Toward Improving Fidelity of Computational Fluid Dynamics Simulations: Boundary Conditions Matter

Christof Karmonik

doi:10.3174/ajnr.A3984

In their paper entitled “Generalized versus Patient-Specific Inflow Boundary Conditions in Computational Fluid Dynamics Simulations of Cerebral Aneurysmal Hemodynamics,” Jansen et al¹ compare results from computational fluid dynamics (CFD) simulations performed with 2 different kinds of boundary conditions: a spatiotemporal inflow waveform measured with 2D phase-contrast MR imaging in the individual patient and a generalized inflow velocity profile previously described in the literature. In their comparison, Jansen et al focus on wall shear stress (WSS) and, derived from it, the oscillatory shear index as well as intra-aneurysmal flow patterns. In agreement with previously published results,^2⇓⇓–5 they report statistically significant differences for the 2 approaches.

Simulating hemodynamics in cerebral aneurysms with CFD techniques is a relatively new approach translating a well-established engineering technology into clinical research. Essentially, a computational model as an approximation of the real world is created and the governing equations for blood flow (Navier Stokes equations) are numerically solved based on this mathematic construct. The output of these simulations includes the velocity fields and the values of other hemodynamic parameters such as WSS or pressure.

The fidelity of the results depends on the kinds of approximations or simplifications made when creating the computational model. For instance, early simulations using 2D models with simple geometric approximations were able to demonstrate low WSS at the aneurysm dome⁶; however, because of inherent limitations, these models could not provide any information about the 3D distribution of the flow or WSS. In many studies to date, 3D volumetric information derived from medical image data specific to the individual patient is used, often from 3D digital subtraction angiography but also from CT angiography or MR angiography. Boundary conditions are approximated by generalized waveforms. These simulations succeed in providing a true 3D description of the spatial and temporal distributions of hemodynamic parameters. As there are no variations in the inflow boundary condition, differences in the simulation results between individual aneurysms originate from the aneurysm geometries alone. With this approach it was demonstrated that CFD can visualize and quantify hemodynamic differences between ruptured and unruptured aneurysms.^7⇓–9

As Jansen et al¹ demonstrate, simulations may be further refined by incorporating patient-derived flow information into the model as the exact shape of the inflow waveform may exert significant effects on at least some of the calculated hemodynamic parameters. However, physiologic waveforms may also vary. For instance, intense physical efforts or emotional excitement typically result in a sudden change in heart rate and blood pressure. A CFD study investigating the effects of increase in cardiac frequency found significant changes in the overall intra-aneurysmal flow patterns (eg, vortex formation and translation) and an increase in WSS.¹⁰ These effects may also need to be considered for an accurate assessment of hemodynamics in cerebral aneurysms with CFD techniques.

CFD simulations are the results of mathematic constructs and validation of their results is necessary. Validation studies comparing virtual angiograms (derived from CFD) with acquired angiograms^{11⇓⇓–14} and comparing simulated intra-aneurysmal flow patterns with those measured with 2D phase-contrast MR imaging^{15⇓⇓–18} or 4D phase-contrast MR imaging^19,20 reported generally good agreement and thereby encourage the continued advancement of CFD. Still, a better understanding of the limitations of CFD simulations is warranted.^21⇓–23

Computational simulations will play an increased role in the future for enhancing and complementing the information in medical images. Furthermore, such simulations will not be limited to studies of hemodynamics in cerebral aneurysms. As an indicative example, CFD studies have been recently performed for investigating CSF flow in Chiari malformations.^24,25 Further validation and optimization of CFD techniques as well as streamlining the simulation process itself, eg, by using dedicated CFD simulation and visualization systems,²⁶ may foster further integration of this exciting technology into clinical research.

