Ebook Advances in hemodynamic research: Part 1

(BQ) Part 1 book Advances in hemodynamic research presents the following contents: Historical and current role of hemodynamic research, hemodynamic assessment and flow visualization in echocardiography, flow visualization in magnetic resonance imaging, computational modeling of blood flow, emodynamics and ventricular dynamics evaluated with catheter.

A DVANCES IN H EMODYNAMICS

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C ONTENTS

Part I: Basic Science of Hemodynamic Research 1 Chapter 1 Historical and Current Role of Hemodynamic Research 3

Keiichi Itatani and Katsu Takenaka

Chapter 2 Hemodynamic Assessment and Flow

Hiroaki Semba and Tokuhisa Uejima

Chapter 3 Flow Visualization in Magnetic Resonance Imaging (MRI) 79

Yasuo Takehara and Masataka Sugiyama

Chapter 4 Computational Modeling of Blood Flow 99

Masanori Nakamura

Chapter 5 Hemodynamics and Ventricular Dynamics Evaluated with Catheter 137

Hidekatsu Fukuta and Nobuyuki Ohte

Part II: Clinical Application of Hemodynamic Research 163 Chapter 6 Congenital Heart Disease and Circulatory Physiology 165

Takashi Honda, Kagami Miyaji and Masahiro Ishii

Chapter 7 Ventricular Sucking Forces and Diastolic Function: Intraventricular

Pressure Gradient in Ventricle during Early Diastole Gives Us New

Ken Takahashi and Takahiro Ohara

Chapter 8 Hemodynamics in Coronary Arterial Disease and

Chapter 10 Application to Cardiovascular Surgery 263

Shohei Miyazaki, Keiichi Itatani, Sachi Koyama,

Kouki Nakashima, Tetsuya Horai, Norihiko Oka,

Tadashi Kitamura and Kagami Miyaji

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P REFACE

Hemodynamics is the study of the dynamics of the circulatory system Hemodynamics has been essentials in the clinical practice pertaining to cardiovascular diseases from ancient days Although it is essential, because it is based on dynamics and physics, the understanding

of hemodynamics is hard work for all those concerned with cardiovascular diseases In addition, with the rapid progress of recent imaging and computer technology, hemodynamics research undergone an evolution that provides beautiful colorful blood flow visualization This kind of innovation contributes novel insights into the approach to the pathophysiology of cardiovascular diseases This textbook includes the comprehensive knowledge regarding hemodynamic research from basic physiology to recent clinical problems

This textbook has two parts: first includes the basics of hemodynamics research and the second presents its clinical applications as follows

Part I: Basic Science of Hemodynamic Research

Chapter 1: Historical and Current Role of Hemodynamic Research

Chapter 2: Hemodynamic assessment and flow Visualization in Echocardiography Chapter 3: Flow Visualization with Magnetic Resonance Imaging

Chapter 4: Computational Modeling of the Cardiovascular System

Chapter 5: Hemodynamics and Ventricular Dynamics Evaluated with Catheter

Part II: Clinical Application of Hemodynamic Research

Chapter 6: Congenital Heart Disease and Circulatory Physiology

Chapter 7: Ventricular Sucking Forces and Diastolic Function: Intraventricular

pressure gradient in ventricle during early diastole gives us new insights into diastolic function

Chapter 8: Hemodynamics in Coronary Arterial Disease and Myocardial Perfusion Chapter 9: Reperfusion hemodynamics as an early predictor of cardiac function in a

DCDD setting Chapter 10: Application to Cardiovascular Surgery

I believe this textbook covers all the current topics and all the important historical topics related to hemodynamics In this edition of the textbook, I appreciate so much the efforts of the members of the ―Research Committee on Blood Flow and Cardiovascular System‖ http://ketsuryukai.com 『血流会』(ketsuryukai) in Japan Each chapter was written by

professional authors regarding respective topics

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Although this book deals with the least “advances”, careful attentions was paid to make it appeal to a wide range of professionals including clinicians, engineers, physicians, and researchers Each chapter is independent of the others, and this textbook was written both to

be read through and to be used as a reference for any special topics

I hope this textbook will provide new perspectives to all those interested in the research regarding hemodynamics

Keiichi Itatani, MD, PhD

Project Associate Professor Department of Cardiovascular Surgery Kyoto Prefectural University of Medicine

465 Kajiicho, Kawaramachi-Hirokoji,

Kamigyo-ku, Kyoto, Japan, 602-8566 keiichiitatani@yahoo.co.jp keiichiitatani@gmail.com

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P ART I: B ASIC S CIENCE OF

Departments of Hemodynamic Analysis and Cardiovascular Surgery,

Kitasato University School of Medicine, Tokyo, Japan

Although the interests of hemodynamic research have aspects of rheological and fluid dynamic approaches, the clinical measurements have been historically restricted to the pressure in the cardiovascular lumen by catheterization Otherwise, changes in the geometrical configuration of the heart and vessel structure by echocardiography are another frequently utilized hemodynamics evaluation tool On the other hand, the principle of fluid dynamics is described by equations for flow velocity and pressure distribution in arbitrary time; thus, the development of hemodynamic research historically distinct from knowledge accumulated through the study of fluid dynamics As

a result, the outcome of the hemodynamic research was simply descriptive and implicative of the pathological process of the disease, and did not directly venture further into the pathophysiological mechanisms

