大脑中动脉分叉处动脉瘤及其不完全夹闭的血流动力学分析
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摘要
目的：以三维计算机数值模拟观察大脑中动脉分叉处动脉瘤及不完全夹闭瘤颈部的动脉瘤的血流动力学特性。对象：选择2009年10月吉林大学第一医院神经外科住院患者1例。患者,女,69岁,头部CTA检查：右侧大脑中动脉分叉处动脉瘤。方法：利用临床头部3D-CTA血管造影图建立动脉瘤数值模型。使用CATIA软件对患者的动脉瘤进行三维模型的建立。将三维模型转换成IGS格式,导入到Gambit中,进行进一步修改,处理后生成动脉瘤的三维网格。定义边界条件及提取血流速度波后,应用Fluent软件进行动脉瘤数值模拟。结果：大脑中动脉分叉处动脉瘤的血流动力学表现同其他部位动脉瘤相似。其流场表现为动脉瘤的流入动脉的小部分血流流入瘤内,而大部分血流因受到瘤颈部扰流的干扰,直接流入流出动脉。血流流入动脉瘤内后,经过复杂的血流运动后由瘤颈处流出,最后进入流出动脉。动脉瘤瘤顶部的血流速度较缓慢,压力较小,切应力几乎为0。瘤颈部的血流速度较快,压力及切应力相对较大。大脑中动脉分叉处动脉瘤不完全夹闭的血流动力学分析的结果为随着动脉瘤瘤颈部夹闭程度的增高,动脉瘤瘤颈部的血流速度、切应力、压力明显增加。瘤顶部的压力也有所增加,但是相对瘤颈部较小。血流速度及切应力未见明显改变。结论：1.大脑中动脉分叉处动脉瘤瘤顶部的血流速度较缓慢,压力较小,切应力几乎为0,为动脉瘤破裂的好发部位；瘤颈部的血流速度较快,压力及切应力相对较大,为动脉瘤的生长及扩大部位。2.应对大脑中动脉分叉处动脉瘤进行完全性的夹闭,否则治疗意义不大,甚至可能有增加动脉瘤生长速度等危险。
Objective:To observe the hemodynamic characteristics of aneurysm which located middle cerebral artery bifurcation area and after it incompletely clipped by three-dimension computer numerical simulation method.Participant:One inpatient from Department of Neurosurgery, The First Hospital Affiliated to Jilin University was selected at 2009.10.Patient, Female,69-year-old with right middle cerebral artery bifurcation aneurysm.Methods:Aneurysm numerical model was constructed by three-dimensional computed tomography,and reconstructed at CATIA software. The images were transform to IGS file which further introduced into Gambit software to modify and obtain the three-D meshes of aneurysms.Then the computational fluid dynamics software was used to simulate the blood flow and analyze the hydrodynamics.Result:The hemodynamic of Middle cerebral artery bifurcation aneurysm is similar to the other area aneurysm。Its flow distribution is showed to be a small part blood fluid from inlet artery flowing into aneurysm,and a large part blood fluid directly flowing into outlet arteries caused by turbulent flow of the aneurysm neck area.the blood fluid coming from inlet artery flow by complicated way in the aneurysm and finally come out of aneurysm and flow into outlet arteries.At the aneurysm dome area,the blood fluid velocity is slow,the press is low and the wall shear stress is almost 0. At the aneurysm neck area,the blood fluid velocity is fast,the press and the wall shear stress is high.With clipping the aneurysm neck area aggravation, the blood fluid velocity,the press and the wall shear stress is increased at the aneurysm neck area. at the aneurysm dome area the press is also increased, but the degree is smaller than the aneurysm neck area.the blood fluid velocity and the wall shear stress of the aneurysm dome almost don't change.Conclution: 1.At the aneurysm dome area,the blood fluid velocity is slow,the press is low and the wall shear stress is almost 0,Therefore the the aneurysm dome area is likely to rupture. At the aneurysm neck area,the blood fluid velocity is fast,the press and the wall shear stress is high,Therefore the aneurysm neck is the area to make aneurysm growing and enlarging.2. Middle cerebral artery bifurcation aneurysm should be completely clippted, or the treatment may be not effective,even it is possible to make the aneurysm growing.