REFERENCES

1.↵
1. Jansen IG,
2. Schneiders JJ,
3. Potters WV,
4. et al
. Generalized versus patient-specific inflow boundary conditions in computational fluid dynamics simulations of cerebral aneurysmal hemodynamics. AJNR Am J Neuroradiol 2014;35:1543–48
Abstract/FREE Full Text
2.↵
1. Karmonik C,
2. Yen C,
3. Diaz O,
4. et al
. Temporal variations of wall shear stress parameters in intracranial aneurysms–importance of patient-specific inflow waveforms for CFD calculations. Acta Neurochir (Wien) 2010;152:1391–98; discussion 1398
CrossRef PubMed
3.↵
1. Karmonik C,
2. Yen C,
3. Grossman RG,
4. et al
. Intra-aneurysmal flow patterns and wall shear stresses calculated with computational flow dynamics in an anterior communicating artery aneurysm depend on knowledge of patient-specific inflow rates. Acta Neurochir (Wien) 2009;151:479–85; discussion 485
CrossRef PubMed
4.↵
1. Venugopal P,
2. Valentino D,
3. Schmitt H,
4. et al
. Sensitivity of patient-specific numerical simulation of cerebal aneurysm hemodynamics to inflow boundary conditions. J Neurosurg 2007;106:1051–60
CrossRef PubMed
5.↵
1. Marzo A,
2. Singh P,
3. Larrabide I,
4. et al
. Computational hemodynamics in cerebral aneurysms: the effects of modeled versus measured boundary conditions. Ann Biomed Eng 2011;39:884–96
CrossRef PubMed
6.↵
1. Burleson AC,
2. Strother CM,
3. Turitto VT
. Computer modeling of intracranial saccular and lateral aneurysms for the study of their hemodynamics. Neurosurgery 1995;37:774–82; discussion 782–84
CrossRef PubMed
7.↵
1. Byrne G,
2. Mut F,
3. Cebral J
. Quantifying the large-scale hemodynamics of intracranial aneurysms. AJNR Am J Neuroradiol 2014;35:333–38
Abstract/FREE Full Text
8.↵
1. Cebral JR,
2. Mut F,
3. Weir J,
4. et al
. Association of hemodynamic characteristics and cerebral aneurysm rupture. AJNR Am J Neuroradiol 2011;32:264–70
Abstract/FREE Full Text
9.↵
1. Jou LD,
2. Lee DH,
3. Morsi H,
4. et al
. Wall shear stress on ruptured and unruptured intracranial aneurysms at the internal carotid artery. AJNR Am J Neuroradiol 2008;29:1761–67
Abstract/FREE Full Text
10.↵
1. Jiang J,
2. Strother C
. Computational fluid dynamics simulations of intracranial aneurysms at varying heart rates: a “patient-specific” study. J Biomech Eng 2009;131:091001
11.↵
1. Ford MD,
2. Stuhne GR,
3. Nikolov HN,
4. et al
. Virtual angiography for visualization and validation of computational models of aneurysm hemodynamics. IEEE Trans Med Imag 2005;24:1586–92
CrossRef PubMed
12.↵
1. Endres J,
2. Kowarschik M,
3. Redel T,
4. et al
. A workflow for patient-individualized virtual angiogram generation based on CFD simulation. Comput Math Methods Med 2012;2012:306765
PubMed
13.↵
1. Sun Q,
2. Groth A,
3. Bertram M,
4. et al
. Phantom-based experimental validation of computational fluid dynamics simulations on cerebral aneurysms. Med Phys 2010;37:5054–65