However, recent developments in computer engineering and clinical imaging techniques have enabled blood flow visualization, leading to a revolution in the field of hemodynamic research Recent flow visualization methods have illustrated the vortex flow inside the heart chamber and vessel lumen, which has been considered by researchers since ancient times Because these approaches based on flow velocity fields have high affinity with fluid dynamic equipment, they provide several novel indices that

*

Corresponding author: E-mail: keiichiitatani@gmail.com

are applicable to the pathophysiology of the cardiovascular diseases because they are profoundly based on the theorems that govern the phenomenon

Because pressure and flow distribution are not independent parameters in the physics

of fluid, these recent flow visualization imaging should finally aim toward revealing hemodynamics in relation to the absolute pressure distribution Several novel indices derived from the flow visualization modalities have emerged, but most of them is mechanical forces induced by the blood flow These mechanical forces especially flow energy loss should be evaluated in the comparison with the work produced by the circulatory pump: the heart, absolute pressure evaluation will be inevitable Recent novel technologies in the hemodynamic research results will be and should be linked with each other to obtain the profound insight into the pathophysiology of the cardiovascular diseases

This chapter explains the process of hemodynamic research development by introducing several recent topics, and further explains the relationship between the theory

of fluid dynamics and the assessment of cardiovascular disease

Keywords:hemodynamics, circulatory physiology, fluid dynamics, pressure, flow velocity, flow visualization, hemodynamic indices

Hemodynamics is the dynamic in the cardiovascular system The cardiovascular system

is a closed circulatory system through which blood flows to deliver oxygen to all tissues of

the body Blood flow within this system is supported mainly by the central pump: the heart

((Figure 1.1) Other organs that affect or support the circulatory system include the lungs

(breathing results in pulmonary flow and venous return fluctuation), and musculoskeletal system (blood pooled in the venous system is pumped by surrounding muscles) Hemodynamics is therefore critical for the maintenance of blood pressure and blood flow within the heart and vessel lumen In addition to the central pump, the peripheral vasculature has a hemodynamic effect

Because blood is a viscous liquid, the dynamics of blood are closely related to the physics

of fluids: fluid dynamics Therefore, basic concepts in hemodynamics are largely based on the

theorem of fluid dynamics Hemodynamics is often challenging for clinicians because it is based on mathematical and physical principle However, hemodynamics is not a purely academic discipline such as pure mathematics or basic laboratory based-experimentation, but rather a practical tool in daily clinical practice in cardiovascular medicine, and has been a powerful and useful tool used by physicians since ancient times for the systematical description of the cardiovascular diseases using several macroscopic parameters, including systemic blood pressure, cardiac output, arbitrary vessel blood flow rate, and peripheral vessel resistances These parameters are essential in clinical practice and are widely used in settings ranging from outpatient clinics to intensive care units

Historically, discussions regarding hemodynamic research predominantly focused on blood pressure measurements using catheter examination In addition, echocardiography was also used in hemodynamics evaluations For example, noninvasive blood pressure (NIBP) measurement at the calf has been used widely in clinical practice ((Figure 1.2A) The device was invented by Samuel Siegfried Karl Ritter von Basch in 1881 Scipione Riva-Rocci

introduced an easier version in 1896 In 1901, Harvey Cushing modified the device for medical use (Booth J 1977) Direct pressure measurement by arterial cannulation was tried in much elder era, was performed in 1733 by Stephan Hales, who inserted a tube into the carotid artery of a horse ((Figure 1.3) Direct arterial pressure measurements have been widely used

in intensive care and perioperative patient management ((Figure 1.2B) They are useful parameters for evaluating the hemodynamic state of patients with cardiovascular disease Central venous pressure (CVP) measurement by catheterization is a method enabling evaluation of blood volume within the cardiovascular system, and Swan-Ganz catheters ((Figure 1.2C) enable the measurement of pulmonary artery pressure, pulmonary capillary wedge pressure, and cardiac output These methods have increased the detail of hemodynamics parameters particularly in intensive care

Figure 1.1 Explanation of a circulatory system A: an image from Wikipedia with key word

―Circulatory system‖ http://en.wikipedia.org/wiki/Circulatory_system

This describes the location of the heart and large vessels B: an image from ―revision

world‖http://revisionworld.com/a2-level-level-revision/biology/physiology-transport/human-circulatory-system This image describes the function of a circulatory system

Figure 1.2 Pressure measurement equipment A; Manchette calf for NIBP measurement B: arterial

cannulation for direct pressure measurement from ―Medline Plus‖

http://www.nlm.nih.gov/medlineplus/ency/imagepages/19871.htm C: Swan-Ganz catheter and its

insertion Images from ―The critical care nurse‖

http://ccrnnurse.blogspot.jp/2012/05/why-use-swan-ganz-catheter.html

Figure 1.3 Stephan Hale‘s experiment of blood pressure measurement

The fact that the main parameter in evaluating hemodynamics has been the absolute pressure of various sites is quite characteristic and unique when we consider that theoretical basis of the hemodynamics should be conform to the fluid dynamics, because fluid dynamics generally describes and focuses on the flow stream constructed from velocity distribution, and rarely considers absolute pressure values However, flow stream observation itself is much elder than pressure measurement and has been one of the main interests since ancient days Leonardo da Vinci (1452-1519) illustrated the vortex inside the Valsalva sinus in addition to the heart anatomy and vortex flow in a pipe ((Figure 1.4), but actually measured flow stream has not been available until MRI (magnetic resonance imaging) phase velocity mapping emerged recently

