Pedal Force Measurement for Diagnosing Iliac Artery Diseases in

Endurance Athletes

Homme-Auke T. Kooistra september, 2006

BMTE06.46 ID nr: 466367 Eindhoven University of Technology Department of Biomedical Engineering Division of Cardiovascular Biomechanics Supervisors: dr.ir. C. van Pul (MMC) dr. G. Schep (MMC) prof.dr.ir. P.F.F. Wijn (MMC & TU/e) prof.dr.ir. F.N. van de Vosse (TU/e)

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Abstract Introduction Endurance athletes, especially speed skaters and cyclists, may suffer from pain, early fatigue and a powerless feeling in the legs when cycling above specific exercise intensities. These complaints are associated with a disturbed balance between the required and the actual blood flow. The causes of a disturbed balance are iliac vascular diseases, such as stenosis and kinkings. These abnormalities cause, amongst others, a relative decrease in blood supply to the active tissues. Aim This study investigates whether the pain, powerless feeling and early fatigue can be measured by use of independent pedal force measurements during an incremental maximal cycling exercise test. Beside that, this study investigates whether the location of the iliac artery can be determined.

Materials and Methods In total, n=28 cycling related patients with a left unilateral iliac artery disease and n=9 control subjects participate in this retrospective study. The patients were subdivided in respect to the affected common iliac artery (LC), external iliac artery (LE) and the combination of both (LCE). The group sizes were respectively n=5, n=16 and n=7. All performed a maximum voluntary incremental exercise test on a bicycle ergometer (LODE® Excalibur Sport (925900)). Pedal force was measured for both legs using strain gauges, implemented in the crank of the cycle ergometer. Two types of (derivative) parameters were assessed: parameters as a function of the pedal revolution (1) and parameters as a function of the ergometer load (2). The parameters were: (1) Maximum-, minimum and ∆pedal force and as a function of a revolution (2) Maximum-, minimum pedal force, crank angle of maximum and minimum force,

the mean power of revolution, mean power of 90-degree crank angle phase, the mean power of cycling-related-muscle phases and the mean power of muscle phases nourished by the internal and external iliac arteries.

The pedal force parameters as a function of the revolution were analysed by determination of the proportion of patients with the healthiest leg as the strongest leg, in relation to the patients with the abnormal leg as the strongest leg. All pedal force parameters as a function of the ergometer load were post-processed by a algorithm based upon a least summed square fitting technique, in order to asses the data by two linear fits with a forced intersection at the inflection point. The slopes of both linear fits were analysed for all study groups.

Results The results of (1) reveal a suspicious tendency; affected legs perform better at low intensities, and the healthy legs pull by at higher exercise intensity levels. The results of (2) reveal significant different slopes for low and high exercise intensities for the patients’ left leg exerted mean power of two phases of the pedal revolution, namely the 90-180°-phase and the 180-270°-phase (CI=[.134,.668] & p=0.004 and CI=[-.067, -.222] & p

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Contents

Abstract iii

Contents v-vi

Abbreviations xi

Symbols x

Ch. 1 Introduction 11

1.1 Iliac Artery Abnormalities in Endurance Athletes 11 1.2 Aetiology 11 1.3 Decision Algorithm 11

1.3.1 - Patient History, Anamnesis (D.A.1) 12 & Physical Examination (D.A.2)

1.3.2 - Ultrasound Examination (D.A.3) 13 1.3.3 - Ankle/Brachial Index (D.A.4) 13

1.3.4 - Magnetic Resonance Angiography (MRA) (D.A.5) 13 1.4 Aim 14

Ch. 2 Skeletal Muscle 15

2.1 Organisation of the Skeletal Muscle 15 2.2 Contraction of the Skeletal Muscle 16

2.2.1 - Sliding Filament Theory 16 2.2.2 - Force and ATP usage 17

2.3 Metabolism of the Skeletal Muscle 18 2.3.1 - ATP re-synthesis 18 2.3.2 - ATP usage at different levels of exercise 19

2.4 Muscle Fatigue 20 2.5 Oxygen Delivery 21 2.6 An Overview: Muscular Force - Blood Flow 22 Ch. 3 Blood Supply and Vasculature 23

3.1 Anatomy of Iliac Vasculature and related Muscles 23 3.2 Vascular regulation system 25

3.2.1 - Cardiac Output 25 3.2.2 - Vascular Resistance 26

3.3 Vascular Dynamics 27 Ch. 4 Pedal Force Measurement as Diagnostic Tool 29

4.1 Muscle Contraction in Relation to Blood flow 29 4.2 Biomechanics of Pedalling 30

4.2.1 - Muscles used for Pedalling 31 4.2.2 - Pedalling and Blood Supply 32

4.3 Pedal Force Measurement 32 4.3.1 - Cycle Ergometry 32 4.3.2 - Pedal Force Measurement 33 4.3.3 - Calibration 34 4.3.4 - Pedalling Parameters 34