CrossRef PubMed
14.↵
1. Sun Q,
2. Groth A,
3. Aach T
. Comprehensive validation of computational fluid dynamics simulations of in-vivo blood flow in patient-specific cerebral aneurysms. Med Phys 2012;39:742–54
CrossRef PubMed
15.↵
1. Karmonik C,
2. Klucznik R,
3. Benndorf G
. Blood flow in cerebral aneurysms: comparison of phase contrast magnetic resonance and computational fluid dynamics–preliminary experience. Rofo 2008;180:209–15
CrossRef PubMed
16.↵
1. Karmonik C,
2. Klucznik R,
3. Benndorf G
. Comparison of velocity patterns in an AComA aneurysm measured with 2D phase contrast MRI and simulated with CFD. Technol Health Care 2008;16:119–28
PubMed
17.↵
1. Boussel L,
2. Rayz V,
3. Martin A,
4. et al
. Phase-contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: comparison with computational fluid dynamics. Magn Reson Med 2009;61:409–17
CrossRef PubMed
18.↵
1. Rayz VL,
2. Boussel L,
3. Acevedo-Bolton G,
4. et al
. Numerical simulations of flow in cerebral aneurysms: comparison of CFD results and in vivo MRI measurements. J Biomed Eng 2008;130:051011
19.↵
1. Berg P,
2. Stucht D,
3. Janiga G,
4. et al
. Cerebral blood flow in a healthy circle of Willis and two intracranial aneurysms: computational fluid dynamics versus 4D phase-contrast magnetic resonance imaging. J Biomed Eng 2014;136:041003
20.↵
1. Jiang J,
2. Johnson K,
3. Valen-Sendstad K,
4. et al
. Flow characteristics in a canine aneurysm model: a comparison of 4D accelerated phase-contrast MR measurements and computational fluid dynamics simulations. Med Phys 2011;38:6300–12
CrossRef PubMed
21.↵
1. Cebral JR,
2. Meng H
. Counterpoint: realizing the clinical utility of computational fluid dynamics–closing the gap. AJNR Am J Neuroradiol 2012;33:396–98
FREE Full Text
22.↵
1. Kallmes DF
. Point: CFD–computational fluid dynamics or confounding factor dissemination. AJNR Am J Neuroradiol 2012;33:395–96
FREE Full Text
23.↵
1. Strother CM,
2. Jiang J
. Intracranial aneurysms, cancer, x-rays, and computational fluid dynamics. AJNR Am J Neuroradiol 2012;33:991–92
FREE Full Text
24.↵
1. Hentschel S,
2. Mardal KA,
3. Lovgren AE,
4. et al
. Characterization of cyclic CSF flow in the foramen magnum and upper cervical spinal canal with MR flow imaging and computational fluid dynamics. AJNR Am J Neuroradiol 2010;31:997–1002
Abstract/FREE Full Text
25.↵
1. Linge SO,
2. Mardal KA,
3. Haughton V,
4. et al
. Simulating CSF flow dynamics in the normal and the Chiari I subarachnoid space during rest and exertion. AJNR Am J Neuroradiol 2013;34:41–45
Abstract/FREE Full Text
26.↵
1. Karmonik C,
2. Chintalapani G,
3. Redel T,
4. et al
. Hemodynamics at the ostium of cerebral aneurysms with relation to post-treatment changes by a virtual flow diverter: a computational fluid dynamics study. Conf Proc IEEE Eng Med Biol Soc 2013;2013:1895–98
PubMed