Before that, regarding the flow, the available tools are cardiac output estimation based on the echocardiography, and flow velocity measurement based on Doppler ultrasonography ((Figure 1.5) B-mode echocardiography cross-sectional imaging has been used for decades, providing information regarding the geometrical configuration of the heart chambers Left ventricular (LV) dimension and volume measurement estimation have been powerful tools in evaluating congestive heart failure patient The ejection fraction (EF) is a global parameter describing the pump function of the heart ((Figure 1.5A) Doppler echocardiography can be used to detect the unidirectional flow velocity at specific portion of the heart and vessel lumen Although these are simple 2D imaging techniques, they provide essential information regarding the hemodynamic state of patients ((Figure 1.5B)

Figure 1.4 Pictures of Leonardo da Vinci Leonardo da Vinci illustrated vortex flow in the sinus of Valsalva

Figure 1.5 B-mode and Doppler echocardiography A: Shema of the echocardiography scan

https://www.healthtap.com/topics/echo B: B-mode image of the LV geometry configuration and its change in long-axis view C: Pulse wave Doppler flow velocity measurements of the transmitral flow

The ultimate goal of hemodynamic research is not the complete description of blood fluid dynamics, but optimizing the efficiency of oxygen delivery to all organs Attentions should be paid on the process in the clinical settings and on the biological response with change in hemodynamic parameters This chapter describes the use of hemodynamics in solving clinical problems and the development of hemodynamic research to reveal physiological mechanisms and predict the clinical course of patients by discussing several previous studies reported in the hemodynamics literatures Despite this chapter discussing the development of hemodynamic research, all previous important studies could not be described in this book

be detected Diastolic function is estimated by the speed of the decreasing pressure, max –dp/dt or the time constant tau that describes the time constant when the pressure decrease is assumed to be an exponential curve with time ON reduction in preload, the loop shifts

leftward and downward, the loop size reduces, and the end-systolic point would describe a line toward LV dead space V0. Ees represents the gradient of the end-systolic pressure volume relationship and also the end-systolic elastance, measure myocardial contractility Ea is the

arterial elastance and is measured by the gradient of the line connecting the end-systolic and end-diastolic points

In relation to the PV loop and LV work, we provide an explanation of the work and energy generated by the LV The area within the PV loop represents LV wall muscle work, and is estimated to be approximately 1J (=1000 mJ) in the average adult human LV in one cardiac cycle When the heart rate is around 60 beats per minute, the cardiac cycle length lasts 1.0 sec, and LV work becomes 1.0 W (=1000 mW) When the required nutrition of an adult is assumed to be1800 kcal/day (7536240 J = 1800 kcal×4186.8), and the heart is assumed to consume 10% of the total energy intake, the heart consumes energy of

(1.1) This energy would be the total energy consumed by the heart It includes required for the contraction of all 4 chambers, electrical activity, and metabolism of the heart muscle cells Thus, we can conclude that 11-12% of consumed energy for LV ejection power is wasted

Figure 1.6 Pressure-Volume (PV) loop of the left ventricle Ees is the slope of the end-systolic pressure

volume relationship and represents the end-systolic elastance, which provides an index of myocardial contractility Ea is the arterial elastance and is measured by the slope of the line that connects the end-systolic point and end-diastolic point V0 is a chamber volume with zero pressure (dead space)

Figure 1.7 Peripheral vasculatures and their analog to the electrical circuit components

Table 1.1

Resistance (mmHg/ sec/L)

Compliance (ml/mmHg)

Inertance (mmHg sec 2 /ml)

Arterial capillary 3511.2 0.00535 1.13 Pulmonary venous capillary 11 0.888 -

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properties corresponding to resistance R, capacitance C, and inductance L, respectively (Figure 1.7) Vessel resistance R is defined by the decrease in pressure (pressure drop) caused

by blood flow through relatively narrow vessel diameters with a degree of viscosity, as follows

Pressure drop (ΔP) should be measured between the inlet and outlet of the vessel tube

P proximal and P distal represents the absolute value of the pressure at the proximal and distal

measurement sites Peripheral vessels with small diameters have higher R than central vessels with large diameters Arterial capillary have a higher R than venous capillaries, and systemic

arterial capillaries have a higher R than pulmonary arterial capillaries

Vessel compliance C refers to the volume change with increased pressure It is defined as

follows

(1.3)

where ΔP and ΔVolume mean pressure and volume change inside the vessel, respectively