4.4 Pedal Force Measurement as a Diagnostic Tool 34 4.4.1 - Cycle Ergometry Test Protocols 35 4.4.2 - Pedal Force Interpretation – Pedal Force per Revolution 36

4.4.3 - Pedal Force Interpretation – Pedal Power as a function of 37 Ergometer Load

4.4.4 - Analysis Parameters 38

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Ch. 5 Materials and Methods 41 5.1 Subjects 41 5.2 Materials 42 5.3 General Post Processing 42 5.3.1 - Determination of Pedal Force and Workload 42 5.3.2 - Inflection Points (IP) 42 5.4 Detailed Post Processing 45 5.4.1 - Maximum Force as a function of Revolution 45 5.4.2 - ∆Pedal Force as a function of Revolution 45 5.4.3 - Maximum and Minimum Force as a function of 46

Ergometer Load 5.4.4 - Mean Power 47 5.4.5 - Mean Power per 90-degree Crank Angle 47 5.4.6 - Mean Power per Muscle Set 48

5.4.7 - ∆Mean Power of Internal and 49 External Iliac Artery Nourished Phase

5.5 Statistics 50

Ch. 6 Results 51

6.1 General Results 52 6.1.1 - Inflection Points 52 6.2 Detailed Results 52 6.2.1 - Maximum Force as a function of Revolution 52 6.2.2 - ∆Pedal Force as a function of Revolution 53 6.2.3 - Maximum and Minimum Force as a function of 54

Ergometer Load 6.2.4 - Mean Power 55 6.2.5 - Mean Power per 90-degree Crank Angle 56 6.2.6 - Mean Power per Muscle Set 57

6.2.7 - ∆Mean Power of Internal and 58 External Iliac Artery Nourished Phase

6.3 Reproducibility 59

Ch. 7 Discussion 60

D1 Discussion of the Results 60 D1.1 Inflection Points 60 D1.2 Pedal Force Parameters 61 D1.2.1 - Maximum Force 61 D1.2.2 - ∆Pedal Force as a function of Revolution 61 D1.2.3 - Mean Power 61 D1.2.4 - Mean Power per 90° Crank Angle 62 D1.2.5 - Mean Power per Muscle Set 62

D1.2.6 - ∆Mean Power Internal and 63 External Iliac Artery Nourished Phase

D2 General Discussion of Results 64 D2.1 Reproducibility 64 D2.2 Comments and Assumptions in relation to Biomechanics 65 D2.3 Comments and Assumptions in relation to Materials and Methods 65

Ch. 8 Conclusion and Recommendations 67

References 69-71

Appendix A-I 73-96

Dankwoord 97

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Abbreviations ABI Ankle/Brachial Systolic Pressure Index

ADP Adenosine Di-Phosphate

ATP Adenosine Tri-Phosphate

B Bottom Transition Phase

BFsh Biceps Femoris shorthead

CaCo-ratio Ratio of Counter-Acting and Cooperating Forces

CO Cardiac Output

Cr Creatine

D.A. Decision Algorithm

E Extensor Phase

Ex External Iliac Artery

F Flexion Phase

Gas Gastrocnemius

GMAX Gluteus Maximus, Adductor Magnus

HAM Medial Hamstrings, Biceps Femoris longhead

Il Iliacus, Psoas

In Internal Iliac Artery

IP Inflection Point

LC Left Common Iliac Artery

LCE Left Common and External Iliac Artery

LE Left External Iliac Artery

MRA Magnetic Resonance Angiography

MRI Magnetic Resonace Imaging

MVC Maximum Voluntary Contraction

MVF Maximum Voluntary Force

NAD+ Nicotinamide Adenine Dinucleotide (hydrogen acceptor)

NADH Nicotinamide Adenine Dinucleotide

P Phosphate

PCr Phosphocreatine

PF Pedal Force

Pi Free Phosphate Group

PSV Peak Systolic Velocity

RC Right Common Iliac Artery

RCE Right Common and External Iliac Artery

RE Right External Iliac Artery

RF Rectus Femoris

RPM Revolution per Minute

Sol Soleus

SSE Summed Squared Error

T Top Transition Phase

TA Tibialis Anterior

VAS Vastus Lateralis

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Symbols η Viscosity Pa·s α Force needed for initial muscle contracting N β Minimum contracting rate cm/s

mυ Muscle contracting velocity cm/s

µ Mean a.u.

σ Standard Deviation a.u.