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[1] 1.↵
Jansen IG,
Schneiders JJ,
Potters WV,
et al
. Generalized versus patient-specific inflow boundary conditions in computational fluid dynamics simulations of cerebral aneurysmal hemodynamics. AJNR Am J Neuroradiol 2014;35:1543–48
Abstract/FREE Full Text

[2] Jansen IG,

[3] Schneiders JJ,

[4] Potters WV,

[5] et al

[6] 2.↵
Karmonik C,
Yen C,
Diaz O,
et al
. Temporal variations of wall shear stress parameters in intracranial aneurysms–importance of patient-specific inflow waveforms for CFD calculations. Acta Neurochir (Wien) 2010;152:1391–98; discussion 1398
CrossRef PubMed

[7] Karmonik C,

[8] Yen C,

[9] Diaz O,

[10] et al

[11] 3.↵
Karmonik C,
Yen C,
Grossman RG,
et al
. Intra-aneurysmal flow patterns and wall shear stresses calculated with computational flow dynamics in an anterior communicating artery aneurysm depend on knowledge of patient-specific inflow rates. Acta Neurochir (Wien) 2009;151:479–85; discussion 485
CrossRef PubMed

[12] Karmonik C,

[13] Yen C,

[14] Grossman RG,

[15] et al

[16] 4.↵
Venugopal P,
Valentino D,
Schmitt H,
et al
. Sensitivity of patient-specific numerical simulation of cerebal aneurysm hemodynamics to inflow boundary conditions. J Neurosurg 2007;106:1051–60
CrossRef PubMed

[17] Venugopal P,

[18] Valentino D,

[19] Schmitt H,

[20] et al

[21] 5.↵
Marzo A,
Singh P,
Larrabide I,
et al
. Computational hemodynamics in cerebral aneurysms: the effects of modeled versus measured boundary conditions. Ann Biomed Eng 2011;39:884–96
CrossRef PubMed

[22] Marzo A,

[23] Singh P,

[24] Larrabide I,

[25] et al

[26] 6.↵
Burleson AC,
Strother CM,
Turitto VT
. Computer modeling of intracranial saccular and lateral aneurysms for the study of their hemodynamics. Neurosurgery 1995;37:774–82; discussion 782–84
CrossRef PubMed

[27] Burleson AC,

[28] Strother CM,

[29] Turitto VT

[30] 7.↵
Byrne G,
Mut F,
Cebral J
. Quantifying the large-scale hemodynamics of intracranial aneurysms. AJNR Am J Neuroradiol 2014;35:333–38
Abstract/FREE Full Text

[31] Byrne G,

[32] Mut F,

[33] Cebral J

[34] 8.↵
Cebral JR,
Mut F,
Weir J,
et al
. Association of hemodynamic characteristics and cerebral aneurysm rupture. AJNR Am J Neuroradiol 2011;32:264–70
Abstract/FREE Full Text

[35] Cebral JR,

[36] Mut F,

[37] Weir J,

[38] et al

[39] 9.↵
Jou LD,
Lee DH,
Morsi H,
et al
. Wall shear stress on ruptured and unruptured intracranial aneurysms at the internal carotid artery. AJNR Am J Neuroradiol 2008;29:1761–67
Abstract/FREE Full Text

[40] Jou LD,

[41] Lee DH,

[42] Morsi H,

[43] et al

[44] 10.↵
Jiang J,
Strother C
. Computational fluid dynamics simulations of intracranial aneurysms at varying heart rates: a “patient-specific” study. J Biomech Eng 2009;131:091001

[45] Jiang J,

[46] Strother C

[47] 11.↵
Ford MD,
Stuhne GR,
Nikolov HN,
et al
. Virtual angiography for visualization and validation of computational models of aneurysm hemodynamics. IEEE Trans Med Imag 2005;24:1586–92
CrossRef PubMed

[48] Ford MD,

[49] Stuhne GR,

[50] Nikolov HN,

[51] et al

[52] 12.↵
Endres J,
Kowarschik M,
Redel T,
et al
. A workflow for patient-individualized virtual angiogram generation based on CFD simulation. Comput Math Methods Med 2012;2012:306765
PubMed

[53] Endres J,

[54] Kowarschik M,

[55] Redel T,

[56] et al

[57] 13.↵
Sun Q,
Groth A,
Bertram M,
et al
. Phantom-based experimental validation of computational fluid dynamics simulations on cerebral aneurysms. Med Phys 2010;37:5054–65
CrossRef PubMed

[58] Sun Q,

[59] Groth A,

[60] Bertram M,

[61] et al

[62] 14.↵
Sun Q,
Groth A,
Aach T
. Comprehensive validation of computational fluid dynamics simulations of in-vivo blood flow in patient-specific cerebral aneurysms. Med Phys 2012;39:742–54
CrossRef PubMed

[63] Sun Q,

[64] Groth A,

[65] Aach T

[66] 15.↵
Karmonik C,
Klucznik R,
Benndorf G
. Blood flow in cerebral aneurysms: comparison of phase contrast magnetic resonance and computational fluid dynamics–preliminary experience. Rofo 2008;180:209–15
CrossRef PubMed