Because the flow is generated by the vessel volume change with time, the relationship

between the pressure change and flow Q through the vessel can be described with the

following equation

Compliance C is the volume reserve function of the vessel, and the venous system has a higher C than the arterial system This property results from vessel wall elastic motion Inertance is another effect caused by vessel wall motion In the circulatory system, dynamic flow rate changes during a single cardiac cycle Pressure changes when flow increases or decreases within vessels; however, the vessel wall simultaneously has an inertial force that prevents rapid pressure change in response to the flow change This effect causes a

negative pressure gradient within the vessel with constant L

where ΔP represents the potential pressure change or pressure correction within the vessel Inertial force L is higher in the arterial system than in the venous system and higher in central

vessels than in peripheral vessels

These vessel properties combine as in an electrical circuit and can be used to simulate the entire circulatory system This model is termed as ―lumped parameter model‖, because many vessel property parameters for each vessel type are used in model construction Figure 1.8 demonstrates an example of the ―lumped parameter model‖ of the systemic and pulmonary circulation of the Fontan procedure These properties are often used in combination with computer flow simulation models, where peripheral vessel properties may be assumed In

Appendix 1.A.1, the reason why resistance and inertance occur is explained using pipe flow model

Figure 1.8 Electric circuit analog of the Fontan circulation reported by Corcini et al 2014 P: pressure, Q: flow, R resistance, C: compliances, L: inertances, SA: single atrium, SV: single ventricle, PA: pulmonary artery, PV: pulmonary vein, UBA: upper body artery, USV: upper body vein

1.2.3 Wave Propagation and Its Reflection

Despite vessel properties have similarities with electrical circuit components, the actual circulatory system has several bifurcations and is highly complex, i.e it is not structured as a straightforward pipe that entire circulatory system has different characteristics from that of electrical circuit When the pulse wave propagation is considered in the context of a circulatory system, the forward pulse wave collides with vessels at each bifurcation point After the collision, a reflection wave is generated and propagates backwards

In general, the pulse wave is reflected at bifurcation points A measured pulse wave can

be decomposed into the forward and reflection wave Using pressure P and flow Q measurement in a vessel, the forward P f and reflection P r pressure waves are described as follows

c is a wave speed of the pulse, A is the cross-sectional area of the vessel Because the

characteristic impedance is an impedance without reflection,

√∫.

/

The concept of the forward and backward pressure wave is illustrated in Figure 1.9 With

forward flow Q, the pressure P inside the vessel increases in accordance with the

characteristic impedance

Wave propagation is described using the parameter termed Wave Intensity (WI) WI

represents the transmitted energy of the pulse wave Originally it was defined with measured

pressure P and velocity u

Positive WI (WI > 0) represents a forward wave, and negative WI (WI < 0) represents backward wave Here, a forward wave indicates that the wave propagates with flow in a direction away from the pump, whereas a backward wave indicates that the wave propagates with flow in a direction toward the pump (Figure 1.10) WI is a particularly interesting parameter because it provides information regarding the direction of the wave propagation, even though it can be calculated using one measurement point When combined with pressure increase or decrease , indicating compression and expansion waves, wave patterns can be classified into 4 patterns (Figure 1.10)

Wave intensity can be decomposed into positive and negative components

. / . / (1.12)

Figure 1.9 Forward and reflection pressure wave Black solid and dashed lines represent measured pressure and aortic flow, respectively Blue and red solid line represent forward and reflection pressure wave, respectively

where P + , P - represent forward and backward (reflection) pressure wave, respectively like in

Equation (1.6), and u + , u - represents forward and backward (reflection) velocity wave corresponding to their flow (1.10), respectively

Thus, the sum is termed ―Net WI‖

Originally WI was studied to determine the flow wave in arterial systems The first peak detected during early systole is a forward positive wave, and is result of contraction of the LV muscle (Figure 1.11) The second peak detected during late systole is a forward expansion wave and is considered to be due to the deceleration force caused by the ventricular relaxation starting in late systole Presently, these WI analyses can be applied to various situations including artery pulse wave analysis in atherosclerosis or pulmonary arterial pulse wave analysis in pulmonary hypertension with clinical application (Quail et al 2015.) One of the most prominent results of the WI analysis is flow drive detection in coronary arteries (Davies

et al 2006.) Because WI can detect the wave propagation direction, it can clarify the nature

of forces occurring in a system Davies et al demonstrated coronary WI is generated by forward flow through the aortic valve, and by compression and expansion of the capillary within the LV muscle during contraction and relaxation of the LV

Figure 1.10 Classification of wave propagation based on Wave Intensity (WI) Forward wave indicates that flow directs away from the pump, whereas backward wave indicates that flow directs toward the pump Compression and expansion wave indicates pressure increasing or decreasing wave,

respectively

Figure 1.11 Wave intensity (WI) in normal arterial system A: flow and velocity in one cardiac cycle

B: WI in one cardiac cycle WI has two peaks: compression peak and expansion peak (Jones et al

1993)

Figure 1.12 Flow recognition and visualization A and C: Vortex flow in an ocean B and D: Flow inside the vascular lumen with bifurcation A and B: Lagrangian representation, C and D: Eulerian representation

1.3 BASIC THEOREM FORMING BLOOD FLOW DYNAMICS

Richter et al 2006 proposed ―Cardiology Is Flow‖, and they noted the words of Heraclitus (Greek philosopher) ―Everything flows and nothing abides, everything gives way and nothing stays fixed‖ In their editorial, the predicted mechanisms of blood flow causing the cardiovascular disease were illustrated Since then, the flow visualization method has been used in numerous clinical situations