Objective:To observe the hemodynamic characteristics of aneurysm which located middle cerebral artery bifurcation area and after it incompletely clipped by three-dimension computer numerical simulation method.Participant:One inpatient from Department of Neurosurgery, The First Hospital Affiliated to Jilin University was selected at 2009.10.Patient, Female,69-year-old with right middle cerebral artery bifurcation aneurysm.Methods:Aneurysm numerical model was constructed by three-dimensional computed tomography,and reconstructed at CATIA software. The images were transform to IGS file which further introduced into Gambit software to modify and obtain the three-D meshes of aneurysms.Then the computational fluid dynamics software was used to simulate the blood flow and analyze the hydrodynamics.Result:The hemodynamic of Middle cerebral artery bifurcation aneurysm is similar to the other area aneurysm。Its flow distribution is showed to be a small part blood fluid from inlet artery flowing into aneurysm,and a large part blood fluid directly flowing into outlet arteries caused by turbulent flow of the aneurysm neck area.the blood fluid coming from inlet artery flow by complicated way in the aneurysm and finally come out of aneurysm and flow into outlet arteries.At the aneurysm dome area,the blood fluid velocity is slow,the press is low and the wall shear stress is almost 0. At the aneurysm neck area,the blood fluid velocity is fast,the press and the wall shear stress is high.With clipping the aneurysm neck area aggravation, the blood fluid velocity,the press and the wall shear stress is increased at the aneurysm neck area. at the aneurysm dome area the press is also increased, but the degree is smaller than the aneurysm neck area.the blood fluid velocity and the wall shear stress of the aneurysm dome almost don't change.Conclution: 1.At the aneurysm dome area,the blood fluid velocity is slow,the press is low and the wall shear stress is almost 0,Therefore the the aneurysm dome area is likely to rupture. At the aneurysm neck area,the blood fluid velocity is fast,the press and the wall shear stress is high,Therefore the aneurysm neck is the area to make aneurysm growing and enlarging.2. Middle cerebral artery bifurcation aneurysm should be completely clippted, or the treatment may be not effective,even it is possible to make the aneurysm growing.
引文
[1]周良辅,脑动脉瘤.周良辅主编.现代神经外科学.上海：复旦大学出版社.2001,815-880.
[2]伍鸿钧,潘银盛,麦焕好等.大脑中动脉显微解剖及其在神经科的临床应用.功能性和立体定向神经外科杂志,1994,7(2)：61-64.
[3]吕发金,罗天友,谢鹏等.数字减影CTA图像质量影响因素探讨.重庆医科大学学报,2007,32(3)：271-274.
[4]Gibo H,Carver CC,Rhoton AL,et al.Microsurgical anatomy of the middle cerebral artery.Neurosurg,1981,54:151-169.
[5]Tanriover N,Kawashima M,Rhoton AL,Ulm AJ,et al.Microsurgical anatomy of the early branches of the middle cerebral artery:morphometric analysis and classifica-tion with angiographic correlation.Neurosurg, 2003,98(6):1277-1290.
[6]Umansky F,Juarez SM,Ausman JL,et al.Microsurgical anatomy of the proximal segments of the middle cerebral artery.Neurosurg,1984,61:458-467.
[7]谢惠,吕发,金覃川等.大脑中动脉M1段CT数字减影血管成像研究及其临床意义.中国临床解剖学杂志2010,28(2)：150-154.
[8]Gibo H,Carver CC,Rhoton AL,et al.Microsurgical anatomy of the middle cerebral artery[J].Neurosurg,1981,54:151-169.
[9]Umansky F,Juarez SM,Ausman JL,et al.Microsurgical anatomy of the proximsegments of the middle cerebral artery[J].Neurosurg,1984,61:458-467.
[10]张为龙.大脑中动脉的显微解剖学.解剖学报,1981,12(4)：367-375.
[11]曾司鲁,李旭光.国人脑系统的研究Ⅰ大脑外部的动脉.解剖学报,1965,8(2)：259-277.
[12]Yoshimoto Y,Wakai S,Satoh A,et al.Intraparenchymal and intrasylvian haemotomas secondary to ruputured middle cerebral artery aneurysms: prognostic factors and therapeutic considerations.Bri J Neurosurg,1999,13:18.
