COMPUTATIONAL FLUID DYNAMICS FOR THE HEMODYNAMIC INVESTIGATION OF PEDIATRIC CAR

该子项目是众多利用 由美国国立卫生研究院/国家研究资源中心（NIH/NCRR）资助的中心拨款所提供资源的研究子项目之一。该子项目及其 首席研究员（PI）可能已从美国国立卫生研究院的其他来源获得主要资助， 因此也可能出现在其他CRISP条目中。 所列机构为 该中心所属机构，未必是研究负责人的所属机构。 DAC续期目的 我们正在进行的计算流体动力学（CFD）研究旨在：i）理解并量化Fontan手术失败患者群体的亚最佳生理状态，作为我们先前研究的延伸——该研究确定了功能健康患者中由上腔静脉波形驱动的能量代谢机制[1, 2]；ii） 表征胚胎发育中期各时间点的血流动力学负荷，作为本研究组近期记录的基线数据的延伸[3, 4]；iii) 设计交互式手术规划方法，利用数字生成智能辅助时间紧迫、针对特定患者的冠状动脉旁路移植术（CABG）的手术决策过程 [5]。初始资助期内提供的资源支持了两篇待刊论文和两篇已投稿的期刊论文。此外，我们的研究成果在6场会议和特邀报告中被重点介绍，并充分认可了PSC提供的资源。最重要的是，这些模拟结果促成了由卡内基梅隆大学工程学院教师（Pekkan-BME、 Kara-ME、Zhang-ME）共同努力，成功编制了一份极具竞争力的NSF-CDI项目提案。引言：上一期DAC资助期间所开展研究的总结 随着高精度解剖重建技术（通过磁共振成像、血管造影或计算机断层扫描）及稳健数值方案的进步，CFD模拟已成为心血管医学领域手术规划和器械设计的一种可行工具[6-14]。 CFD不仅能够量化特定患者解剖结构内的局部血流动力学，还能评估和优化候选手术设计模板的性能[15-18]。 典型的系统性术前规划场景涉及大量几何变化和非直观的设计方案，需要高性能的计算能力，因为仅此类优化研究的原始数据就占用了约2.4太字节的临时和永久数据存储空间[19, 20]。 功能性单心室婴儿的姑息性外科重建（即方丹手术）的最后阶段是全腔静脉-肺动脉连接术（TCPC），该术式将上腔静脉（SVC）和下腔静脉 (IVC) 直接汇入肺动脉。由于缺乏右心室以及静脉特性发生改变，可用的泵血能量有限，因此需要优化 TCPC 通路内的血流动力学状态，这可通过将功率损耗降至最低来实现。 早期关于Fontan手术血流动力学的研究仅关注病情稳定的患者，而实际上，血流动力学状态逐渐恶化的成人晚期幸存者数量正在不断增加[21]。因此，后者群体的能量状态尚未有相关记录。在我们此前获得匹兹堡超级计算中心（PSC）提供的开发拨款 （DAC）资助项目中，我们发现，在固定几何结构下，上腔静脉血流波形对TCPC通路内的搏动能学具有显著影响（即功率损耗波动范围为2%-34%）[1]。 基于此，功能衰竭的Fontan患者其上腔静脉血流波形拓扑结构与基线健康血流波形存在显著差异。因此，对功能衰竭波形拓扑结构的能量效率进行量化，可能提供一个与心脏功能障碍及术后并发症相关的新型血流动力学参数[22-24]。此外，功能衰竭型Fontan手术患者的能量状态或许也能揭示膈神经损伤（Fontan手术中的手术残留）的后果，因为尽管进行了手术折叠处理，这些缺陷仍会引发与功能衰竭型Fontan循环中观察到的类似的血流动力学紊乱[25]。胚胎期主动脉弓发育：心脏和血管畸形是人类先天性缺陷中至关重要的一类，约占活产婴儿的1% [26]。 遗传和表观遗传（环境及生物力学）因素共同调控心血管（CV）的形态发生与适应过程，该过程涉及心血管结构和功能的动态三维（3D）变化 [27, 28]。血流驱动的血液动力学在此动态过程中起着重要作用，临床上将其描述为“血流依赖性原理”[29-31]。 在心脏形态发生和重塑的关键时期，宫内血流动力学发生改变会导致先天性动脉畸形，例如主动脉弓中断、双主动脉弓和主动脉缩窄[32, 33]。尽管这些畸形的早期起源和进展已得到充分证实， 但关于单个弓的几何形态与血流动力学之间的关系、心输出量在各弓中的分布，以及血流动力学力变化对动态弓重塑的影响，目前所知甚少。 在我们此前获得PSC资助的DAC项目中，我们量化了正常主动脉弓形态发生过程中两个汉堡-汉密尔顿（HH）发育阶段（即HH18至HH24） （在此期间，胚胎质量和心输出量均增长了四倍）期间，对主动脉弓三维（3D）几何形态、血流及剪应力模式的变化进行了定量分析。这项初步研究首次在文献中记录了正常发育中主动脉弓内部的血流分布和血流动力学负荷情况。 因此，该研究为我们实验室正在进行的研究提供了重要的基线数据，这些研究旨在探究通过显微外科技术（即左心房结扎以模拟左心发育不全综合征）构建的先天性缺陷模型（图1）。优化个体化冠状动脉旁路移植术（CABG）方案： 美国心脏协会的统计数据显示，冠心病（CAD）是西方世界发病和死亡的主要原因[34]。作为治疗冠心病的一种常见侵入性方法，搭桥血管可为严重阻塞的动脉提供一条绕行通路。 当前的外科吻合技术及合成冠状动脉旁路移植管的设计，常导致术后并发症，如内膜增厚、再狭窄以及最终的长期移植物功能失效[35]。已知病理性血流动力学状态是内膜增生或血小板沉积的前兆，并会导致移植物闭塞。从流体力学角度来看， 必须减少冠状动脉血流中的异常现象——包括回流区、低剪应力/振荡剪应力、涡流以及滞流区——才能实现无故障的冠状动脉旁路移植术设计。 因此，当前的CABG设计范式旨在改善血流动力学，通过调节简化二维管状移植物中的吻合角度和血管曲率，以减少远端吻合口区域的增生。 尽管平面（2D）优化适用于识别这些主要设计特征，但要准确评估CABG的血流动力学，仍需基于患者特异性3D解剖信息以获得可靠的反馈。在我们之前的DAC资助周期内，我们着手开发一种基于CFD耦合的多维形状优化方法，以辅助患者特异性CABG设计。 依托高性能计算（HPC）资源，该框架将使我们能够分析端侧吻合至左前降支（LAD）的血流动力学效率，以及序贯移植策略——即从主冠状动脉旁路移植血管（CABG）引出多条（平行）分支。 方法示例：功能衰竭的Fontan手术中的能量耗散：采用理想化的1DO标准TCPC几何模型进行数值模拟，以阐明血流波形拓扑结构对功率损耗的孤立影响[1]。CFD模型整合了经实验验证的非定常二阶精度求解器[10, 14]，用于模拟具有恒定血液动力学特性（ρ = 1060 kg/m³，κ = 3.71 × 10⁻³ Pa·s）的不可压缩牛顿流体。 循环系统内的功率耗散采用控制体积法计算，忽略热损失及血管壁所做的功。匹兹堡大学儿童医院通过经机构审查委员会（IRB）批准的方案，利用多通道同步心电图、呼吸及实时超声测量技术，在院内采集了Fontan手术后腔静脉波形数据。 图2展示了1名严重血流动力学亚优状态患者（NYHA功能分级III级，年龄：16岁，体表面积： 1.2，心率：56，呼吸频率：32/min）的3个呼吸周期的重建波形如图2所示。为比较相对能量效率，本文从文献中可获取的、针对该患者的实时PC-MRI腔静脉波形数据集（ [36]中获取的患者特异性实时PC-MRI腔静脉波形数据集，重构了相应的Fontan波形。由于两个数据集中均观察到严重的逆向血流，我们发现先前研究中提出的（针对单向腔静脉血流）流出道质量分流边界条件[10]在存在流出道逆流的情况下无法保持质量守恒，因此在此进行了改进。 取而代之的是，将一个用户定义的压力边界条件子程序（该程序采用了基于伯努利方程推导出的数值方案）应用于肺动脉出口。在每次迭代中，该数值方案会逐步调整肺动脉出口压力，以达到左肺与右肺之间50/50的指定基线血流分配值。 针对这种特别适用于存在回流的失效丰坦波形的全新出口边界条件，进行了系统性的验证测试和特性分析。 胚胎主动脉弓发育：利用荧光染料注射、微CT、多普勒速度记录以及针对该对象的脉动特异性计算流体力学（CFD）技术，构建了鸡胚胎主动脉弓的复合三维模型。