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University of California
Radiological Sciences Dept.

Medical Science I B140
Irvine, CA 92697-5000
 
Angiographic Fractional Flow Reserve

       

        Limitations in the visual assessment of intermediate severity stenoses by coronary angiography are known to suffer from intra- and inter-observer variability as well as discordance with their true physiologic importance [1-6].  Previous studies have performed functional analyses of stenoses using acquired images to predict pressure gradients [7-9], to estimate coronary flow reserve [10-12], to assess coronary flow through Thrombolysis in Myocardial Infarction (TIMI) frame count [13-15], and to assess functional improvement after coronary intervention [16, 17].  An important index not already estimated from coronary angiography is fractional flow reserve (FFR).  Pressure-based fractional flow reserve (FFR) has proven to aid the cardiologist in evaluating the flow-limiting potential of stenoses as well as the therapeutic gain of angioplasties [18, 19].  

        FFR quantifies the reduction in maximum coronary blood flow from a theoretical maximum normal flow in the presence of a stenosis.  How can FFR be determined if the maximum normal flow is unknown?  The pressure-based approach has elegantly circumvented the need to know the theoretical maximum normal flow by approximately FFR as a ratio of diseased perfusion pressure over the maximum inflow pressure from the aorta.  However, a limitation to the current pressure-based FFR method is the need to insert a pressure wire (0.014”) into distal parts of coronary arteries.

Unlike pressure measurements, x-ray imaging provides geometric information, such as diameter, length, and volume, of coronary vessels with the aid of a radio-opaque contrast material.  Moreover, cine-fluoroscopy can measure absolute coronary blood flow through monitoring changes in gray values in time.  Densitometry using coronary angiograms from the cardiac catheterization laboratory has been shown to measure lumen diameter [20], coronary blood flow [12, 21, 22], and arterial lumen volume [23] accurately.  Although substantial work has been done on determining arterial branch length [24-27], determining arterial branch lengths reproducibly for the entire arterial tree down to the spatial resolution limit of the imaging system (~500 mm) has remained elusive because of branch overlap.  Although the diseased blood flow is measurable with coronary angiography, the question of determining the maximum normal blood flow remains.

The study of allometric scaling laws has been the context of numerous studies and debates over the previous 150 years.  The seminal introduction of the 3/4-law by Kleiber [28], which relates the basal metabolic rate (B) to the body mass (M) through the following power law:

Ba M3/4,                                                                                              (1)

has been generally accepted, although unequivocal experimental and theoretical explanation for it remains ambiguous.  Recently, an enlightening explanation of the 3/4-law was provided based on nutrient delivery through self-similar, fractal-like networks [29, 30].  In addition, the volume flow rate (Q) can be linearly related to metabolism since the required delivery of oxygen and nutrients as well as the removal of byproducts is controlled by the blood flow: Q a B.  Moreover, the minimization of the energy required to sustain a space-filling network supplying every part of the object requires that the total blood volume (V) in the network scales linearly with the mass that the network supplies: V a M.  Substitution of Q and V into Equation 1 yields the necessary scaling law for estimating normal flow as expressed in Equation 4, with k being a proportionality constant.

Q = kQLL                                                                                             (2)

V = kVLL4/3                                                                                          (3)

Q =kV3/4                                                                                              (4)

In addition Zhou et al. applied the principle of  minimum energy to the design of the coronary arterial system [31].  Their model predicted a linear relationship between volume blood flow rate (Q) in a segment and the cumulative arterial length of all its distal branches (L) (Equation 2).  Zhou et al. also predicted a power law relation between the cumulative lumen volume and cumulative branch length of the arterial branches (Equation 3).  The proportionality constants kQL and kVL provide absolute (instead of relative) values of flow rate and arterial volume from arterial length, respectively.  An analysis of available in vivo and simulation data from various organs of various species support the linearity and exponent value of Equations 2 and 3, respectively [32].  A combination of Equations 2 and 3 would yield the same scaling law predicted by West et al.  Thus the network model applied to whole-body parameters by West et al. compare well with the optimized vascular network model by Zhou et al.  The scaling laws governing self-similar subtree design of the coronary arterial system extends across different organs and species.

 

fig1

 

From Equation 4 and the definition of FFR, an alternative expression for FFR can be obtained in terms of the measured blood flow and total lumen volume from angiographic images:

FFR =QHD/QHN=QT/kV3/4                                                              (5)

where QHDand QHN  are the maximum diseased and normal blood flow rates, respectively, QT is the measured flow in the target artery, and k is the proportionality constant relating the measured volume to the theoretical maximum normal flow.  Similarly, in the presence of a normal arterial subtree, a relative form of FFR can be defined in order to account for dependencies on experimental conditions such as systemic pressure, venous pressure, heart rate, and level of vasodilation.  This relative FFR (FFRR) is defined as follows:

FFRR=FFRT/FFRN=(kNQHT/kTQHN)(VN/VT)3/4                                                             (6)

where the T subscripts refer to the artery under investigation and the N subscripts refer to another artery used as the normal reference.

 

Simulation studies.

 

 

fig2
 
 

The coronary arterial system is modeled as a tree that can be recursively decomposed into a stem and crown [33-35]. A stem is any segment between two consecutive branching points in the coronary arterial tree, and the corresponding crown is the collection of all the distal branches to the stem.  A requirement of this stem-crown system is that the terminal branches of all crowns are of the same diameter size.  Morphometric information on the proximal branches of the left anterior descending (LAD), left circumflex (LCX), and right coronary (RCA) arteries were obtained from previous polymer cast data [36].  A method for the reconstruction of a fully reconstructed coronary vascular tree from partial measurements has been developed recently [37].  The distribution of pressures and flows throughout the reconstructed coronary arterial tree was then determined using Poiseuille’s equation, an electrical circuit model consisting of resistances in series and parallel, and defined aortic and outflow pre-capillary pressure boundary conditions.

 

In vivo swine studies.
 
fig3
 

Standard preparatory, surgical, and imaging techniques as described in a previous study will be used.  The proximal portion of the left anterior descending artery is dissected free from the epicardium so that an ultrasonic transit-time flow probe and a silastic vascular occluder can be attached around the artery.  Percent diameter stenoses ranging from 30-70% are implemented by the vascular occluder.  Standard techniques will be used to cannulate the left main ostium with a 7F multipurpose diagnostic catheter through the left carotid artery under fluoroscopic guidance.  Electrocardiogram, carotid artery blood pressure, and volume flow are continuously recorded.  Each animal is positioned on its back under the image intensifier and orthogonal projections are optimized for separating the left anterior descending artery (LAD) and left circumflex artery (LCX) perfusion beds.  Pressure-based FFR and the proposed angiographic FFR are evaluated and compared.

 

Human patients studies.

Coronary angiograms from consented patients that have undergone elective coronary angiography and pressure-based FFR measurement are analyzed.  The correlation between pressure-based FFR and the proposed angiographic FFR under clinical setting is evaluated.

 

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