When considering how (Figure 1.12), flow can only be understood when the distribution

of velocity and pressure is completely known There are two ways in describing flow One is based on Lagrangian representation (Figure 1.12A, B), in which flow is described with the moving particle, and the other is Eulerian representation (Figure 1.12C, D), in which flow is described with the fixed coordinate system

Velocity has both quantity and direction and it should be described as a vector

Because blood is a liquid, it is incompressible fluid The fluid dynamics of an

incompressible fluid is determined by 4 parameters, composed of one scalar P and three velocity vector components (u x , u y , u z) at each point in space and at arbitrary time

The mass and momentum preservation equation for an incompressible fluid, called the

Navier-Stokes equation is described in Eulerian representation becomes as follows

⃗⃗ ( ⃗ ) ⃗ ⃗ (1.18) where ρ represents density, and μ represents viscosity In the literature, the ρ of blood is commonly reported to be 1.06 kg/m3, and μ between 0.003 - 0.005 Pa・s when assuming blood is a Newtonian fluid Here, ∂ is a partial differential operator, which differentiates with respect to a defined parameter

in the denominator, while all other parameters are fixed For example, refers to the differential with respect to x, whereas y, z, and t, are fixed Nabla is a vector partial differential operator

. / (1.19) Further, Laplasian is defined as follows

Equation (1.17) is commonly termed the continuity equation, representing the mass flow

preservation law, whereas the Navier-Stokes equation (1.18) represents the flow momentum

preservation law Equations (1.4) and (1.5) can be written with partial differential as follows

/ / (1.22)

/ – / (1.23)

/ / (1.24) Thus, this equation composed of 4 describes for 4 unknown parameters They have one-order partial differential in time, and second order partial differential in space, and have non-linear components The left hand side of the equation (1.18) defines the temporal change in velocity: acceleration multiplied by unit mass giving the force generated by blood per unit volume In the right hand side of the equation, the first term, (the convection term), describes convectional or rotational force, the second term describes flow drive under a pressure gradient, and the third term describes the frictional force resulting from blood viscosity The

Navier-Stokes equation includes only the pressure gradient, not the absolute pressure value,

and relies on an arbitrary uniform constant pressure value as a reference pressure Again we emphasize

that the historical development of hemodynamics started with blood pressure measurement is unusual when considering that the theorem of physics should enable a complete description of organ system physiology or at least, that of a model that is compatible with theory of physics

The momentum preservation Navier-Stokes equation (1.18), (1.22-24) is based on the

Eulerian expression Lagrangian representation which describes the flowing particle (Figure 1.12A, B) can be expressed as follows

⃗⃗ ⃗ (1.25)

The derivative is called material derivative or material time derivative, and the derivative is based on the moving particle The forces given to the moving particles are only pressure gradient and viscous friction forces Thus, the derivative should be expressed in Eulerian partial differentials

(1.26) Thus, the convective term appears after transposing latter terms to the left side of the

Navier-Stokes equation (1.18), (1.22-24) Another characteristic feature of hemodynamics is

the complicated boundary condition applied to the circulatory system Boundary condition is

a technical terms in differential equations referring to values set within the boundary surfaces

of given domain If we consider the fluid dynamics of the circulatory system, boundary conditions should be compatible with the pressure and velocity conditions of each boundary surface of the heart and vascular lumen Generally in problems of fluid physics, either the pressure or velocity should have the absolute value (Diriclet) condition, and the other value have to constant gradient (Neumann) condition In a closed circulation, the wall boundary should be given as the fixed wall shape or their movements as velocity condition Thus, historically, hemodynamic research has dealt with geometrical configurations and change in structure of the heart and vessel wall; however, these analysis have focused only on boundary conditions when considering hemodynamics as fluid dynamics of the circulatory system

1.4.1 Flow Visualization Methods

Blood flow visualization is a method for the detection of blood flow in the cardiovascular lumen The flow visualization method provides the blood flow velocity vector distribution These techniques are novel techniques and some of them are based on complete

measurement, while others are based on calculation of the Navier-Stokes equations (1.17),

(1.18), (1.21)-(1.24) Because they assess visualized flow including vortex flow patterns, they are predominantly based on imaging modalities The methods can be classified into the following two types

1 Flow visualization based on computational modeling (Chapter 4)

2 Flow visualization based on medical imaging (Chapter 2 and 3)

The following chapters describe further details In this chapter, we introduce hemodynamic indices that have been applied to practice and been the focus of previously reported research articles

1.4.2 Computational Modeling

Computational Fluid Dynamics (CFD) is a method that uses numerical computation to solve and analyze fluid flows Recent improvements in computer performance have made CFD a powerful evaluation tool for numerous industries because it reduces time and cost compared with experimental approaches related to fluid flow, and the CFD modeling method has recently begun to be applied The original application of CFD simulation in

cardiovascular medicine was in the Fontan procedure, a congenital open heart surgery for single ventricular physiology CFD has been used to inform selection of surgical procedures Recently, CFD has been used as a noninvasive method of predicting ischemic severity in coronary arterial disease, and later in Chapter 8, hemodynamic research regarding coronary arterial flow and perfusion will be introduced and discussed The process of CFD modeling using clinical imaging data such as CT (computed tomography) slices is illustrated in Figure 1.13

