Quantitative Hemodynamics in Aortic Dissection: Comparing in vitro MRI with FSI Simulation in a Compliant Model
Judith Zimmermann, Kathrin Baeumler, Michael Loecher, Tyler E. Cork, Fikunwa O. Kolawole, Kyle Gifford, Alison L. Marsden, Dominik Fleischmann, Daniel B. Ennis
QQuantitative Hemodynamics in Aortic Dissection:Comparing in vitro
MRI with FSI Simulation in aCompliant Model.
Judith Zimmermann , − − − , Kathrin Bäumler , MichaelLoecher , , Tyler E. Cork , Fikunwa O. Kolawole , Kyle Gifford , Alison L.Marsden , Dominik Fleischmann , and Daniel B. Ennis , Department of Radiology, Stanford University, USA Department of Computer Science, Technical University of Munich, Germany Division of Radiology, VA Palo Alto Health Care System, USA Department of Pediatrics, Stanford University, USA Department of Mechanical Engineering, Stanford University, USA
Abstract.
The analysis of quantitative hemodynamics and luminal pres-sure may add valuable information to aid treatment strategies and prog-nosis for aortic dissections. This work directly compared in vitro
In vitro flow andpressure information were used to tune the CFD FSI Windkessel bound-ary conditions. Results showed very good overall agreement of complexflow patterns, true to false lumen flow splits, and pressure distribution.This work demonstrates feasibility of a tunable experimental setup thatintegrates a patient-specific compliant model and provides a test bed forexploring critical imaging and modeling parameters that ultimately mayimprove the prognosis for patients with aortic dissections.
Keywords:
Aortic dissection · CFD FSI · 4D-flow MRI
An aortic dissection is a life-threatening vascular disorder in which a focal teardevelops within the inner aortic wall layer. This leads to subsequent formationof a secondary channel (‘false lumen’, FL) that is separated from the primarychannel (‘true lumen’, TL) by a dissection flap. Patients with type-B aortic dis-section (TBAD, i.e. without involvement of the ascending aorta) often receivepharmacologic treatment and frequent monitoring is used in an attempt to pre-dict late adverse events. Prognosis of late adverse events is largely informed bymorphologic imaging features, but conflicting results have been reported amongseveral predictors [7]. a r X i v : . [ phy s i c s . f l u - dyn ] F e b J. Zimmermann et al.
To improve prognosis several hemodynamic quantities are of potential in-terest and may confer added sensitivity of individual risk. Recent studies havesuggested high FL outflow [6] as strong predictor for late adverse events, andFL ejection fraction [2] as indicator for false lumen growth rate.To retrieve these hemodynamic markers, computational fluid dynamics (CFD)frameworks provide simulated patient-specific flow fields at high spatio-temporalresolution; and those that integrate fluid-structure interaction (FSI) at deformablewalls amplify the realism of patient-specific modeling even further. If simula-tions were able to reliably replicate hemodynamics, it would further enable non-invasive prediction of risk related to pathological changes (e.g. tear size). WhileCFD FSI approaches show great potential, a direct validation with measureddata in highly controlled, but realistic environments is missing. Previous com-parisons between simulations and in vivo invitro
MRI including catheter-based pressure mapping. We utilized a patient-specific, compliant TBAD model embedded into a highly-controlled flow circuit.Uniaxial tensile testing of the compliant material, image-based flow splits andcatheter-based pressure recordings informed simulation tuning.
A 3D computed tomography angiogram (CTA) of a patient (31 y/o, female)with TBAD was selected from our institution’s database. A proximal intimal‘entry’ tear was present distal to the left subclavian artery and an ‘exit’ tear waslocated proximal to the celiac trunk. Each tear measured . in area size.The lumen of the thoracic aorta was segmented using the active contour al-gorithm with supplementary manual refinements (itk-SNAP v3.4, Fig. 1a). Twotetrahedral meshes were generated (Fig. 1b): the ‘fluid domain’ representing thefull aortic lumen; and the ‘wall domain’ (as extruded fluid domain) representingthe outer aortic wall and dissection flap that separates TL and FL with uni-form thickness ( h = 2 mm ). The wall domain mesh was further refined with (i)cylindrical caps that facilitated tubing connections, and (ii) visual landmarksto define image analysis planes. Meshing and refinements were done using Sim-Vascular (release 2020-04) and Meshmixer (v3.5, Autodesk). Further details onmodel generation are given in [1].The wall model was 3D-printed using a novel photopolymer technique (Poly-Jet J735, Stratasys Inc.), as shown in Fig. 1d. The print material underwentuniaxial tensile testing and proved to be comparable to in vivo aortic wall com-pliance (tangent Young’s modulus E y,t = 1 . ) emodynamics in TBAD: FSI vs. 4D-Flow 3 inlet DAO1(TL, FL)DAO2(TL, FL)DAO3(TL, FL)exit tearentry tearDAo outlet B C T L CC L SA * **** * ** c a DAO1 level DAO3 level d fluid domainwall domain b Fig. 1. (a) CTA images with lumen segmentation. (b) Tetrahedral meshes of fluid(gray) and wall domains with dissection flap (blue). (c) Cross-sectional landmarks andpressure mapping points (*). (d) Photograph of finished 3D-printed model.