通过向胚胎心室或心房注入印度墨水和荧光染料，可直观显示左右主动脉弓的形态及血流情况。发育中大血管的三维形态通过聚合物铸模技术获得，随后进行微CT扫描（图1）。主动脉弓内部的流场采用非结构化四面体单元进行离散化（Gambit，Ansys Inc.，宾夕法尼亚州）。开展了一项详细的网格敏感性研究，以探究表面和核心网格细化的影响 （即9次辅助CFD模拟）的影响。在每个阶段，均采用约600,000个四面体单元获得了与网格无关的解。网格生成使用Gambit（ANSYS公司，卡农斯堡，宾夕法尼亚州）完成，并采用了前述的脉动二阶CFD求解器。 主动脉弓入口处的血流以及从躯干到大脑的血流分配数据，来源于20MHz脉冲多普勒速度测量结果和文献数据。改进的患者特异性冠状动脉旁路移植术（CABG）配置：该全自动优化框架基于将基于CFD的成本函数评估自动耦合到优化算法中（图3）。 通过用户自定义子程序生成所需的冠状动脉旁路移植术（CABG）形状变体，并确保形状优化器与CFD求解器 （包括自研代码和商业代码）。左前降支（LAD）冠状动脉旁路移植术（CABG）从升主动脉起始，与狭窄区域远端的原发冠状动脉进行吻合。近端和远端吻合位置是根据在牛心脏上进行的实际近端LAD移植手术设置选定的 （图4）中实际进行的近端左前降支（LAD）搭桥手术的临床参数来确定。为了进行平面内优化，冠状动脉旁路移植术（CABG）被简化为一个二维圆柱管。 冠状动脉支架采用三阶贝塞尔曲线构建，其形状由四个设计参数决定，即近端（?p）和远端（?d）吻合角度，以及近端和远端曲率向量（sp、sd）。 通过比较六个网格细化级别的解，确保了解的网格无关性。使用Fluent（ANSYS Inc.，宾夕法尼亚州卡农斯堡）的稳态CFD求解器，针对每种几何改变求解控制的纳维-斯托克斯方程。 在移植物的入口边界处规定了抛物线形的流速分布，以实现更逼真的冠状动脉血流。一旦获得优化的二维移植物形状，便利用内部开发的解剖编辑工具将其转换为三维环境。最终移植物设计的效率采用经实验验证的Fluent （ANSYS Inc., PA）中经实验验证的二阶CFD求解器，该求解器采用了针对模拟冠状动脉血流而调优的基于阻抗的出口边界条件。 初步结果 功能失常的方丹手术中的能量耗散：对于功能正常的方丹手术数据，一个呼吸周期内计算出的功率损耗为9.82 mW；而功能失常的方丹手术患者中的功率损耗为11.3 mW，比功能正常方丹手术患者计算出的功率损耗高出15%。 在此危急状态下，更高的功率损耗值会导致心输出量进一步降低[37]。对时间平均流场结构的详细比较表明，在功能失常的Fontan波形配置中，轴向流速增加，且二次流的涡度显著增强（图5）。 因此，较高的功率损耗值与沿肺动脉（PAs）方向反向旋转涡旋的旋转强度增加有关。胚胎主动脉弓发育：图6显示了心动周期峰值时HH18和HH24左右侧支流中的壁面剪应力（WSS） 在HH18和HH24阶段心脏峰值期左右侧的分布情况。研究发现，在分流区和狭窄部位，壁面剪应力较高，而在主动脉囊附近，其分布较为复杂。针对HH18和HH24阶段的代表性心脏周期，计算了时间平均壁面剪应力，结果分别为 分别为15.5达因/平方厘米和28.5达因/平方厘米。与HH18相比，HH24阶段壁面剪应力增加，这与心输出量的增加相对应。各侧壁面时间平均剪应力与HH18和HH24阶段三个主动脉弓平均中点直径呈相关性。 HH18时主动脉弓右侧平均中点直径（108 ± 0.022 μm）显著大于左侧平均中点直径（101 ± 0.015 μm，p<0.05）。同样，在CFD模型中，HH18阶段右侧主动脉弓的峰值和平均侧向时间平均壁面剪应力（分别为16达因·厘米⁻²和55达因·厘米⁻²，p<0.05） 。类似的结论也适用于HH24发育阶段。改进的个体化冠状动脉旁路移植术（CABG）配置：初步结果表明，该二维优化方案旨在将CABG几何结构调整为曲率最小、长度最小的配置 （图6）。因此，通过最小化端点切线向量的大小和吻合角度，任意的高度弯曲移植物拓扑结构可转变为相对平直的配置。此外，针对给定问题设置的优化结果表明，移植物内部的能量耗散和涡度从次优配置降低至最优配置约20% 。另一方面，通过对原发性冠状动脉循环进行稳态三维模拟计算得到的左前降支（LAD）血流速率，与先前的超声血管造影测量结果吻合良好[38]。结论与未来研究目标：功能衰竭的Fontan患者中的能量耗散： 本研究是首次尝试对功能失常的Fontan患者进行血流动力学研究和定量分析。在相同的归一化心输出量条件下，与功能正常的Fontan患者相比，所分析的功能失常Fontan患者在1DO TCPC中能量损耗更高，这源于下腔静脉（IVC）和上腔静脉（SVC）波形的波动。 鉴于TCPC水动力功率损耗对心输出量的影响相当显著（敏感性 = -0.88 L/Min/伍兹单位) [37]，因此腔静脉波形的能量效率可与心脏功能相关联，并进一步用于规划血流动力学恶化患者的术后管理。未来的研究将通过更多临床研究来扩充有限的实时数据，并利用高性能计算（HPC）在真实的患者特异性解剖模板内进行计算流体动力学（CFD）模拟，以期 对整个疾病进程中Fontan手术能量代谢的理解。由于患者间心肺相互作用存在个体差异（即上腔静脉血流波形存在差异），需要较大的患者样本量（每组≥10名患者），才能对成人Fontan功能衰竭患者的能量代谢状态进行定量评估。 因此，我们估计该CFD建模工作的总行数据将占用约2太字节的存储空间。胚胎主动脉弓发育：在先前心内血流动力学研究的基础上， 本研究首次尝试基于鸡胚胎的解剖铸模，重建发育关键期正常（健康）主动脉弓的微三维形态及血流分布。在HH18至HH24阶段，发育中主动脉弓及颅内血管在尺寸、 曲率及发育中主动脉弓和颅内血管的取向，表明中间阶段HH21可能是主动脉弓发育的关键阶段。我们正在进行的显微外科手术和铸模制作表明，HH21阶段呈现出快速、 不稳定的形态变化以及多种弓的形态模式。因此，通过利用多能干细胞（PSC）重构发育性主动脉弓（DAC），我们旨在表征HH21阶段复杂且引人入胜的血流动力学特征 （约50个胚胎铸模重建；约0.5-1太字节的原始数据存储）中引人入胜的血流动力学特征——在此阶段，遗传和表观遗传因素均可能导致突发的形态学变化，包括先天性弓畸形的发生。改进的患者：本研究展示了一个全自动的高效框架，可在理想化的心血管几何结构中将最优形状设计与二维非牛顿血液流动模拟相结合。作为一项主要成果，根据移植物几何结构导致的血管阻力降低，CABG内部功率损耗较小这一临床现象可能与冠状动脉灌注增加相关。 因此，本研究首次揭示了长期被忽视的冠状动脉旁路移植术（CABG）设计中整体形状的重要性。未来在搏动性冠状动脉血流条件下进行的研究将探讨涡度和振荡剪切应力的重要性。这些流动参数与血管调节和疾病状态密切相关[39]。 在瞬态血流条件下，为了实现符合解剖学特征的优化冠状动脉旁路移植术设计，需要采用包含较大设计空间（即 20-100 个模板）的优化范式，这要求极高的计算能力（单个冠状动脉旁路移植术设计约需 1 太字节）。 我们正在进行的努力将对提出的二维优化范式进行并行化处理，以整合高性能计算（HPC）资源，并研究三维顺序旁路移植血管配置的血流动力学效率（图7）。综上所述， 此前通过PSC获得的DAC项目，不仅使我们在管理HPC资源方面能力显著提升，还为我们推进前沿心血管研究提供了必要工具。尽管最初我们获得了Rachel系统的计算配额，但大部分计算工作是在PSC慷慨提供的、基于Pople的友好用户账户在Pople系统上进行（即未使用项目拨款分配的计算时间），该账户由PSC慷慨提供。为继续开展当前研究，我们再次寻求超越本校现有资格限制的高计算能力。参考文献：[1] Dur, O., DeGroff G, C. 和 Pekkan, K., 2009, “为最小化总腔静脉-肺动脉功率损耗而优化流入波形拓扑结构”，《生物力学工程杂志》。