[13]Shimoda M,Oda S,Mamata Y,et al.Surgical indications in patients with an intracerebral hemorrhage due to ruptured middle cerebral artery aneurysm.J Neurosurg,1997,87:170.
[14]Rinne J, Hernesniemi J, Niskanen M,et al. Analysis of 561 patients with 690 middle cerebral artery aneurysms:anatomic and clinical features as correl-ated to management outcome[J]. Neuro-surgery,1996,38(1):2-11.
[15]Wanebo J,Zabramski J,Spetzler R.Superficial temporal artery-to-middle cerebral artery bypass grafting for cerebral revascularization. Neurosurgery,2004,55(2):395-398.
[16]朱贵华,张波,王任直.大脑中动脉动脉瘤的解剖特点和手术治疗.神经疾病与精神卫生,2004,4(5)：329-330.
[17]杨鹏飞,刘建民,黄清海等.自膨胀颅内专用支架治疗大脑中动脉宽颈动脉瘤.中国微侵袭神经外科杂志,2009,14(9)：391-394.
[18]王忠诚,赵继宗,刘阿力.颅内动脉瘤.王忠诚,主编.神经外科学.第1版.武汉：湖北科学技术出版社,2005：759-805.
[19]Berstad AE, Bo SH, Sortland O. Cerebral computer tomography in subarachnoid hemorrhage. Tidsskr Nor Laegeforen,2002,122(3):267-271.
[20]Pritz MB,Chandler W.The transsylvian approach to cerebral artery bifurcation/trifurcation aneurysms. Surg Neurol,1994,41:217-220.
[21]Ogilvy CS,Crowell RC,Heros RC,et al.Surgical management of middle cerebral artery aneurysms:experience with transsylvian and superior temporal gyrus approaches.Surg Neurol,1995,43:15-24.
[22]Suzuki J,Yoshimoto T,Kayama T.Surgicl treatment of middle cerebral artery aneurysms.J Neurosurg,1984,61:17-23.
[23]HeroRC, FritschMJ. Surgicalmanagement ofmiddle cerebral artery aneurysms. Neurosurgery,2001,48(4):780-786.
[24]Suzuki J, Yoshimoto T, Kayama T. Surgical treatment of middle cerebral artery aneurysms. JNeurosurg,1984,61(1):17-23.
[25]夏玉成,师维红,孙涛等.3 D-CTA对破裂大脑中动脉瘤诊断及手术指导意义.中国医师协会神经外科医师分会——第四届全国代表大会论文汇编。
[26]Ferguson GPhysical factors in the initiation,growth,and rupture of human intracranial saccular aneuryams. J Neurosurg 1972;37:666-667.
[27]Gonzalez CF,Cho YI,Ortega HV,et al.Intracranial aneurysms:flow analysis of their origin and progression. AJNR 1992; 13:181-188.
[28]Strother CM,Graves VB,Alan Rappe.Aneurysm Hemodynamics:an experimental study.AJNR 1992;13:1089-1095.
[29]Ohkuma H,Suzuki S,Shimamura N,et al.Dissecting aneurysms of the middle cerebral artery:neuroradiological and clinical features. Neurora-diology, 2003,45(3):143～148.
[30]王盛章,陈家亮,鲁刚等.带子瘤的脑动脉瘤的非牛顿流体血流动力学研究.九届全国水动力学学术会议暨第二十二届全国水动力学研讨会文集：111-116.
[31]Shojima M, Oshima M, Takagi K, et al. Magnitude and role of wall shear stress on cerebral aneurysm-Computational fluid dynamic study of 20 middle cerebral artery aneurysms. Stroke.2004.35:2500-2505.
[32]Leung JH. Wright AR, Cheshire N, et al. Fluid structure interaction of patient specific abdominal aortic aneurysms:a comparison with solid stress models.Biomed Eng online.2006,5:33.
[33]Oshima M, Torii R. Numerical evaluation of elastic models in blood flow-arterial wall interaction. Int I Comput Fluid Dynamics.2006,20:223-228.
[34]张莹,杨新健,李海等.带子瘤颅内动脉瘤的二维血流动力学数值模拟分析.中国脑血管病杂志2007；4(9)：392-396.