τ Torque N·m ω Rotational Speed rad·s-1

ε error a.u

F Force N

F0 load at which the muscle does not change length N

Fm Muscle Force N

Fm,max Maximum Muscular Force N

c constant (Hill's equation) N·cm/s

f rate of myosin-actin attachments 1/s

g rate of myosin-actin detachments 1/s

Q Blood Flow ml/min

P∆ Blood Pressure Gradient mmHg or N·m2

R Vascular Resistance MPa·s/m3

r vessel radius m

L Length m

P Power W

Iflw Moment of Inertia kg·m2

m Mass kg

CO Cardiac Output L/min

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Ch. 1 Introduction 1.1 - Iliac Artery Abnormalities in Endurance Athletes A case study in the Máxima Medical Center in 1993 describes a female triathlete suffering from pain, early fatigue and a powerless feeling in the left leg during cycling above a specific exercise intensity. The subject was diagnosed to have a stenotic lesion in the left external iliac artery [Schep, 1995]. The complaints were reproducible at the same exercise intensity. Chevalier treated 223 patients with cycling related iliac vascular inconsistencies [Chevalier 1991 and 1997]. It turned out that iliac vascular diseases correspond with the previously described complaints. Chevalier categorized three types of lesions: a) lesions in the external iliac artery (90%); b) in the common iliac artery (5%); and c) in the deep femoral artery (10%). Combinations of these types are possible. Nowadays, diagnosis of vascular abnormalities in endurance athletes is based on a series of examinations. In this chapter the aetiology of the disease and the methods for present diagnosis are described. Based on the drawbacks of these well-established methods, the aim of this study will be explained.

1.2 - Aetiology In general, the patients’ complaints are caused by abnormalities in the vessels. Two types of vessel abnormalities may cause a disturbed blood flow [Schep, 1995]. In healthy subjects, flexion of the hip as a result of psoas muscle contraction causes a temporary re-orientation of the iliac arteries; the arteries move more ventral. Since arteries are composed of elastic materials, the arteries will return to their original positions during relaxation. Because of the large number of hip flexions of endurance athletes, vessels near the bifurcation of the communis iliac artery and/or the external iliac artery may become fixated to the psoas muscle or other surrounded tissues. The resulting immobility may cause kinking of the vessel because of surplus of vessel. Due to kinking, the vessel orientation changes, which result in a disturbed blood flow [Bender, 2003]. Another study does not support kinking as the origin of the complaints, but designates stenosis as the initial cause of the blood flow obstruction [Chevalier 1997]. The second cause of blood flow limitation is endofibrotic thickening of the intima. Endofibrosis, the result of abnormal hemodynamic and mechanical stress of the vascular wall, brings on an increased vessel resistance, which in its turn causes flow disturbances. 1.3 - Decision Algorithm As described previously, the diagnosis of abnormal iliac arteries is nowadays established by performing a number of successive tests in order to diagnose and classify the vascular abnormalities in the legs. This decision algorithm (D.A.) includes several examinations and tests: (1) patient history and anamnesis; (2) physical examination with the aim to exclude other diseases; (3) exercise testing with the aim to determine the Ankle-Brachial Index after maximal exhaustion; and (4) echo Doppler examination with the objective of detecting lesions and kinking and of determining flow velocities. When no conclusion can be drawn, Magnetic Resonance Angiography of the vessels (when the hips are flexed) is performed (5). Following this algorithm, a previous study revealed that 82% of the legs in the study group could be classified (59% had a vascular origin and 22% had a non-vascular origin) whereas 13% could not be classified. The remaining 5% of the study

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group stopped with sport activities and therefore those results were inconclusive [Schep 2002-1 and 2]. The clinical decision can be shown as a decision algorithm shown in figure 1.1.

Figure 1.1 Overview of the Decision Algorithm for clinical classification. ? = no convincing outcome (adapted from Schep 2002-1)

1.3.1 Patient History, Anamnesis (D.A.1) and Physical Examination (D.A.2)

Although patient history and physical examination provide very important and significant information, these examinations are not discussed in detail (considering the scope of this report). Anamnesis reveals the complaints of the patients. The complaints appear most frequently in the left leg with a specific distribution along the leg. When rising above certain exercise intensity, the athletes experience pain and fatigue in the quadriceps (medial and posterior side of upper leg) which progresses to the calf [Chevalier 1997, Abraham 1997, Schep 2002-2]. The cause of this distribution may lie in the location of the vascular abnormality. From the abdominal aorta (figure 1.1, 1) blood is distributed to the common iliac artery (4) which provides the whole leg with blood. The internal iliac artery (2) provides the buttock with blood and the external iliac artery (3) provides the blood supply of the legs’ tissue (figure 1.2).