[2] Dur, O., Sundareswaran, K., DeGroff, C., Yoganathan, A. 及 Pekkan, K., 2008, “基于患者特异性实时超声和MRI数据，通过上腔静脉血流波形优化总腔静脉-肺动脉功率损耗”， 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This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Purpose of DAC Renewal The aim of our ongoing computational fluid dynamics (CFD) studies are i) to understand and quantify the suboptimal physiological state of the failing Fontan patient group as an extension of our previous study that identified the caval waveform driven energetics of the functionally healthy patients [1, 2], ii) to characterize the hemodynamic loading at the intermediate embryonic development time points as an extension of the baseline data that was recently documented by our group [3, 4] iii) to design interactive surgical planning methods to enable cyber generated intelligence for aiding surgical decision making process in time critical, patient specific coronary artery bypass (CABG) operations [5]. Resources provided during our initial grant period supported two in press and two submitted journal publications. In addition our results are featured and PSC resources are fully acknowledged in 6 conferences and invited presentations. Most importantly the simulations enabled a competitive NSF-CDI proposal prepared by the joint effort of CMU engineering faculty (Pekkan-BME, Kara-ME, Zhang-ME). Introduction: Summary of studies undertaken during previous DAC grant period With the advance of accurate anatomical reconstruction modalities (via magnetic resonance imaging, angiograms or computational tomography) and robust numerical schemes, CFD simulations has been a viable tool for surgical planning and device design in cardiovascular medicine [6-14]. CFD allow not only quantifying the local hemodynamics inside patient-specific anatomies but also to evaluate and optimize the performance of candidate surgical design templates [15-18]. A typical systematic pre-surgical planning scenario incorporating large number of geometrical variations and non-intuitive design alternatives require high performance computing power as the raw data of such an optimization study alone allocates ~2.4Terabytes of temporary and permanent data storage systems [19, 20]. Energy dissipation in failing Fontans: Last stage of the palliative surgical reconstruction (i.e. Fontan procedure) for the infants with functional single-ventricle is total cavopulmonary connection (TCPC), where the superior vena cavae (SVC) and inferior vena cavae (IVC) are routed directly into the pulmonary arteries. Limited pumping energy available due to the absence of right-ventricle and altered venous characteristics require optimized hemodynamics inside the TCPC pathway, which can be achieved by minimizing the power losses. Earlier studies on Fontan hemodynamics exclusively focused on patients who are doing well despite the growing number of adult late survivors with declining hemodynamic states [21]. Hence, the energy state in the latter group has not been documented. During our previous Development Allocation (DAC) grant provided by Pittsburgh Supercomputing Center (PSC) we discovered that caval flow waveforms have significant impact on pulsatile energetics (i.e. 2-34% power loss variation) inside the TCPC pathway for the fixed geometry [1]. Along this line, the caval waveform topologies