[67] Karmonik C,

[68] Klucznik R,

[69] Benndorf G

[70] 16.↵
Karmonik C,
Klucznik R,
Benndorf G
. Comparison of velocity patterns in an AComA aneurysm measured with 2D phase contrast MRI and simulated with CFD. Technol Health Care 2008;16:119–28
PubMed

[71] Karmonik C,

[72] Klucznik R,

[73] Benndorf G

[74] 17.↵
Boussel L,
Rayz V,
Martin A,
et al
. Phase-contrast magnetic resonance imaging measurements in intracranial aneurysms in vivo of flow patterns, velocity fields, and wall shear stress: comparison with computational fluid dynamics. Magn Reson Med 2009;61:409–17
CrossRef PubMed

[75] Boussel L,

[76] Rayz V,

[77] Martin A,

[78] et al

[79] 18.↵
Rayz VL,
Boussel L,
Acevedo-Bolton G,
et al
. Numerical simulations of flow in cerebral aneurysms: comparison of CFD results and in vivo MRI measurements. J Biomed Eng 2008;130:051011

[80] Rayz VL,

[81] Boussel L,

[82] Acevedo-Bolton G,

[83] et al

[84] 19.↵
Berg P,
Stucht D,
Janiga G,
et al
. Cerebral blood flow in a healthy circle of Willis and two intracranial aneurysms: computational fluid dynamics versus 4D phase-contrast magnetic resonance imaging. J Biomed Eng 2014;136:041003

[85] Berg P,

[86] Stucht D,

[87] Janiga G,

[88] et al

[89] 20.↵
Jiang J,
Johnson K,
Valen-Sendstad K,
et al
. Flow characteristics in a canine aneurysm model: a comparison of 4D accelerated phase-contrast MR measurements and computational fluid dynamics simulations. Med Phys 2011;38:6300–12
CrossRef PubMed

[90] Jiang J,

[91] Johnson K,

[92] Valen-Sendstad K,

[93] et al

[94] 21.↵
Cebral JR,
Meng H
. Counterpoint: realizing the clinical utility of computational fluid dynamics–closing the gap. AJNR Am J Neuroradiol 2012;33:396–98
FREE Full Text

[95] Cebral JR,

[96] Meng H

[97] 22.↵
Kallmes DF
. Point: CFD–computational fluid dynamics or confounding factor dissemination. AJNR Am J Neuroradiol 2012;33:395–96
FREE Full Text

[98] Kallmes DF

[99] 23.↵
Strother CM,
Jiang J
. Intracranial aneurysms, cancer, x-rays, and computational fluid dynamics. AJNR Am J Neuroradiol 2012;33:991–92
FREE Full Text

[100] Strother CM,

[101] Jiang J

[102] 24.↵
Hentschel S,
Mardal KA,
Lovgren AE,
et al
. Characterization of cyclic CSF flow in the foramen magnum and upper cervical spinal canal with MR flow imaging and computational fluid dynamics. AJNR Am J Neuroradiol 2010;31:997–1002
Abstract/FREE Full Text

[103] Hentschel S,

[104] Mardal KA,

[105] Lovgren AE,

[106] et al

[107] 25.↵
Linge SO,
Mardal KA,
Haughton V,
et al
. Simulating CSF flow dynamics in the normal and the Chiari I subarachnoid space during rest and exertion. AJNR Am J Neuroradiol 2013;34:41–45
Abstract/FREE Full Text

[108] Linge SO,

[109] Mardal KA,

[110] Haughton V,

[111] et al

[112] 26.↵
Karmonik C,
Chintalapani G,
Redel T,
et al
. Hemodynamics at the ostium of cerebral aneurysms with relation to post-treatment changes by a virtual flow diverter: a computational fluid dynamics study. Conf Proc IEEE Eng Med Biol Soc 2013;2013:1895–98
PubMed

[113] Karmonik C,

[114] Chintalapani G,

[115] Redel T,

[116] et al

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