Figure 1.13 CFD (computational fluid dynamics) flow visualization process A case of the aortic arch

of a child After the extraction of a vascular structure from medical image such as CT or MRI slice data, boundary conditions are set to realize the physiological flow The extracted 3D geometry is subdivided with computational mesh to determine the pressure and velocity distribution at each point

Incompressible Navier-Stokes equation is calculated using computers Flow is visualized with the

calculated results

CFD computes the Navier-Stokes equations (1.17), (1.18), (1.21)-(1.24) and provides

spatial and temporal fields of velocity (1.14) and pressure (1.16) in the analysis domain The analysis domain is subdivided into a computational mesh, and velocity vectors (1.14) and pressure (1.16) on each node is provided by calculating the mass and momentum preservation

in each of the subdivided small elements In the CFD calculation process, the Navier-Stokes

equations are solved iteratively until errors in the mass and momentum preservation termed

‗residual‘ becomes sufficiently small (convergence criteria)

The balance between space and time resolution is generally controlled by Friedrichs-Levy condition based on a parameter known as the Courant number

(1.27) where Δx is the spatial resolution (mesh size), Δt is a time step size of the transient

calculation, u represents the representative velocity, and C max is a constant A Courant number

of < 1.0 is recommended,

In CFD analysis boundary conditions should be applied to inlets, outlets and wall surfaces Boundary conditions majorly define the features of flow: inlet boundary conditions should be compatible to the cardiac output, wall motion should be comparable with that observed in actual physiology

Because CFD is a flow simulation, not an actual measurement, there are several advantages and disadvantages With the progress in computational equipment and the sophistication in data analysis processes, recent studies have dealt with a large number of patient-specific models, and enabled establishment of statistically significant evidences However, CFD can be used to create simplified models and arrive at generalized conclusions

We introduced the concept of ―Idealized geometry‖ based on averaged patient data to investigate generalized knowledge related to therapeutic strategies This approach can aid in determining optimal surgical procedure with use of few models with limited calculation cost Itatani et al 2009 used this approach to determine the optimal conduit size and pulmonary arterial size when using the extracardiac Fontan procedure Idealized 3D geometry models based on angiograms were generated for several patients (Figure 1.14)

Another advantage of CFD is ―computerized virtual surgery‖, in combination with 3D computer graphics Virtual surgery enables prediction of post-operative blood flow which improves optimization of operative methods based on individual hemodynamics For example attempted ―virtual coronary arterial bypass‖ using CT data from several patients before the actual surgery, to determine the optimal bypass graft design

Although CFD has the advantage of low invasiveness and virtual simulation, CFD results are largely dependent on calculation assumptions and parameter settings These algorithms and parameters, including boundary conditions, do not always realize the actual physiological blood flow Thus, elaborate modeling strategies for the realization of physiological flow is essential particularly in boundary conditions Many recent studies have adopted the lumped parameter model which uses a combination of circuit components resistance, condenser and impedance to model peripheral arteries as outlet boundary conditions However, the setting of these ―lumped‖ parameters is a cumbersome procedure, and as the number of modeled parameters increases, the accuracy is likely to reduce

Figure 1.14 CFD studies of a Fontan extracardiac conduit reported by Itatani et al 2009

Figure 1.15 MRI flow analysis process After the extraction of cardiovascular lumen, the binarized geometrical mask is superposed with PC MRI data, and blood flow velocity vector is visualized Because MRI has acculturated slices, 3D blood flow with pulsatile fluctuation is reconstructed

1.4.3 Flow Visualization with MRI (Magnetic Resonance Imaging)

Modalities used in flow visualization based on medical imaging are predominantly MRI (magnetic resonance imaging) and echocardiography Flow visualization based on measurements have the advantages of using actual flow information; however, the accuracy

of measurements is not precisely known Temporal and spatial resolutions are particularly insufficient when using current imaging modalities These methods are unable provide explicit pressure information

Figure 1.16 Examples of 4D flow analysis in aortic diseases A: spiral flow inside the ascending aortic

aneurysm reported by Markl et al 2011 B: Visualization of the false lumen flow of the chronic aortic dissection patients are reported by Clough et al 2012

MRI flow measurements are based on PC (phase contrast) MRI PC MRI is a mode of MRI that provides the flow velocity distribution of the direction in which the magnetic gradient fields are generated PC MRI has 4 image series: magnitude and 3 phase image series (Figure 1.15) The magnitude image provides geometrical information; however, the contrast

is insufficient Phase image series has one through-plane flow and 2 in-plane flow (vertical

and horizontal flow) images PC MRI does not require contrast medium Using PC MRI, the blood flow field can be visualized as velocity vectors, a process termed phase velocity mapping In PC MRI, magnitude images depict the vessel geometry and phase images depict the blood flow velocity distribution Recent development of MRI machines has enabled multi-slice phase velocity mapping The accumulation of multiple slices by PC MRI, to determine a time-resolved three-dimensional blood flow field is term ―Four Dimensional flow MRI (4D Flow MRI)‖