of failing Fontan patients are considerably different than the baseline healthy flow waveforms. Therefore, quantification of the energy efficiency of the failing waveform topology may provide an additional hemodynamic parameter that can correlate with cardiac malfunction and postoperative complications [22-24]. In addition, energetic state of failing Fontans may also shed light to the consequences of the phrenic nerve injury (a surgical remnant in Fontan surgery) since despite the surgical plication these defects pose similar perturbed hemodynamics such as those seen in failing Fontan circulation [25]. Embryonic aortic arch development: Heart and vascular abnormalities comprise a vital category of human birth defects, occurring in approximately 1% of live born infants [26]. Genetic and epigenetic (environmental and biomechanical) factors regulate the cardiovascular (CV) morphogenesis and adaptation which involves dynamic three-dimensional (3D) changes in CV structure and function [27, 28]. Flow-driven hemodynamics plays a significant role in this dynamic process which is clinically described as a flow-dependency principle [29-31]. Altered intrauterine hemodynamics during critical windows of cardiac morphogenesis and remodeling leads to congenital arterial defects, such as interruption of aortic arch, double aortic arches, and coarctation of aorta [32, 33]. While the early origins and progression of these defects are well established, little is known regarding the relationships between individual arch geometry and hemodynamics, the distribution of cardiac output through each of the arches, and the influence of altered hemodynamic forces on dynamic arch remodeling. During our previous DAC grant awarded by PSC, we quantified the changes in the three-dimensional (3D) geometry of aortic arch, blood flow, and shear stress patterns between two Hamburger-Hamilton (HH) developmental stages i.e. HH18 - HH24 (where both embryonic mass and cardiac output quadruples) of normal arch morphogenesis. This initial study documents the flow distribution and hemodynamic loading inside the normal developing aortic arch for the first time in the literature. Hence, it provides an important baseline data for our ongoing studies to investigate congenitally defected models created via microsurgery techniques (i.e. left-atrium ligation to simulate hypoplastic left heart syndrome) in our laboratory (Fig.1). Improved patient-specific CABG configurations: Statistics by the American Heart Association identify coronary artery disease (CAD) as the primary cause of morbidity and mortality in the western world [34]. As a common invasive treatment to CAD, bypass conduits provide an alternative route around critically blocked arteries. Current surgical anastomosis techniques and the design of synthetic CABG frequently lead to post-surgical complications such as intimal thickening, restenosis and eventual long term graft failure [35]. Pathological hemodynamic states are known as the precursors of intimal hyperplasia or platelet deposition and result in graft occlusion. From fluid mechanics perspective, abnormalities in coronary flow, which include recirculation zones, low/oscillating shear stresses, vortices, and areas of stagnation, have to be reduced to achieve a failure-free CABG design. Hence, the current CABG design