[35]Torii R, Oshima M, Kobayashi T, et al. ComputerModeling of cardiovascular fluid-structure interactions With the deforming-spatial-domain/ stabi-lizedspace-time formulation. Comp Methods Appl Mech Eng.2006,195: 1885-1895.
[36]Bazilevs Y, Calo VM, Zhang Y, et al. Isogeometric fluid-structure interaction analysis with applications To arterial blood flow. Comput Mech. 2006,38:310-322.
[37]Isaksen, Jorgen G, Bazilevs Y, et al. Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke.2008,39(12): 3172-3178.
[38]Cebral JR, CastroMA, Burgess JE, et a.l Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific compu-tational hemodynamics models [J]. AJNR Am J Neuroradiol,2005,26(10): 2550-2559.
[39]Metcalfe RW. The promise ofcomputational fluid dynamics as a tool for delineating therapeutic options in the treatmentofaneurysms [J]. Am J Neuroradio,l 2003,24(4):553-554.
[40]Canton G, LevyDI, Lasheras JC. Hemodynamic changes due to stent placement in bifurcating intracranial aneurysms [J]. J Neurosurg,2005,103(1): 146-155.
[41]NakataniH, HashimotoN, KangY. Cerebral blood flow patterns atmajor vesselbifurcations and aneurysms in rats J]. JNeurosurg,1991,74: 258-262.
[42]KringsT, M ller-HartmannW, Hans FJ, et a.l A refined method for creating saccular aneurysms in the rabbit [J]. Neuroradiology,2003,45(7): 423-429.
[43]Feng Y, Wada S, Tsubota K, et a.l The application of computer simulation in the genesis and development of intracranial aneurysms [J]. Technol-Health Care,2005,13(4):281-291.
[44]ShojimaM, Oshima M, Takagi K, et a.l Role of the bloodstream impacting force and the local pressure elevation in the rupture of cerebral aneurysms [J]. Stroke,2005,36(9):1933-1938.
[45]Gibbons GH,Dzau VJ.The emerging concept of vascular rimodeling[J].N Engl J Med,1994,330:1431.
[46]Malek AM,Alper SL,Izumo S.Hemodynamic shear stress and its role in atherosclerosis[J].JAMA,1999,282:2035-2042.
[47]MalekAM, Alper SL, Izumo S. Hemodynamic shear stress and its role in atherosclerosis [J]. JAMA,1999,282(21):2035-2042.
[48]Gobin YP, Counord JL, Flaud P, et a.l In vitro study of heamodynamics in a giantsaccularaneurysm mode:l influence of flow dynamics in the parent vessel and effects of coil embolisation[J]. Neuroradiology,1994, 36:530-536
[49]陈旭东,陈洪,杨地等.动脉瘤的血流动力学数值模拟初步分析.中风与神经疾病杂志.2006,4(23)：204-206.
[50]李淼,张莹,王捷,等.不同大小、形态动脉瘤的血液动力学差异.中国实验诊断学2007,11(9)：1174-1176.
[51]黄清海,张星,施洋等.不同类型脑动脉瘤内流体力学的三维数值模拟研究.中华神经外科疾病研究杂志.2009,8(1)：60-72
[52]张新元,马廉亭,王启弘等.动脉瘤模型栓塞前后血流动力学的改变.中华实验外科杂志.2006,3(23)：354-355.
[2]伍鸿钧,潘银盛,麦焕好等.大脑中动脉显微解剖及其在神经科的临床应用.功能性和立体定向神经外科杂志,1994,7(2)：61-64.
[3]吕发金,罗天友,谢鹏等.数字减影CTA图像质量影响因素探讨.重庆医科大学学报,2007,32(3)：271-274.
[4]Gibo H,Carver CC,Rhoton AL,et al.Microsurgical anatomy of the middle cerebral artery.Neurosurg,1981,54:151-169.
[5]Tanriover N,Kawashima M,Rhoton AL,Ulm AJ,et al.Microsurgical anatomy of the early branches of the middle cerebral artery:morphometric analysis and classifica-tion with angiographic correlation.Neurosurg, 2003,98(6):1277-1290.
[6]Umansky F,Juarez SM,Ausman JL,et al.Microsurgical anatomy of the proximal segments of the middle cerebral artery.Neurosurg,1984,61:458-467.