Figure 1.17 Echo PIV images of a human LV reported by Hong et al 2008 During ejection (A to C), the direction of the contrast-vector flow was from LV apex to LV outflow tract After the aortic valve closure, in the early isovolumic relaxation (IVR) period, the direction of flow reversed from LV base to apex During mid-late IVR period (E and F), the nonvertical columnar flow was seen directed from base to apex (early ejection: 16 ms after aortic valve opening (A); mid-ejection: 118 ms after aortic valve opening (B); late ejection: 245 ms after aortic valve opening (C); IVR: 32 ms, 80 ms, and 112 ms after aortic valve closure (D to F)

4D Flow MRI is based on in vivo actual measurement, and requires no assumptions in reconstructing flow However, because 4D Flow MRI is a comparatively new flow visualization modality, and post-processing and data acquisition methods for simple post-processing have not yet been completely demonstrated, several case reports with impressive images have recently emerged, but large cohort observation studies have yet to be conducted Figure 1.16 illustrates the application of 4D flow analysis to blood flow analysis in aortic disease Analysis of blood flow in chronic aortic dissection may help predict the prognosis of false lumen from the blood flow feature In applications other than aortic disease, Eriksson et

al 2013 performed pathline analysis in the LV of a DCM patient, and in a normal control, and described that in the DCM case, a higher percentage of the blood flowing from the left atrium stayed within the LV even after one cardiac contraction cycle, compared with the normal control However, current 4D flow MRI has several limitations including poor spatial and temporal resolutions, insufficient imaging contrast, low signal to noise ratio, need to control breathing, and dependency on complicated post-processing (Figure 1.15) Regarding the resolution of the 4D flow MRI, the spatial resolution is 1.0 - 3.5 mm, unsuitable for calculating hemodynamic parameters defined by spatial differentials that are described later The frame rate is approximately 10-30 This value is rather coarse and insufficient for the capture of the peak systolic flow in the aorta or peak diastolic filling of the LV When the fine temporal resolutions in CFD are considered, Courant-Friedrichs-Levy conditions (1.33), the relative coarseness of MRI temporal resolution becomes apparent

1.4.4 Flow Visualization with Echocardiography

When compared with MRI, echocardiography is a portable tool, and has higher spatial and temporal resolution Flow visualization with echocardiography is currently based on 2D imaging Currently, echocardiography flow visualization is largely classified into two groups: B-mode image based methods and color Doppler based methods Echo-PIV (particle imaging velocimetry), first reported experimentally by Kim et al 2004 and utilized clinically by Hong

et al 2008, is a representative B-mode image based method, that traces a speckle pattern of small particles filling the chamber using intravenous contrast medium It is an application of optical PIV (Particle Imaging Velocimetry), a well-known principle allowing the velocity and direction of fluid streams to be determined by tracing small particles In Echo-PIV, intravenous contrast medium is used to trace small particles in the LV (Figure 1.17) It is commercialized by Siemens Medical Solutions Clinical application studies of Echo-PIV have been reported including in post mitral valve surgery, and post myocardial infarction Technically improvements are also reported to visualize 3D vortex flow by combining multi-plane measurements The accuracy of the Echo-PIV system has been validated with moving phantoms Prinz C et al 2012, demonstrated velocity estimation with Echo-PIV is accurate up

to a velocity around 40 cm/s, not always a sufficiently high value when intraventricular flow velocity field measurement is necessary Another B-mode based visualization method is B-flow (Figure 1.18) commercialized by GE Healthcare The B-flow technique uses digitally encoded sonographic technology to suppress tissue clutter and can improve sensitivity for the direct visualization of blood reflectors in gray scale Because this method is based on high frame rate B-mode images, it has been widely applied even to the small-size vessel flow, including that in fetal congenital heart disease, and hepatic vessels, and abdominal visceral

flow However, this method does not provide the flow velocity field, or provide hemodynamic parameters derived from flow velocity fields

The oldest flow visualization using echocardiography is the Color Doppler based flow visualization method first reported by Ohtsuki et al 2006 Their principle is based on the division of flow into basal flow and vortex, defined by the integral of the stream function calculated using color Doppler data toward the azimuthal direction Their methods was initially termed ―Echodynamography‖, and later a commercial package software was released from Hitachi-Aloka Medical, where the velocity vector estimation method was named

―Vector Flow Mapping (VFM)‖ This method was numerically validated with reasonable accuracy (Uejima et al 2010); however, a theoretical problem was detected First the stream function was integrated without boundary condition, and did not satisfy non-slip wall conditions Second, division of basal and vortex flow was non-unique Garcia et al 2011 reported a novel color Doppler based flow visualization method based on the integral of the continuity equation, whose boundary conditions were given by wall motion tracking Their method overcame theoretical weak points of VFM Itatani et al 2013 modified Garcia‘s vector estimation method in weight function of the two solutions of the azimuthal velocity obtained by the bilateral wall boundaries Their method was developed to calculate hemodynamic parameters based on the differential of velocity fields, and Hitachi-Aloka medical updated VFM by adopting their algorism (Figure 1.19) Clinical applications of VFM have begun to be reported Honda et al 2014 presented a case of intra-cardiac repair of Tetralogy of Fallot, which has the post-stenotic dilatation with pulmonary valve stenosis due