paradigm aims improved hemodynamics, to achieve reduced hyperplasia at the distal anastomosis region by modulating the anastomosis angle and the vessel curvature in simplified 2D tubular conduits. Although in-plane (2D) optimization is appropriate to identify these primary design features, an accurate assessment on the CABG hemodynamics requires patient-specific 3D anatomical information for reliable feedback. During our previous DAC grant period we embark upon developing a CFD coupled multi-dimensional shape optimization method to aid patient specific CABG design. Supported by the high performance computing (HPC) resources, this framework will allow us to analyze hemodynamics efficiency of end-to-side anastomosis to left anterior descending artery (LAD) and sequential grafting strategies, i.e. raising multiple (parallel) braches from a parent CABG. Example Methodology Energy dissipation in failing Fontans: Numerical simulations are performed using the idealized 1DO standard TCPC geometry in order to illustrate the isolated effect of flow waveform topology on power loss [1]. CFD model incorporates the experimentally validated unsteady 2nd order accurate solver [10, 14] in FLUENT version 6.3.26 (ANSYS Inc., Canonsburg, PA) to simulate incompressible and Newtonian blood flow with constant hemodynamic properties (? = 1060 kg/m3, ? = 3.71 10-3 Pa.s). The power dissipation inside the circulation is calculated using the control volume approach neglecting the heat losses and rate of work done by the walls. Failing Fontan caval waveforms are acquired in-house at University of Pittsburgh, Childrens Hospital through an approved IRB using multichannel simultaneous ECG, respiration and real-time ultrasound measurements. Reconstructed waveforms for a patient with severe suboptimal hemodynamics (NYHA functional class III, Age:16, BSA: 1.2, HR:56, respiration rate: 32/min) for 3 respiratory cycles is given in Figure 2. To compare the relative energy efficiency corresponding functional Fontan waveforms are reproduced from the patient-specific real-time PC-MRI caval waveform data set available in literature [36]. Due to the severe retrograde flow observed in both data sets the outflow mass split boundary condition that is introduced in our previous work (for unidirectional caval flow) [10] is found to be incapable of preserving the mass conservation in the presence of backflow from the outlets and improved here. Instead, a user-defined pressure boundary condition subroutine, incorporating a numerical scheme derived from the Bernoulli equation is assigned to the pulmonary outlets. At each iteration this numerical scheme adjusts the pulmonary outlet pressure incrementally in order to reach the specified 50/50 baseline flow split value between left and right lung. Systematic verification tests and characterization of this new outlet boundary condition that is specifically useful for failed Fontan waveforms with backflow are conducted. Embryonic aortic arch development: Composite 3D models of the chick embryo aortic arches were generated at the Hamburger-Hamilton (HH) developmental stages HH18 and HH24 using fluorescent dye injection, micro-CT, Doppler velocity recordings and pulsatile subject-specific computational fluid dynamics (CFD). India ink and fluorescent dyes were injected into the embryonic ventricle or atrium to visualize left and right aortic arch morphologies and flows. 