Imaging was performed on a
MRI machine (Skyra, Siemens). An MRI-compatible flow circuit, including a programmable pump (CardioFlow 5000 MR,Shelley), was engineered to provide physiological and controllable flow and pres-sure conditions. Glycerol-water (ratio = 40/60) with contrast (ferumoxytol) wasused as a blood-mimicking fluid; and a typical aortic flow waveform was applied(heart rate = / min , stroke volume = . / s , total flow = .
45 L / min ).The circuit was tuned on the scanner table prior to image acquisition, tar-geting a flow split of 70/30 (DAo outlet vs. arch branches), and luminal systolicpressure (at model inlet) of
120 mmHg . A pressure transducer (SPR-350S, Mil-lar) was inserted through ports at the model inlet and DAo outlet, and luminalpressures were recorded at eight points (Fig. 1c). Ultrasonic flow and pressuresignals were fed into PowerLab (ADInstruments) for analysis.
Two-dimensional (2D) acquisitions at landmarks(Fig. 1c) included: (1) 2D cine gradient echo (2D-cine) with pixel size = . × . , slice thickness = , T E /T R = / .
75 ms , flip angle = °, avg. = 2,retro. gating (40 frames); and (2) 2D phase-contrast (2D-PC) with pixel size = . × . , slice thickness = , T E /T R = / .
25 ms , flip angle = °,avg. = 2, V enc = 90–120 cm s − , retro. gating (40 frames). A four-point encoded Cartesian 4D-flow sequence was acquiredas follows: FoV = × ×
84 mm , matrix = × × , voxel size = . × . × . , T E /T R = . / . , flip angle = °, parallel imaging(GRAPPA, R=2), V enc =
120 cm s − , lines/seg. = 2, retro. gating (20 frames). Image analysis
Lumen contours were automatically tracked through timebased on 2D-cine data, which provided values of cross-sectional area and served
J. Zimmermann et al. as the boundary for net flow calculation. 2D-PC images were corrected for phaseoffsets (via planar 2nd order fitting) and then processed to retrieve the inlet flowand net flow splits across outlets.4D-flow MRI data was corrected for (i) Maxwell terms, (ii) gradient non-linearity distortion, and (iii) phase offsets (via 2nd order fitting). Five landmarksalong the dissected region were used for analysis (Fig. 1c). 4D-flow MRI offsetcorrection, flow calculations, and streamline visualization were done using MEV-ISFlow (v11.2, Fraunhofer Institute) and ParaView (v5.7); quantitative resultswere exported as numeric files for comparison with simulation results.
The governing equations for fluid flow and structuralmechanics were solved in the fluid and wall domain, respectively. In the fluiddomain, the working fluid was considered incompressible and Newtonian ( (cid:37) f =1100 kg m − , µ f = 0 .
003 92 Pa s ). Momentum and mass balance were describedby the Navier-Stokes Equations in arbitrary Lagrangian Eulerian formulation toaccount for motion. The structural material was modeled with a Neo-Hookeanmodel for homogeneous, isotropic hyperelastic materials ( E y = 1 . , (cid:37) s =1450 kg / m ). Both domains were coupled at the interface via kinetic and dynamicinterface conditions. CFD FSI boundary conditions
Three-element Windkessel boundary condi-tions were applied at fluid outlets and coupled to the 3D domain with the coupledmultidomain method [4]. The catheter-based pressure values used as simulationtuning targets were:
119 mmHg ,
42 mmHg , and
77 mmHg for the systolic ( P s ),diastolic ( P d ), and pulse pressure ( (cid:52) P ), respectively. Tuning was stopped oncea
10 % error margin was reached. The 2D-PC derived flow waveform was pre-scribed at the model inlet, assuming a parabolic velocity profile. 2D-PC flowsplits (w.r.t. inlet flow) were prescribed with . , . , . , and . forthe DAo outlet, BCT, LCC, and LSA, respectively. Numerical formulation
The numerical simulations were performed with theSVFSI finite element solver (SimVascular). SVFSI features linear elements forvelocity and pressure and is based on the Residual Based Variational MultiscaleMethod. The fluid and wall domain were solved in a monolithic approach andbackflow stabilization was applied at the fluid outlets. To avoid mesh degenera-tion, a nodal mesh smoothing was performed after each time step.