to fused commissures In this case, following commissurotomy to relieve pulmonary stenosis, flow EL in the right ventricular outflow tract (RVOT) and main pulmonary prominently was reduced Because this system enables estimation of hemodynamic parameters related to flow energy, a few researchers have used this method to investigate the pathophysiology of diastolic dysfunction Nogami et al 2014 revealed the role of the diastolic flow kinetic energy index in diastolic sucking functions Currently, VFM has several limitations First, because they are based on the 2D continuity equation, the measurement plane should detect main dominant flow Not through plane flow, but its spatial differential that disturbs 2D assumption

of the continuity equation, thus highly distorted 3 dimensional flow is not suitable in VFM analysis The second limitation is the echo window Because it requires bilateral wall boundaries, echo-window should cover the whole heart structure The biggest limitation of the color Doppler dependent VFM is the Nykist limit Current VFM manually collects the aliasing flow, but highly aliased color flow mapping cannot be corrected Current VFM cannot always deal with diseased jet flow in a heart valve case

Another reported flow visualization method using the color Doppler method is Doppler vortography, a unique method of vortex detection based on the red and blue color Doppler mapping pattern Mehregan et al 2014 validated this method with in-vitro PIV and compared vorticity derived from vortography with that derived from VFM Because their method does not rely on information regarding boundary tracking, it‘s the clinical application may be challenging in dilated large LV where the wall edge may be difficult to detect in a single echo window

Figure 1.18 B-flow image of carotid artery flow http://www3.gehealthcare.com

Figure 1.19 Normal LV flow visualized with the VFM (vector flow mapping) in the apical long axis view VFM can visualize blood flow with hemodynamic parameter including vorticity, flow energy loss During systole a clockwise flow in the basal portion of the LV facilitate the smooth outflow flow energy dissipation inside the vortex is small During diastole, two opposite directed vortices are formed beneath the anterior and posterior leaflets of the mitral valve The vortex beneath the posterior leaflet gradually decreases in size and finally disappears, whereas the vortex beneath the anterior mitral leaflet propagates to the apex and gradually increases in size, and flow energy loss gradually decreases, preserving energy for the preparation of the efficient ejection

Figure 1.20 Intraventricular pressure difference or gradient (IVPD or IVPG) based on the color mode image A: color M-mode image with corrected aliasing B: surface mapping of pressure during diastole

M-1.4.5 Pressure Estimation Method with Echocardiography

Greenberg et al 2001 reported a novel concept of ―Intraventriuclar Pressure Difference (IVPD)‖ or ―Intraventricular Pressure Gradient (IVPG)‖ by solving the Euler equation based

on M-mode color Doppler imaging during the diastolic filling phase (Figure 1.20) The Euler

equation is a modification of the Naiver-Stokes equation without the viscous dissipation term

⃗⃗ ( ⃗ ) ⃗ – (1.28)

In their assumption, the M-mode should coincide with the centerline of the diastolic filling flow; thus, the flow direction is one-dimensional, and the equation (1.28) can be changed into one dimension from the basal to the apical portion of the LV

( ) ( ) ( ) (1.29)

Because color M-mode describes the flow velocity distribution with depth (x) and time (t), its partial differential with space (x) and time (t) can be easily calculated with the original color M-mode image Thus, the pressure difference can be obtained

(1.30)

As much as the assumption that the flow streamline coincides with the M-mode beam line is applicable, the pressure distribution can be estimated using this method This method represents a simple and powerful method for the estimation of pressure change and distribution, because the color M-mode has sufficiently high temporal resolution

IVPD has recently attracted attention, because it is closely related to the diastolic sacking force and may provide information regarding the cause of diastolic heart failure (Rovner et al 2005) Chapter 7 will describe the relationship between IVPD generated by the diastolic sucking force and diastolic heart functions

1.5.1 Swirling Flow Indices: Vorticity, Circulation and Helicity

In the vortex flow evaluation, swirling flow direction and strength should be visualized

and estimated One of the traditional and famous parameters is ―vorticity‖ ω

Figure 1.21 Hemodynamic indices in a combined pipe Symmetrical vortices are formed in a larger pipe A: streamline and vorticity Counterclockwise and clockwise vortices are formed in a larger pipe

in the left and right portion, respectively B: High wall shear stress (WSS) are detected around the center

of the vortices Almost zero WSS is found at the top of the vortex, where vertical flow to the wall dose not shear neither upwardly or downwardly C: Flow energy loss is high inside the vortices, but small in the laminar flow

If Green‘s theorem is applied to a region D bounded with closed loop C, Circulation

becomes

∬ ( ⃗ ) ⃗ ∬ ⃗⃗ ⃗ (1.35)

where dA indicates area incremental Thus, circulation is the surface integral of the vorticity

inside a region D Vortex flow structures in the human LV are believed to facilitate smooth

diastolic filling (Martínez-Legazpi et al 2014) or smooth ejection toward outflow (Itatani K 2014); thus, swirling flow characteristics are believed to be important underlying mechanisms