3D morphology of the developing great vessels was obtained from polymeric casting followed by micro-CT scan (Fig.1). The flow domain inside the aortic arches is discretized using unstructured tetrahedral elements (Gambit, Ansys Inc., PA). A detailed grid sensitivity study was conducted to investigate the effects of both surface and core mesh refinements (i.e. 9 auxiliary CFD simulations). Mesh independent solutions were obtained using approximately 600,000 tetrahedral elements at each stage. Mesh generation was performed using Gambit (ANSYS Inc, Canonsburg, PA) and the aforementioned pulsatile 2nd order CFD solver was utilized. Inlet aortic arch flow and body-to-brain flow-split was obtained from 20MHz pulsed Doppler velocity measurements and literature data. Improved patient-specific CABG configurations: The fully automated optimization framework is built upon coupling the CFD based evaluation of the cost function into the optimization algorithm in an automated fashion (Fig.3). User defined subroutines are used to generate desired CABG shape variations and to ensure robust communication between the shape optimizer and the CFD solver (both in house code and commercial codes). LAD CABG initiates from the ascending aorta and anastamosed to the native coronary artery distal to the stenosed region. The proximal and end anastomosis locations are selected according to the surgical settings of an actual proximal LAD grafting performed in Bovine heart (Fig.4). CABG is simplified as a 2D cylindrical tube for the in-plane optimization. The scaffold of the coronary vessel is created using a 3rd order Bezier curve whose shape is dictated by four design parameters namely the proximal (?p) and distal (?d) anastomosis angles, proximal and distal curvature vectors (sp, sd). Grid independency of the solution is ensured by comparing the solutions at six refinement levels. Steady state CFD solver of Fluent (ANSYS Inc., Canonsburg, PA) is used to solve the governing Navier-Stokes equations for each geometric alteration. A parabolic velocity profile is prescribed at the inlet boundary of the graft to achieve more realistic coronary flow. Once the optimized 2D graft shape is obtained, it is translated to 3D environment by using the in-house anatomical editing tool. Efficiency of the final graft design is evaluated using experimentally validated 2nd order CFD solver of Fluent (ANSYS Inc, PA) incorporating impedance based outlet boundary conditions tuned to simulate coronary blood flow. Preliminary Results Energy dissipation in failing Fontans: For the functional Fontan data power loss calculated for one respiratory cycle returns 9.82 mW, whereas, power loss in failing Fontan patients is 11.3 mW which is 15% higher than the power loss calculated for functional Fontan patient. Having higher power loss values at this critical condition create further reductions in cardiac output [37]. A detailed comparison of the time averaged flow structures indicates that the axial flows are increased and the vorticity of the secondary flows are significantly amplified in the failing Fontan waveform configuration (Fig.5). Hence, higher power loss value is associated with the increase in the rotational strength of the counter-rotating vortices along