index(OSI),relative residence time(RRT),between the two Pump-TCPC models.Numerical results indicate that the Pump-TCPC with diffuser has better flow field stability,less damage on endothelial cell of vessel wall,and lower risk of vascular injury and thrombosis formation than that without diffuser.
文摘BACKGROUND Alagille syndrome(ALGS)is an autosomal dominant genetic disorder caused by mutations in the JAG1 or NOTCH2 gene.It is characterized by decreased intrahepatic bile ducts associated with a variety of abnormalities in many other organ systems,such as the cardiovascular,skeletal,and urinary systems.CASE SUMMARY We report a rare case of ALGS.A 1-month-old male infant presented with sustained jaundice and had a rare congenital heart disease:Total anomalous pulmonary venous connection(TAPVC).Sustained jaundice,particularly with cardiac murmur,caught our attention.Laboratory tests revealed elevated levels of alanine aminotransferase,aspartate aminotransferase,gamma-glutamyl transpeptidase,total bilirubin,and total bile acids,indicating serious intrahepatic cholestasis.Imaging confirmed the presence of butterfly vertebra at the seventh thoracic vertebra.This suggested ALGS,which was confirmed by genetic testing with a c.3197dupC mutation in the JAG1 gene.Ursodiol was administered immediately after confirmation of the diagnosis,and cardiac surgery was performed when the patient was 1.5 month old.He recovered well after treatment and was discharged at the age of 3 mo.At the age of two years,the patient returned to our clinic because multiple cutaneous nodules with xanthomas appeared,and their size and number increased over time.CONCLUSION We report a unique case of ALGS associated with TAPVC and severe xanthomas.This study has enriched the clinical manifestations of ALGS and emphasized the association between JAG1 gene and TAPVC.
文摘Introduction: To present a rare occurrence of coronary sinus atrial septal defect (ASD) associated with total anomalous pulmonary venous connection (TAPVC). Case Report: A 16-year-old girl was diagnosed with features of an atrial septal defect (ASD) by transthoracic echocardiography and the absence of PLSVC (persistent left superior vena cava) connection to coronary sinus was confirmed by saline contrast echocardiography (“bubble study”). Discussion: The cause of the dilated coronary sinus was due to total anomalous pulmonary venous connection. Conclusion: Coronary sinus atrial septal defect (ASD) is a rare interatrial shunt that is commonly associated with a persistent left superior vena cava (PLSVC) and occurs in less than 1% of cases of ASDs. It is characterized by the absence of at least a portion of the common wall that separates the coronary sinus and left atrium. Isolated defects are associated with low rate of morbidity and mortality.
文摘The question associated with total domination on the queen’s graph has a long and rich history, first having been posed by Ahrens in 1910 [1]. The question is this: What is the minimum number of queens needed so that every square of an n × n board is attacked? Beginning in 2005 with Amirabadi, Burchett, and Hedetniemi [2] [3], work on this problem, and two other related problems, has seen progress. Bounds have been given for the values of all three domination parameters on the queen’s graph. In this paper, formations of queens are given that provide new bounds for the values of total, paired, and connected domination on the queen’s graph, denoted , , and respectively. For any n × n board size, the new bound of is arrived at, along with the separate bounds of , for with , and , for with .
基金supported by Natural Sciences Foundation of Guangxi Province(2012GXNSFBA053005)
文摘The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of length k-1 in G,and their union forms either a cycle or a path of length k+1.Let Ek={(v,p),p E V(P_(k)(G)),v is an end vertex of p in G},we define total P_(k)-graphs T_(k)(G)as Yk(G)=(V(G)UV(P_(k)(G)),E(G)U E(PI(G))U Ek).In this note,we introduce total P,-graphs Th(G)and study their edge connectivity,as the generaliza-tion of total graphs.