[7]谢惠,吕发,金覃川等.大脑中动脉M1段CT数字减影血管成像研究及其临床意义.中国临床解剖学杂志2010,28(2)：150-154.
[8]Gibo H,Carver CC,Rhoton AL,et al.Microsurgical anatomy of the middle cerebral artery[J].Neurosurg,1981,54:151-169.
[9]Umansky F,Juarez SM,Ausman JL,et al.Microsurgical anatomy of the proximsegments of the middle cerebral artery[J].Neurosurg,1984,61:458-467.
[10]张为龙.大脑中动脉的显微解剖学.解剖学报,1981,12(4)：367-375.
[11]曾司鲁,李旭光.国人脑系统的研究Ⅰ大脑外部的动脉.解剖学报,1965,8(2)：259-277.
[12]Yoshimoto Y,Wakai S,Satoh A,et al.Intraparenchymal and intrasylvian haemotomas secondary to ruputured middle cerebral artery aneurysms: prognostic factors and therapeutic considerations.Bri J Neurosurg,1999,13:18.
[13]Shimoda M,Oda S,Mamata Y,et al.Surgical indications in patients with an intracerebral hemorrhage due to ruptured middle cerebral artery aneurysm.J Neurosurg,1997,87:170.
[14]Rinne J, Hernesniemi J, Niskanen M,et al. Analysis of 561 patients with 690 middle cerebral artery aneurysms:anatomic and clinical features as correl-ated to management outcome[J]. Neuro-surgery,1996,38(1):2-11.
[15]Wanebo J,Zabramski J,Spetzler R.Superficial temporal artery-to-middle cerebral artery bypass grafting for cerebral revascularization. Neurosurgery,2004,55(2):395-398.
[16]朱贵华,张波,王任直.大脑中动脉动脉瘤的解剖特点和手术治疗.神经疾病与精神卫生,2004,4(5)：329-330.
[17]杨鹏飞,刘建民,黄清海等.自膨胀颅内专用支架治疗大脑中动脉宽颈动脉瘤.中国微侵袭神经外科杂志,2009,14(9)：391-394.
[18]王忠诚,赵继宗,刘阿力.颅内动脉瘤.王忠诚,主编.神经外科学.第1版.武汉：湖北科学技术出版社,2005：759-805.
[19]Berstad AE, Bo SH, Sortland O. Cerebral computer tomography in subarachnoid hemorrhage. Tidsskr Nor Laegeforen,2002,122(3):267-271.
[20]Pritz MB,Chandler W.The transsylvian approach to cerebral artery bifurcation/trifurcation aneurysms. Surg Neurol,1994,41:217-220.
[21]Ogilvy CS,Crowell RC,Heros RC,et al.Surgical management of middle cerebral artery aneurysms:experience with transsylvian and superior temporal gyrus approaches.Surg Neurol,1995,43:15-24.
[22]Suzuki J,Yoshimoto T,Kayama T.Surgicl treatment of middle cerebral artery aneurysms.J Neurosurg,1984,61:17-23.
[23]HeroRC, FritschMJ. Surgicalmanagement ofmiddle cerebral artery aneurysms. Neurosurgery,2001,48(4):780-786.
[24]Suzuki J, Yoshimoto T, Kayama T. Surgical treatment of middle cerebral artery aneurysms. JNeurosurg,1984,61(1):17-23.
[25]夏玉成,师维红,孙涛等.3 D-CTA对破裂大脑中动脉瘤诊断及手术指导意义.中国医师协会神经外科医师分会——第四届全国代表大会论文汇编。
[26]Ferguson GPhysical factors in the initiation,growth,and rupture of human intracranial saccular aneuryams. J Neurosurg 1972;37:666-667.
[27]Gonzalez CF,Cho YI,Ortega HV,et al.Intracranial aneurysms:flow analysis of their origin and progression. AJNR 1992; 13:181-188.
[28]Strother CM,Graves VB,Alan Rappe.Aneurysm Hemodynamics:an experimental study.AJNR 1992;13:1089-1095.
[29]Ohkuma H,Suzuki S,Shimamura N,et al.Dissecting aneurysms of the middle cerebral artery:neuroradiological and clinical features. Neurora-diology, 2003,45(3):143～148.