the PAs. Embryonic aortic arch development: Figure 6 shows the distribution of wall shear stress (WSS) on the left and right laterals of HH18 and HH24 at peak cardiac phase. It is found that WSS was high at the flow divider and narrowing parts and distribution is complex in the vicinity of aortic sac. Time-averaged WSS was calculated for representative cardiac cycles at HH18 and HH24 and found to be 15.5 dynes cm-2 and 28.5 dynes cm-2, respectively. Increased WSS correspond to increased cardiac output at HH24 relative to HH18. Average lateral time-averaged WSS correlated with average mean midpoint diameter of the three aortic arches at HH18 and at HH24. Average right lateral midpoint diameter of the aortic arches at HH18 (108 0.022 ?m) was significantly larger than the average left lateral diameter (101 0.015 ?m, p<0.05). Likewise, the higher peak and mean lateral time-averaged WSS (16 dynes cm-2 and 55 dynes cm-2 respectively, p<0.05) at HH18 were observed in the right sided arches versus the left sided arches in the CFD model. Similar conclusions also apply for development stage HH24. Improved patient-specific CABG configurations: Preliminary results indicate that the 2D optimization scheme attempts to alter the CABG geometry to minimum curvature and minimum length configuration (Fig.6). Hence, an arbitrary highly curved graft topology transforms into a relatively straight configuration by minimizing the magnitude of the end tangent vectors and anastomosis angles. In addition, the optimization results for the given problem settings indicate that the energy dissipation and vorticity inside the graft decreases about 20% from suboptimal to optimal configurations. On the other hand, LAD flow rate calculated through steady state 3D simulations of native coronary circulation agrees well with the previous ultrasound angiography measurements [38]. Concluding Remarks and Future Research Aims: Energy dissipation in failing Fontans: This study is a first attempt towards investigating and quantifying hemodynamics in failing Fontan patients. Higher energy losses in 1DO TCPC found for the analyzed failing Fontan patient compared to the functional Fontan at the same normalized cardiac output originates due to the fluctuating IVC and SVC waveforms. Since the influence of TCPC hydrodynamic power loss on cardiac output is quite significant (sensitivity = -0.88 L/Min/Woods Unit) [37], the energy efficiency of the caval waveforms can be correlated with cardiac function and further be used in planning the post-operative management of patients with declining hemodynamics. Future efforts will expand the limited real-time data through additional clinical studies and utilize HPC to perform CFD simulations within realistic patient-specific anatomical templates for improved understanding of Fontan energetics throughout the disease timeline. Due to the patient-to-patient variations in cardiopulmonary interactions (i.e. variations in caval flow waveforms) a large patient population (>10 patient from each group) is required for making a quantitative assessment on the energetic state of adult failing Fontan patients. Hence, we estimate the total row data of this CFD modeling effort about ~2 Terabytes of storage. Embryonic aortic arch development: Expanding on the previous intra-cardiac hemodynamic investigations, the