(19) United States
`(12) Patent Application Publication (10) Pub. No.: US 2013/0246034 A1
`(43) Pub. Date:
`Sep. 19, 2013
`Sharma et al.
`
`US 20130246034A1
`
`(54) METHOD AND SYSTEM FOR NON-INVASIVE
`FUNCTIONAL ASSESSMENT OF CORONARY
`ARTERY STENOSIS
`
`(71) Applicants:Puneet Sharma, Monmouth Junction,
`NJ (US); Lucian Mihai Itu, Brasov
`(RO); Ali Kamen, Skillman, NJ (US);
`Bogdan Georgescu, Plainsboro, NJ
`(US); Xudong Zheng, Plainsboro, NJ
`(US); Huseyin Tek, Princeton, NJ (US);
`Dorin Comaniciu, Princeton Junction,
`NJ (US); Dominik Bernhardt, March
`(DE); Fernando Vega-Higuera,
`Erlangen (DE); Michael Scheuering,
`Nuemberg (DE)
`
`(72) Inventors: Puneet Sharma, Monmouth Junction,
`NJ (US); Lucian Mihai Itu, Brasov
`(RO); Ali Kamen, Skillman, NJ (US);
`Bogdan Georgescu, Plainsboro, NJ
`(US); Xudong Zheng, Plainsboro, NJ
`(US); Huseyin Tek, Princeton, NJ (US);
`Dorin Comaniciu, Princeton Junction,
`NJ (US); Dominik Bernhardt, March
`(DE); Fernando Vega-Higuera,
`Erlangen (DE); Michael Scheuering,
`Nuemberg (DE)
`
`(73) Assignees: Siemens Aktiengesellschaft, Munich
`(DE); Siemens Corporation, lselin, NJ
`(Us)
`
`(21) App1.No.: 13/794,113
`
`(22) Filed:
`
`Mar. 11, 2013
`
`Related US. Application Data
`
`(60) Provisional application No. 61/610, 134, ?led on Mar.
`13, 2012.
`
`Publication Classi?cation
`
`(51) Int. Cl.
`G06F 19/12
`(52) Us. or.
`CPC .................................... .. G06F 19/12 (2013.01)
`
`(2006.01)
`
`USPC .......................................................... .. 703/11
`
`ABSTRACT
`(57)
`A method and system for non-invasive assessment of coro
`nary artery stenosis is disclosed. Patient-speci?c anatomical
`measurements of the coronary arteries are extracted from
`medical image data of a patient acquired during rest state.
`Patient-speci?c rest state boundary conditions of a model of
`coronary circulation representing the coronary arteries are
`calculated based on the patient-speci?c anatomical measure
`ments and non-invasive clinical measurements of the patient
`at rest. Patient-speci?c rest state boundary conditions of the
`model of coronary circulation representing the coronary
`arteries are calculated based on the patient-speci?c anatomi
`cal measurements and non-invasive clinical measurements of
`the patient at rest. Hyperemic blood flow and pressure across
`at least one stenosis region of the coronary arteries are simu
`lated using the model of coronary circulation and the patient
`speci?c hyperemic boundary conditions. Fractional ?oW
`reserve (FFR) is calculated for the at least one stenosis region
`based on the simulated hyperemic blood How and pressure.
`
`‘Systemic tree’
`i 113 Modsi 001110001
`.1‘;
`> +
`
`__ 421
`
`404
`Ascending
`aorta
`CA FICA
`
`$06
`
`4%2
`1*?"
`
`424
`.
`.. .fM
`(3103211111426
`
`15
`
`430
`
`~' P?» I 418
`
`PM I,“
`Left ventricular
`pressure
`
`N.‘ Pm»
`Right ‘mam-Sugar
`pressure
`
`lumped‘émz
`
`Heart Model
`
`CATHWORKS EXHIBIT 1010
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`

`

`Patent Application Publication
`
`Sep. 19, 2013 Sheet 1 0f 6
`
`US 2013/0246034 A1
`
`FIG. 1
`
`102
`
`Heart Rate etc
`
`ilsmnan; 11?