CFD FSI analysis
Time-resolved parameters were extracted from the last sim-ulation cycle: (i) flow rate, (ii) area change, and (iii) pressure. We extracted datafrom every 50th simulated time step, which totaled 80 incremental results withan effective temporal resolution (cid:52) t = 12 . . Quantitative metrics were ana-lyzed at cross-sectional landmarks (Fig. 1c) using ParaView (v5.7) and exportedas numeric files for direct 4D-Flow MRI comparison. emodynamics in TBAD: FSI vs. 4D-Flow 5 f l o w r a t e [ m l / s ] Inlet fl ow a p r e ss u r e [ mm H g ] Inlet pressure
CathCFD FSI b Fig. 2.
CFD FSI (blue) tuning conditions, showing (a) flow rate and (b) pressurewaveform at TBAD model inlet, in comparison to 4D-flow and catheter measurements(green).
Boundary conditions
Inlet flow (Fig. 2a) for CFD FSI was directly prescribedbased on 2D-PC results and agreed well with 4D-flow MRI. CFD-FSI flow splitsacross model outlets aligned well with 2D-PC splits (errors ≤ . ). Aftertuning, CFD FSI pressure (Fig. 2b) matched catheter measurements within thepre-defined
10 % error margin ( . for P s , for P d ). While catheter-basedmeasurements showed oscillations and a fast pressure drop at end-systole ( t =0 . ), CFD FSI pressure decayed slower and without oscillation. As a results,mean pressure differed by . . Flow patterns and velocities
Qualitative flow visualizations (Fig. 3) showedwell-matched flow patterns between CFD FSI and 4D-flow MRI. Particularly,streamlines depicted helical flow in FL aneurysm during systole and distal FLduring diastole, as well as increased velocities through the proximal FL entrytear and along the distal TL. Overall, velocities were higher in CFD FSI, butthe intra-model spatial distribution of velocities matched well.
Pressure, area, and flow
Systolic TL pressure exceeded FL pressure (Fig.4a) for both simulation and catheter measurements. At peak systole, the TL-FL presure difference was greater for CFD FSI data at landmarks DAO1 andDAO2, but matched well at DAO3. During diastole, the TL-FL difference wasclose to zero for CFD FSI, but was 1 to 2 mmHg for the catheter measurements.Cross-sectional area (Fig. 5, dashed lines) expanded most in FL cross-sectionswith up to
11 % based on CFD FSI and up to based on 2D-cine MRI.Net flow volumes (Fig. 5) revealed a FL to TL flow split of 78/22 for CFDFSI and 73/27 for 4D-flow MRI measurements. Flow waveform shapes (Fig. 5,solid lines) aligned well, particularly regarding the peak flow timepoint, systolicupslope ( t = 0 . ), and oscillatory lobes in diastole. CFD FSI flow rates werehigher in systole and lower in diastole when compared to 4D-flow values. J. Zimmermann et al. D - f l o w M R I C F D - F S I XYZ X YZ X YZ
Fig. 3.
Streamline visualization at systole ( t = 0 . ) for CFD FSI (top) and 4D-flowMRI (bottom) data. Pressure-area loops showed a steeper slope for in vitro data (Fig. 4b). FLpeak flow preceded peaks of pressure and area change. This temporal delay waslonger for CFD FSI, which was consistent for all DAO landmarks (Fig. 4c).
This study leveraged compliant 3D-printing as well as a highly-controlled MRI-compatible flow circuit setup to directly compare CFD FSI and MRI resultswith regards to flow and pressure dynamics in a patient-specific TBAD model.The aorta’s secondary lumen and proximal FL aneurysm presented complex flowpatterns with a large velocity range. These characteristics were well captured byboth modalities and streamline visualizations were in very good agreement.Our approach links measured luminal pressure with CFD FSI boundary con-ditions, which presents a major advantage over comparisons with in vivo datathat usually lacks invasive pressure measurements. During simulation tuning,pressure targets ( P s , P d ) were met, but pressure waveform shapes differed—i.e.faster and oscillatory pressure decay in catheter measurements versus slowerand steady decline in CFD FSI. We expect that oscillations originate from wavereflections at multiple connecting components of the flow circuit.Overall, parameters in the dissected region matched well between measure-ments and simulation. TL-FL pressure differences were comparable such thatthey were almost consistently positive, and that the most distal landmark showeda smaller difference compared to the two proximal points. Interestingly, CFD FSITL-FL pressure difference briefly dropped to negative ( t = 0 . ) and then to zero emodynamics in TBAD: FSI vs. 4D-Flow 7 a CFD FSIin vitro c f l o w r a t e [ m l / s ] r e l . a r e a c h a n g e p r e ss u r e [ mm H g ] DAO2 FL: waveform delays d i ff [ mm H g ] TL-FL pressure di ff erence DAO1DAO2DAO3 fl ow ratearea changepressure b p r e ss u r e [ mm H g ] FL: pressure-area loops
DAO1DAO2DAO3
Fig. 4. (a) TL-FL pressure difference. (b) FL pressure-area loops. (c) Flow rate peakspreceding both pressure and area peaks, with greater delay times for CFD FSI. ( t > .