present study is a first attempt to reconstruct the normal (healthy) micro 3D aortic arch morphology and flow distribution during a critical period of development based on anatomical casts in chick embryo. Between stages HH18 and HH24 extensive 3D anatomical changes in size, curvature and orientation of the developing arches and cranial vessels indicate that the intermediate stage, HH21 may be the key stage in aortic arch development. Our ongoing microsurgeries and cast formations indicate that HH21 pose rapid, instable morphological changes and multiple arch modalities. Therefore, with the renewal of DAC from PSC we aim to characterize the intriguing hemodynamics of complex HH21 stage (~50 embryonic cast reconstructions; ~0.5-1 Terabytes row data storage) where both the genetic and epigenetic factors could result in abrupt morphological changes including the initiation of congenital arch malformations. Improved patient-specific CABG configurations: This study illustrates a fully automated efficient framework for coupling optimal shape design to 2D non-Newtonian blood flow simulations in idealized cardiovascular geometries. As a major outcome, the clinical interpretation of less power loss inside the CABG may correlate with increased coronary perfusion based on the decreased vascular resistance of the graft geometry. Therefore, for the first time this study identifies the significance of the bulk shape in the CABG design that has long been overlooked. Future studies under pulsatile coronary flow settings will investigate the importance of vorticity and oscillating shear stress. These flow parameters correlate strongly with the vasoregulation and disease states [39]. Under transient flow conditions, optimization paradigm incorporating a large design space (i.e. 20-100 templates) to account for the anatomically correct optimal CABG design requires high computational power (~1 Terabyte per single CABG design). Our ongoing efforts will parallelize the proposed 2D optimization paradigm to incorporate HPC resources and investigate the hemodynamic efficiency of 3D sequential bypass graft configurations (Fig.7). In conclusion, our previous DAC from PSC enabled us to excel our skills in managing HPC resources and provided the necessary tools to advance our cutting-edge cardiovascular research. Although initially we are awarded with allocations on the Rachel system, we conducted majority of our computations via our friendly-user-account on Pople (i.e. without using the computation time allocated with the grant) which was generously provided to us by PSC. To continue our ongoing studies we are, once again, looking for high computing power which is beyond the limits of that is currently eligible through our university. References: [1] Dur, O., DeGroff G, C., and Pekkan, K., 2009, "Optimization of inflow waveform topology for minimized total cavopulmonary power loss," Journal of Biomechanical Engineering. [2] Dur, O., Sundareswaran, K., DeGroff, C., Yoganathan, A., and Pekkan, K., 2008, "Optimization of Total Cavopulmonary Power Loss via Caval Flow Waveforms based on Patient Specific Real Time Echo and MRI Data," Biomedical Engineering Symposium St. Louis, MO. [3] Pekkan, K., Dasi, L. P., Nourparvar, P., Yerneni, S., Tobita, K., Fogel, M. 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