`
`Sagmematim, ?ente?ima
`
`108
`
`FFR: 5‘
`PAD
`
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`Page 2 of 17
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`

`

`Patent Application Publication
`
`Sep. 19, 2013 Sheet 2 of6
`
`US 2013/0246034 A1
`
`FIG. 2
`
`Receive Medical Image Data and
`Clinical Measurments of Patient
`
`Extract Measurements of Coronary
`Arteries from Medical Image Data
`
`Perform Patient-Specific Blood Flow
`Simulation Using Boundary Conditions
`Calculated Based on Non-Invasive
`Patient-Specific Measurements
`
`Calculate Fractional Flow Reserve for
`Each Stenosis Based on Blood Flow
`Simulation
`
`202
`
`204
`
`206
`
`208
`
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`Patent Application Publication
`
`Sep. 19, 2013 Sheet 3 0f 6
`
`US 2013/0246034 A1
`
`FIG. 3
`
`300
`
`310
`
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`

`Patent Application Publication
`
`Sep. 19, 2013 Sheet 4 0f 6
`
`US 2013/0246034 A1
`
`FIG. 4
`
`Ra ~ moximai men's? resishance
`
`Rv yer-mus wig???‘ \
`
`424/
`
`-
`
`Le?ventricular
`pressure
`
`'
`
`_ \_
`
`Lumpedkmz
`
`Rigntventricuiar
`pressure
`
`Hem Mode!
`
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`

`Patent Application Publication
`
`Sep. 19, 2013 Sheet 5 0f 6
`
`US 2013/0246034 A1
`
`FIG. 5
`
`Heart rate
`
`Lat} wanh‘ir: ar
`
`15m!
`
`FIG. 6
`
`Haari rate
`{HR}
`
`TEE-‘vii
`
`H§an
`Madei
`
`Csmnmy \iesssel
`Gamma“
`
`Hypammic ?aw
`
`Hyparemin \mmm/
`
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`

`Patent Application Publication
`
`Sep. 19, 2013 Sheet 6 of 6
`
`US 2013/0246034 A1
`
`FIG. 7
`
`706
`Network
`Interface j
`
`702
`J
`
`708
`
`I/O
`
`/_ 704
`Processor
`
`Storage
`
`712
`
`Memory f 710
`
`r- 720
`
`Image Acquisition
`Device
`
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`US 2013/0246034 A1
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`Sep. 19, 2013
`
`METHOD AND SYSTEM FOR NON-INVASIVE
`FUNCTIONAL ASSESSMENT OF CORONARY
`ARTERY STENOSIS
`
`[0001] This application claims the bene?t of US. Provi
`sional Application No. 61/610,134, ?led Mar. 13, 2012, the
`disclosure of Which is herein incorporated by reference.
`
`BACKGROUND OF THE INVENTION
`
`[0002] The present invention relates to non-invasive func
`tional assessment of coronary artery stenosis, and more par
`ticularly, to non-invasive functional assessment of coronary
`artery stenosis from medical image data and blood ?oW simu
`lations.
`[0003] Cardiovascular disease (CVD) is the leading cause
`of deaths WorldWide. Among various CVDs, coronary artery
`disease (CAD) accounts for nearly ?fty percent of those
`deaths. Despite signi?cant improvements in medical imaging
`and other diagnostic modalities, the increase in premature
`morbidity and mortality for CAD patients is still very high.
`The current clinical practice for diagnosis and management
`of coronary stenosis involves the assessment of the diseased
`vessel either visually or by Quantitative Coronary Angiogra
`phy (QCA). Such assessment provides the clinician With an
`anatomical overvieW of the stenosis segment and parent ves
`sel, including the area reduction, lesion length, and minimal
`lumen diameter, but does not provide a functional assessment
`of the effect of the lesion on blood ?oW through the vessel.