[30]王盛章,陈家亮,鲁刚等.带子瘤的脑动脉瘤的非牛顿流体血流动力学研究.九届全国水动力学学术会议暨第二十二届全国水动力学研讨会文集：111-116.
[31]Shojima M, Oshima M, Takagi K, et al. Magnitude and role of wall shear stress on cerebral aneurysm-Computational fluid dynamic study of 20 middle cerebral artery aneurysms. Stroke.2004.35:2500-2505.
[32]Leung JH. Wright AR, Cheshire N, et al. Fluid structure interaction of patient specific abdominal aortic aneurysms:a comparison with solid stress models.Biomed Eng online.2006,5:33.
[33]Oshima M, Torii R. Numerical evaluation of elastic models in blood flow-arterial wall interaction. Int I Comput Fluid Dynamics.2006,20:223-228.
[34]张莹,杨新健,李海等.带子瘤颅内动脉瘤的二维血流动力学数值模拟分析.中国脑血管病杂志2007；4(9)：392-396.
[35]Torii R, Oshima M, Kobayashi T, et al. ComputerModeling of cardiovascular fluid-structure interactions With the deforming-spatial-domain/ stabi-lizedspace-time formulation. Comp Methods Appl Mech Eng.2006,195: 1885-1895.
[36]Bazilevs Y, Calo VM, Zhang Y, et al. Isogeometric fluid-structure interaction analysis with applications To arterial blood flow. Comput Mech. 2006,38:310-322.
[37]Isaksen, Jorgen G, Bazilevs Y, et al. Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke.2008,39(12): 3172-3178.
[38]Cebral JR, CastroMA, Burgess JE, et a.l Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific compu-tational hemodynamics models [J]. AJNR Am J Neuroradiol,2005,26(10): 2550-2559.
[39]Metcalfe RW. The promise ofcomputational fluid dynamics as a tool for delineating therapeutic options in the treatmentofaneurysms [J]. Am J Neuroradio,l 2003,24(4):553-554.
[40]Canton G, LevyDI, Lasheras JC. Hemodynamic changes due to stent placement in bifurcating intracranial aneurysms [J]. J Neurosurg,2005,103(1): 146-155.
[41]NakataniH, HashimotoN, KangY. Cerebral blood flow patterns atmajor vesselbifurcations and aneurysms in rats J]. JNeurosurg,1991,74: 258-262.
[42]KringsT, M ller-HartmannW, Hans FJ, et a.l A refined method for creating saccular aneurysms in the rabbit [J]. Neuroradiology,2003,45(7): 423-429.
[43]Feng Y, Wada S, Tsubota K, et a.l The application of computer simulation in the genesis and development of intracranial aneurysms [J]. Technol-Health Care,2005,13(4):281-291.
[44]ShojimaM, Oshima M, Takagi K, et a.l Role of the bloodstream impacting force and the local pressure elevation in the rupture of cerebral aneurysms [J]. Stroke,2005,36(9):1933-1938.
[45]Gibbons GH,Dzau VJ.The emerging concept of vascular rimodeling[J].N Engl J Med,1994,330:1431.
[46]Malek AM,Alper SL,Izumo S.Hemodynamic shear stress and its role in atherosclerosis[J].JAMA,1999,282:2035-2042.
[47]MalekAM, Alper SL, Izumo S. Hemodynamic shear stress and its role in atherosclerosis [J]. JAMA,1999,282(21):2035-2042.
[48]Gobin YP, Counord JL, Flaud P, et a.l In vitro study of heamodynamics in a giantsaccularaneurysm mode:l influence of flow dynamics in the parent vessel and effects of coil embolisation[J]. Neuroradiology,1994, 36:530-536
[49]陈旭东,陈洪,杨地等.动脉瘤的血流动力学数值模拟初步分析.中风与神经疾病杂志.2006,4(23)：204-206.
[50]李淼,张莹,王捷,等.不同大小、形态动脉瘤的血液动力学差异.中国实验诊断学2007,11(9)：1174-1176.
[51]黄清海,张星,施洋等.不同类型脑动脉瘤内流体力学的三维数值模拟研究.中华神经外科疾病研究杂志.2009,8(1)：60-72
[52]张新元,马廉亭,王启弘等.动脉瘤模型栓塞前后血流动力学的改变.中华实验外科杂志.2006,3(23)：354-355.