65 s ), while catheter measurements showed preserved positive TL-FL dif-ferences at all locations and times. Moreover, with only difference betweenmodalities, results suggest a well-matched TL-FL flow split.Multiple results indicate that the performed tensile testing underestimated E y,t : a steeper slope of the pressure-area loop for in vitro data, shorter flow-pressure-area waveform delays, and consistently lower outer wall expansion.In conclusion, this work presented valuable information on hemodynamic sim-ilarities and differences as retrieved from CFD FSI, in vitro MRI, and catheter-based pressure measurements in a TBAD case.
Acknowledgements
We thank the Stanford Research Computing Center for computational resources(Sherlock HPC cluster), Dr. Anja Hennemuth for making available softwaretools, and Nicole Schiavone for technical advice. Funding was received fromDAAD (to J.Z.) and NIH R01 HL13182 (to D.B.E).
References
1. Bäumler, K., Vedula, V., Sailer, A.M., Seo, J., Chiu, P., Mistelbauer, G., Chan,F.P., Fischbein, M.P., Marsden, A.L., Fleischmann, D.: Fluid–structure interactionsimulations of patient-specific aortic dissection. Biom Mod Mech , 1607–28 (2020)2. Burris, N.S., Nordsletten, D.A., Nordsletten, D.A., Sotelo, J.A., Sotelo, J.A., Sotelo,J.A., Grogan-Kaylor, R., Houben, I.B., Alberto Figueroa, C., Alberto Figueroa, C.,Uribe, S., Uribe, S., Uribe, S., Patel, H.J.: False lumen ejection fraction predictsgrowth in type B aortic dissection: Preliminary results. Eur J Cardio-thorac Surg (5), 896–903 (2020)3. Dillon-Murphy, D., Noorani, A., Nordsletten, D., Figueroa, C.A.: Multi-modalityimage-based computational analysis of haemodynamics in aortic dissection. BiomMod Mech (4), 857–76 (2016)4. Esmaily-Moghadam, M., Bazilevs, Y., Marsden, A.L.: A new preconditioning tech-nique for implicitly coupled multidomain simulations with applications to hemody-namics. Comp Mechanics (5), 1141–1152 (2013) J. Zimmermann et al. area change 2D-cinerel. area change CFD FSI fl ow rate 4D- fl ow fl ow rate CFD FSILegend f l o w r a t e [ m l / s ] DAO3 FL r e l . a r e a c h a n g e f l o w r a t e [ m l / s ] DAO1 FL r e l . a r e a c h a n g e f l o w r a t e [ m l / s ] DAO2 FL r e l . a r e a c h a n g e f l o w r a t e [ m l / s ] DAO3 TL r e l . a r e a c h a n g e f l o w r a t e [ m l / s ] DAO1 TL r e l . a r e a c h a n g e f l o w r a t e [ m l / s ] DAO2 TL r e l . a r e a c h a n g e f l o w r a t e [ m l / s ] entry tear r e l . a r e a c h a n g e f l o w r a t e [ m l / s ] exit tear r e l . a r e a c h a n g e Fig. 5.
Flow rate and area change (w.r.t area of first frame) at eight landmarks. Netflow values for CFD FSI (blue) and 4D-flow MRI (green) are given.5. Pirola, S., Guo, B., Menichini, C., Saitta, S., Fu, W., Dong, Z., Xu, X.Y.: 4D FlowMRI-Based Computational Analysis of Blood Flow in Patient-Specific Aortic Dis-section. IEEE Trans Biom Eng (12), 3411–19 (2019)6. Sailer, A.M., van Kuijk, S.M., Nelemans, P.J., Chin, A.S., Kino, A., Huininga, M.,Schmidt, J., Mistelbauer, G., Bäumler, K., Chiu, P., Fischbein, M.P., Dake, M.D.,Miller, D.C., Schurink, G.W.H., Fleischmann, D.: Computed Tomography ImagingFeatures in Acute Uncomplicated Stanford Type-B Aortic Dissection Predict LateAdverse Events. Circ Cardiovasc Imaging (4) (2017)7. Spinelli, D., Benedetto, F., Donato, R., Piffaretti, G., Marrocco-Trischitta, M.M.,Patel, H.J., Eagle, K.A., Trimarchi, S.: Current evidence in predictors of aorticgrowth and events in acute type B aortic dissection. J Vasc Surg68