`Measuring the fractional ?oW reserve (FFR) by inserting a
`pressure Wire into the stenosed vessel has been shoWn to be a
`better option for guiding revasculariZation decisions, since
`the FFR is more effective in identifying ischemia causing
`lesions, as compared to invasive angiography. QCA only
`evaluates the morphological signi?cance if the stenosis and
`has a number of other limitations. Pressure Wire based FFR
`measurements involve risks associated With the intervention
`necessary to insert the pressure Wire into the vessel, and for a
`very narroW stenosis, the pressure Wire may induce an addi
`tional pressure drop.
`
`BRIEF SUMMARY OF THE INVENTION
`
`[0004] The present invention provides a method and system
`for non-invasive functional assessment of coronary artery
`stenosis. Embodiments of the present invention provide a
`functional assessment of the severity of a coronary artery
`stenosis by calculating fractional ?oW reserve (FFR) and/or
`other functional measurements from medical image data and
`How simulations. Embodiments of the present invention uti
`liZe an underlying reduced-order patient-speci?c hemody
`namic analysis using computational ?uid dynamics (CFD)
`simulations. This makes it possible to calculate FFR and other
`hemodynamic quantities characterizing the severity of a
`lesion in near real-time during the image acquisition process,
`thus alloWing for an interactive Work?oW With a clinician.
`Embodiments of the present invention also utiliZe other non
`image based non-invasive patient information to calculate
`boundary conditions for patient-speci?c CFD simulations.
`[0005] In one embodiment of the present invention, patient
`speci?c anatomical measurements of the coronary arteries are
`extracted from medical image data of a patient acquired dur
`ing rest state. Patient-speci?c rest state boundary conditions
`of a model of coronary circulation representing the coronary
`arteries are calculated based on the patient-speci?c anatomi
`cal measurements and non-invasive clinical measurements of
`
`the patient at rest. Patient-speci?c hyperemic boundary con
`ditions of the model of coronary circulation are calculated
`based on the rest boundary conditions and a model for simu
`lated hyperemia. Hyperemic blood How and pressure across
`at least one stenosis region of at least one coronary artery are
`simulated using the model of coronary circulation and the
`patient-speci?c hyperemic boundary conditions. Fractional
`?oW reserve (FFR) of the at least one stenosis region is cal
`culated based on the simulated hyperemic blood How and
`pressure.
`[0006] In another embodiment of the present invention,
`Patient-speci?c anatomical measurements of the coronary
`arteries from medical image data of a patient acquired during
`hyperemia state. Patient- speci?c hyperemic boundary condi
`tions of a model of coronary circulation representing the
`coronary arteries are calculated based on the patient-speci?c
`anatomical measurements and non-invasive clinical measure
`ments of the patient at hyperemia. Hyperemic blood How and
`pressure across at least one stenosis region of at least one
`coronary artery are simulated using the model of coronary
`circulation and the patient-speci?c hyperemic boundary con
`ditions. Fractional ?oW reserve (FFR) of the at least one
`stenosis region is calculated based on the simulated hyper
`emic blood How and pressure.
`[0007] These and other advantages of the invention Will be
`apparent to those of ordinary skill in the art by reference to the
`folloWing detailed description and the accompanying draW
`1ngs.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`[0008] FIG. 1 illustrates a frameWork for non-invasive
`functional assessment of coronary artery stenosis according
`to an embodiment of the present invention;
`[0009] FIG. 2 illustrates a method for non-invasive func
`tional assessment of coronary artery stenosis according to an
`embodiment of the present invention;
`[0010] FIG. 3 illustrates exemplary results for generating a
`patient-speci?c anatomical model of the coronary vessel tree;
`[0011] FIG. 4 illustrates a reduced-order model for simu
`lating coronary circulation according to an embodiment of
`the present invention;
`[0012] FIG. 5 illustrates a method for estimating rest-state
`microvascular resistance according to an embodiment of the
`present invention;
`[0013] FIG. 6 illustrates the calculation of FFR using a
`personaliZed reduced order model according to an embodi
`ment of the present invention; and
`[0014] FIG. 7 is a high-level block diagram of a computer
`capable of implementing the present invention.
`
`DETAILED DESCRIPTION
`
`[0015] The present invention relates to a method and sys
`tem for non-invasive functional assessment of coronary artery
`stenosis using medical image data and blood ?oW simula
`tions. Embodiments of the present invention are described
`herein to give a visual understanding of the methods for
`simulating blood How and assessing coronary artery stenosis.
`A digital image is often composed of digital representations
`of one or more objects (or shapes). The digital representation
`of an object is often described herein in terms of identifying
`and manipulating the objects. Such manipulations are virtual
`manipulations accomplished in the memory or other cir
`cuitry/hardWare of a computer system. Accordingly, is to be
`
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`

`US 2013/0246034 A1
`
`Sep. 19,2013
`
`understood that embodiments of the present invention may be
`performed Within a computer system using data stored Within
`the computer system.
`[0016] FIG. 1 illustrates a framework for non-invasive
`functional assessment of coronary artery stenosis according
`to an embodiment of the present invention. As illustrates in
`FIG. 1, the framework includes an image acquisition stage
`102, an anatomical modeling stage 104, a blood ?oW simu
`lation stage 106, and a fraction ?oW reserve (FFR) computa
`tion phase 108. In the image acquisition stage 102, medical
`image data, such as coronary computed tomography (CT), of
`a patient is acquired, as Well as other non-invasive clinical
`measurements, such as heart rate, blood pressure, etc. In the
`anatomical modeling stage 104, image segmentation and cen
`terline extraction algorithms are used to generate patient
`speci?c anatomical models of the patient’s coronary arteries.
`The patient-speci?c anatomical models can be adjusted based
`on feedback from a clinician 110. In the blood ?oW simulation
`stage 106, computational ?uid dynamics are used to simulate
`blood ?oW through the coronary arteries. In one embodiment,
`a reduced-order circulation model can be used for patient
`speci?c blood-?oW simulations in the vessel tree coupled
`With a separate model of each stenosis, and the underlying
`boundary conditions. Patient-speci?c boundary conditions
`are calculated using patient-speci?c modeling of maximal
`hyperemia conditions and the auto-regulation mechanism.
`The clinician 110 can provide feedback regarding the blood
`?oW simulations, for example to change various parameters
`of the circulation model or to change the level of modeling of
`the circulation model. In the FFR computation stage 108,
`FFR is calculated for each stenosis based on the simulated
`pressures resulting from the blood ?oW simulation. The
`image acquisition stage 102, anatomical modeling stage 104,
`blood ?oW simulation stage 106, and FFR computation stage
`108 are described in greater detail While referring to the
`method of FIG. 2
`[0017] FIG. 2 illustrates a method for non-invasive func
`tional assessment of coronary artery stenosis according to an
`embodiment of the present invention. Referring to FIG. 2, at
`step 202, medical image data and non-invasive clinical mea
`surements of a patient is received. Medical image data from
`one or multiple imaging modalities can be received. For
`example, the medical image data can include, computed
`tomography (CT), Dyna CT, magnetic resonance (MR),
`Angiography, Ultrasound, Single Photon Emission computed
`Tomography (SPECT), and any other type of medical imag
`ing modality. The medical image data can be 2D, 3D or 4D
`(3D+time) medical image data. The medical image data can
`be received directly from one or more image acquisition
`devices, such as a CT scanner, MR scanner, Angiography
`scanner, Ultrasound device, etc., or the medical image data
`may be received by loading previously stored medical image
`data for a patient.
`[0018] In an advantageous embodiment, 3D coronary CT
`angiography (CTA) images are acquired on a CT scanner. The
`CTA images ensure that the coronary vasculature, including
`the vessel(s) that contain the stenosis, is adequately imaged
`using a contrast agent that is injected into the patient. At this
`stage, the clinician may be provided With an option of iden
`tifying lesions (stenoses) of interest by interactively vieWing
`them on the images. This step can also be performed on the
`anatomical models that are extracted from the image data
`(step 204). Alternatively, the stenoses may be automatically
`detected in the image data using an algorithm for automatic
`
`detection of coronary artery stenosis, such as the method for
`automatic detection of coronary artery stenosis described in
`United States Published Patent Application No. 2011/
`0224542, Which is incorporated herein by reference. In addi
`tion to the medical image data, other non-invasive clinical
`measurements, such as the patient’s heart rate and systolic
`and diastolic blood pressure are also acquired.
`[0019] At step 204, measurements of the coronary arteries
`are extracted from the medical image data of the patient. In an
`exemplary embodiment, the medical image data is acquired at
`rest-state and the measurements of the coronary arteries are
`extracted from the image data acquired at rest-state. In an
`advantageous embodiment, the measurements of the coro
`nary arteries are extracted by generating a patient-speci?c
`anatomical model of the coronary vessel tree is generated
`from the medical image data, but the present invention is not
`limited thereto. In order to generate the patient-speci?c ana
`tomical model of the coronary arteries, the coronary arteries
`are segmented in the 3D medical image data using an auto
`mated coronary artery centerline extraction algorithm. The
`coronary arteries can be segmented using any coronary artery
`segmentation method. For example, the coronary arteries can
`be segmented in a CT volume using the method described
`United States Published Patent Application No. 2010/
`0067760, Which is incorporated herein by reference. Once a
`coronary artery centerline tree is extracted, cross-section con
`tours can be generated at each point of the centerline tree. The
`cross-section contour at each centerline point gives a corre
`sponding cross-section area measurement at that point in the
`coronary artery. A geometric surface model is then generated
`for the segmented coronary arteries. For example, methods
`for anatomical modeling of the coronary arteries are
`described in US. Pat. No. 7,860,290 and US. Pat. No. 7,953,
`266, both of Which are incorporated herein by reference. In
`addition to the coronaries, the patient-speci?c anatomical
`model can include the aortic root together With the proximal
`part of the aorta. A detailed 3D model of each stenosis is also
`extracted using similar algorithms, Which includes the quan
`ti?cation of the proximal vessel diameter and area, distal
`vessel diameter and area, minimal lumen diameter and area,
`and length of stenosis. FIG. 3 illustrates exemplary results for
`generating a patient-speci?c anatomical model of the coro
`nary vessel tree. Image 300 of FIG. 3 shoWs coronary CTA
`data. Image 310 shoWs a centerline tree 312 extracted from
`the CTA data. Image 320 shoWs a cross-section contours 322
`extracted at each point of the centerline tree 312. Image 330
`shoWs a 2D surface mesh 332 of the coronary arteries, the
`aortic root, and the proximal part of the aorta.
`[0020] The above described anatomical modeling tasks can
`be performed automatically or can be user-driven, thereby
`alloWing the user (clinician) to interactively make changes to
`the anatomical models to analyZe the effects of such changes
`on the subsequent computation of FFR. In addition to the
`coronary vessel tree, the myocardium is also segmented (ei
`ther automatically or manually) in the medical image data to
`determine an estimate of the left ventricular mass, Which
`according to an embodiment of the present invention, is used
`to estimate the absolute resting ?oW for the patient. In an
`exemplary embodiment, a patient-speci?c anatomical model
`of the heart that is automatically generated from the image
`data. The anatomical heart model is a multi-component
`model having multiple cardiac components, including the
`four chambers (left ventricle, left atrium, right ventricle, and
`right atrium). The anatomical heart model may also include
`
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`
`components such as the heart valves (aortic valve, mitral
`valve, tricuspid valve, and pulmonary valve) and the aorta.
`Such a comprehensive model of the heart is used to capture a
`large variety of morphological, functional, and pathological
`variations. A modular and hierarchical approach can be used
`to reduce anatomical complexity and facilitate an effective
`and ?exible estimation of individual anatomies. The 4D ana
`tomical heart model can be generated by generating indi
`vidual models of each heart component, for example using
`marginal space learning (MSL), and then integrating the heart
`component models by establishing mesh point correspon
`dence. Additional details regarding generation of such a 4D
`patient-speci?c heart model are described in United States
`Published Patent Application No. 2012/0022843, Which is
`incorporated herein by reference
`[0021] Returning to FIG. 2, at step 206, a patient-speci?c
`blood ?oW simulation is performed using boundary condi
`tions calculated based on non-invasive patient-speci?c clini
`cal measurements. The hemodynamic quantities of interest
`for coronary circulation, such as FFR, are based on average
`values of How or pressure over the cardiac cycle. For an
`e?icient clinical Work?oW for evaluation of FFR via simula
`tions, a balance betWeen model complexity and computation
`time, Without compromising on the accuracy of the results is
`desirable. In an advantageous embodiment of the present
`invention, reduced-order models are used for the patient
`speci?c blood ?oW simulation, Which enables the assessment
`of the functional signi?cance of a coronary artery stenosis.
`The reduced-order models provide accurate estimates of How
`and pres sure distribution in the vessel tree, and are computa
`tionally e?icient, thus enabling a seamless integration With
`the clinical Work?oW. Although the reduced order model is
`described herein for coronary circulation simulation, the
`present invention is not limited thereto, and a full-scale model
`or a multi-scale model can be used as Well.
`[0022] FIG. 4 illustrates a reduced-order model for simu
`lating coronary circulation according to an embodiment of
`the present invention. As shoWn in FIG. 4, a heart model 402
`is coupled at the root of the aorta. The heart model 402 may be
`implemented as a full 3D heart model or may be implemented
`as a lumped model parameteriZed through patient-speci?c
`data. The aorta and the large arteries (e.g., the left coronary
`artery (LCA), right coronary artery (RCA), etc.) are repre
`sented as 1D blood ?oW models 404, 406, 408, 410, 412, 414,
`416, 418, and 420 since these 1D blood ?oW models 404-418
`produce reliable results in terms of pressure and How rate
`values and take into account Wave propagation phenomena.
`All microvascular beds Will be simulated through lumped
`parameter models 422, 424, 426, 428, and 430 Which account
`for the resistance applied to the blood How and for the com
`pliance of the distal vessels. For the coronary arterial tree, the
`How in the large (epicardial) vessels is computed through 1D
`models in a systemic tree model 421. The stenosis segments
`432 and 434 (i.e., areas in the vessels Were stenosis or nar
`roWing is detected) cannot be simulated using the 1D blood
`?oW models since there is a high variation in cross-sectional
`area and the shape of the stenosis in?uences the blood ?oW
`behavior and especially the trans-stenotic pressure drop
`Which plays a major role in the assessment of the functional
`importance of such a stenosis. The coronary vascular bed is
`modeled through lumped parameter models 424, 426, 428,
`and 430, Which are adapted to the coronary circulation in the
`sense that they take into account the effects of the myocardial
`contraction on the How Waveform.
`
`Reduced-Order Model of Coronary Circulation
`
`[0023] As shoWn in FIG. 4, the aorta (404), the large arter
`ies supplied by the aorta (406, 408, 410, 412,414, 416, 418,
`and 420), and the coronary epicardial vessels (421) are mod
`eled as axi-symmetric 1-D vessel segments, Where the blood
`?oW satis?es the folloWing properties: conservation of mass,
`conservation of momentum, and a state equation for Wall
`deformation. The vessel Wall can modeled as a purely elastic
`or visco-elastic. The inlet boundary condition can be pre
`scribed through an implicit coupling With the heart model
`402, or through measured ?oW data. The outlet boundary
`condition is given by the implicit coupling With the models of
`the coronary vascular beds (424, 426, 428, and 430), While the
`junctions (bifurcations) are solved by considering the conti
`nuity of total pressure and How. Additionally, the folloWing
`loss coef?cients may be introduced Which account for the
`energy loss at the junctions, Which depend on the angles
`betWeen the vessel segments:
`
`34(1) 6W) _
`T + W - O
`
`6W) 6
`412(1)
`AU) 3P0) _
`41(1)
`T + ELIWJ-FT 6x _KRM
`
`(1)
`
`(2)
`
`Where q is the How rate, A is the cross-sectional area, p is the
`pressure, 0t is the momentum-?ux correction coe?icient, KR
`is a friction parameters, p is the density, E is the Young
`modulus, h is the Wall thickness and r0 is the initial radius. The
`Wall properties may be determined through an empirical rela
`tionship ?t to the measured data in the extracted patient
`speci?c anatomical model or based on patient-speci?c esti
`mations of the Wall compliance. Other alternative
`formulations of the quasi-1-D ?oW equations can also be
`used, modeling the effects of visco-elasticity, non-NeWtonian
`behavior, etc.
`
`Stenosis Model
`
`[0024] The above quasi 1-D equations (Equations 1-3) are
`derived by considering a series of simplifying assumptions
`Which all hold Well for normal, healthy vessels. One of the
`assumptions is that the axial velocity is dominant and the
`radial components are negligible. This assumption no longer
`holds in case of sudden changes in lumen diameter, eg for a
`stenosis, and the radial components can no longer be
`excluded. Hence, the quasi 1-D equations do not correctly
`capture the pressure drop across the stenosis.
`[0025] In terms of previous research activities, much atten
`tion has been directed toWards the local velocity ?elds, but for
`the FFR assessment only the trans-stenotic pressure drop is
`important. In an advantageous implementation, semi-empiri
`cal stenosis models can be included in the 1-D blood ?oW
`models, Which obtain accurate results as compared to full
`scale models. For example, in the model beloW, the pressure
`drop is expressed as a sum of three terms (viscous term,
`turbulent or Bernoulli term, and inertance term):
`
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`
`Where [1. is the blood viscosity, LS is the stenosis length, Kv, Kt
`and K” are the viscous, turbulent, and iner‘tance coe?icients,
`respectively (all the quantities indexed With 0 refer to the
`normal dimensions While the quantities indexed With s refer
`to the stenosed values). In an advantageous embodiment,
`such a semi-empirical model for each stenosis segment (432
`and 434) is coupled With the vessel tree (and the underlying
`heart and coronary bed models) to compute the physiological
`pressure drop across the stenosis, both during rest state and at
`maximal hyperemia. It is to be understood that the present
`invention is not limited to the semi-empirical stenosis model
`of Equation (4), and other such models of the stenosis, With
`multiple pressure drop factors, may be used alternatively.
`Additionally, in an alternative implementation, a full-order
`3D model of each stenosis may be coupled With the rest of the
`vessel tree to simulate the pressure drop across the stenosis. In
`this case, the patient-speci?c 3D geometric model of the
`stenosis extracted from the medical image data (e.g., CTA
`data) is used in conjunction With quantitative coronary
`angiography (QCA)-like measures to personaliZe the stenosis
`model for the individual patient.
`[0026] Regarding coupling of the reduced-order or full
`order stenosis model to the rest of the coronary vessel tree, in
`a ?rst possible implementation, the momentum equation is
`adapted and the additional pressure drop determined by the
`turbulent term is included on the right hand side of the equa
`tion as an additional loss term. In a second possible imple
`mentation, the regular momentum equation is disregarded
`completely and replaced by Equation
`The segments
`treated as stenosis segments are coupled to the regular seg
`ments of the coronary vessel tree by considering continuity of
`total pressure and ?oW rate.
`
`Patient-Speci?c Modeling of Coronary Bed Boundary
`Conditions
`
`[0027] An important aspect of the ?oW simulations is rep
`resented by the boundary conditions at the termination of the
`coronary vessel tree (out?oW boundary conditions). Gener
`ally, pressure, ?oW, or a relationship betWeen ?oW and pres
`sure may be imposed at the terminal sites of the arterial vessel
`tree. If measured data, e. g. time-varying velocity, ?oW rate, or
`even pressure, are available, they can be readily applied. In
`the absence of such information (Which is typically the case),
`embodiments of the present invention calculate special
`boundary conditions that model the behavior of the distal
`arterial segments. Hence, the microvascular beds are modeled
`through lumped or O-D models: the systemic beds can rep
`resented by regular Windkessel elements containing varying
`number of elements (for example, betWeen tWo and four
`elements), While coronary beds are represented by special
`models Which account for the in?uence of the myocardial
`contraction on the ?oW Waveform (loW during systole and
`high during early diastole). FIG. 4 displays an example of
`such specialiZed models for the coronary circulation and pre
`sents the detailed elements of this type of boundary condition.
`[0028] The main characteristic of such lumped models is
`that the myocardial contraction is taken into account by intro
`ducing the left or right ventricular pressure, depending on the
`location of the coronary tree on the heart. The model dis
`played in FIG. 4 treats the microvascular bed as a single unit,
`but it is also possible to utiliZe more specialiZed models Which
`consider separately the contribution of the subepicardial and
`subendocardial microvascular beds. Generally, subepicardial
`vessels are less affected by heart contraction (they represent
`
`the outer layers of the myocardium), While subendocardial
`vessels are more affected by the action of the outer (they
`represent the inner layers, closer to the heart chambers). This
`is the main reason Why subendocardial are more prone to
`ischemia and to myocardial infarction.
`[0029] Since the resistance values of the large vessels are
`very small compared to the resistances of the arterioles and
`capillaries, the overall pressure levels are almost solely deter
`mined by the microvascular beds. In the context of non
`invasive FFR evaluation, the microvascular beds in general,
`and the coronary beds in particular play another major role.
`Since FFR is based on values determined at hyperemia, in
`order to non-invasively determine the value of this diagnostic
`indicator, the blood ?oW simulation has to model the hyper
`emic state. In clinical practice, FFR is measured after the
`intravenous or intracoronary administration of a vasodilator.
`In case of multi-vessel disease or serial stenosis it is important
`to have an increased duration of the hyperemic state in order
`to evaluate the functional signi?cance of all stenosis and to
`generate reliable pull-back curves. Hence, often intravenous
`administration of the vasodilator is preferred. This leads to a
`slight increase of heart rate and decrease of blood pressure.
`Since for a simulation the effect of an intracoronary vasodi
`lator can be extended inde?nitely, and this alternative to
`obtain hyperemia does not in?uence heart rate and blood
`pressure, thus being easier to model, this approach is desir
`able. HoWever, although the intravenous administration can
`be simulated, all microvascular beds have to be adapted
`accordingly.
`[0030] The administration of hyperemia inducing drugs
`(adenosine, papaverine etc.) leads to a vasodilation effect of
`the microvascular beds, Which represents an important
`decrease of the resistance values. The resistance values inside
`the systemic or coronary lumped models (for the normal
`state) may be obtained from patient-speci?c measurements,
`from literature data, or from the non-linear relationship
`betWeen resistances and lumen siZe. Compliances play a sec
`ondary role since they only in?uence the transient values and
`not the average pressures Which are of interest for the evalu
`ation of FFR. The coronary hyperemic state is modeled
`through a corresponding decrease in the microvascular resis
`tances, as caused by the administration of intracoronary
`adenosine (it has been shoWn that the epicardial, i.e. large
`arteries are not in?uenced by the vasodilator) and leads to a
`three to ?ve-fold increase of normal coronary ?oW in healthy
`vessels. Coronary auto-regulation protects the myocardium
`against ischemia during rest state and leads to decreased
`resistances for the diseased vessel, the reference value being
`the ?oW Which has to be identical to the noon-diseased case.
`The normal state can thus be easily modeled but does not
`represent a very high interest for the evaluation of FFR.
`[003 1] The main parameters Which have to be estimated are
`the mean arterial pressure (MAP) and the coronary mic