Figure 1.2 X-ray picture of the iliac vessel tree (abdominal aorta (1), common iliac arteries

(2), external (3) and internal iliac arteries (4)

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1.3.2 Ankle/Brachial index (D.A.3)

Next step in the D.A. is the determination of the Ankle/Brachial index (ABI) during intensive exercise (D.A.3). Kinking or stenosis changes the resistance of the vessels as a result of the vessel orientation and/or property changes. Vessel resistance influences the blood flow and blood pressure; a blood pressure drop over the vascular abnormality may occur. Therefore, the blood pressure distal to the region of interest, divided by the blood pressure proximal to the region of interest, is related to the systemic vascular resistance and the peripheral resistance. The resistance of the vascular abnormality can be assessed by the ratio of the systolic blood pressure at the calf or ankle and the systolic blood pressure at the brachial artery (ABI). The ABI should be measured after intensive exercise. The interpretation of the ABI outcome is shown in table 1.1. However, Carman et. al. have determined the ABI at rest. Even though the classification table following exercise differs, this table can give an indication of the severity of the illness. Table 1.1: Classification of Ankle / Brachial index

ABI Classification >0.95 Normal

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1.4 - Aim Complaints of endurance athletes with vascular problems are pain or insensibility, early fatigue and a powerless feeling in the left and/or right leg during intensive cycling. Pain and insensibility may be related to powerlessness. Therefore, measurements of the generated power and force during an intensive cycling test may be an additional tool to detect the complaints/abnormalities. In this study, the assessment of pedal force measurements to diagnose iliac artery disease is investigated. An incremental effort-cycling test was performed on a volunteer study group of endurance athletes. The aim was to develop a suitable method for distinguishing healthy subjects from subjects suffering from iliac artery disease. Different pedal force parameters were determined during specific phases of the pedal cycle. Since most complaints appear to have a specific distribution, the possibility to assess pedal force parameters to identify such a distribution was examined. Additionally, the possibility to locate the disease was investigated.

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Ch. 2 Skeletal Muscle The anatomy and physiology of the skeletal muscle structure, its function and its performance are discussed in this chapter. Specialised muscles (smooth and cardiac muscles) as well as the functioning of the controlling nervous system are not discussed within this report. In section 2.1 the organisation of the skeletal muscle is described. Section 2.2 deals with the theory of contraction, section 2.3 discusses the metabolism of the skeletal muscle and section 2.4 describes muscle fatigue. Section 2.5 and section 2.6 couple muscle contractions properties to its blood requirements. In this chapter, the properties and background of the individual skeletal muscle are explained and in chapter 4 the collaboration of muscles during cycling are discussed. 2.1 - Organisation of the Skeletal Muscle Human muscles can be divided into skeletal, smooth and cardiac muscles. About 80 percent are skeletal muscles and 20 percent the other specialised muscle cells [Guyton]. By complex teamwork of specific skeletal muscles, locomotion and stability is created by developing force on the environment. Cycling (on an ergometer) is a type of locomotion. The skeletal muscle is a highly organized tissue. At the ends, the muscle is enclosed by strong connective tissue, the tendons. The tendons are connected to the bony system which is in direct contact with the environment. Thus skeletal muscles can develop force on the skeleton. A skeletal muscle consists of several fasciculi, all enclosed by the epimysium (figure 2.1 I). Fasciculi are bundled muscle cells or muscle fibres with up to 100µm in diameter and a length of up to several centimetres, lying parallel to each other. Each fascicle contains 150 muscle fibres which are enclosed by the perimysium. Each muscle fibre is wrapped and separated from its neighbouring fibres by a fine layer of connective tissue; the endomysium (figure 2.1 I).

Figure 2.1 The skeletal muscle and its fiber structures (IIA), striated pattern (IIB) and the

Myosin-Actin filaments (IIC).

The muscle cells consist of thousands of smaller functional units that lie parallel to the longitudal axis of the contraction direction. These are called myofibrils and have a size of approximately 1µm in diameter. The muscle cells have multiple nuclei and an abundant

Skeletal muscle

Epimysium

Perimysium

Fascicle

Endomysium

Muscle fiber (cell)

I

Skeletal muscle

Epimysium

Perimysium

Fascicle

Endomysium

Muscle fiber (cell)

I II

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quantity of mitochondria which are needed for the supply of energy. These mitochondria are associated with aerobic metabolism (figure 2.2) [Rodney 1995]. The myofibrils show a repetitive striped pattern which is caused by actin and myosin molecules. Myosin filaments are enclosed by two actin filaments. Each myofibril has about 1500 myosin filaments (or thick filaments) and 3000 actin filaments (or thin filaments). The light bands (as shown in figure 2.1 I - B & C) only contain actin filaments and are called the isotropic bands; I-bands. The dark bands contain both actin and myosin filaments; the anisotropic- or A-band (see figure 2.1 (right) B and C). The repetitive striped pattern can be subdivided in units from the centre of the I-band (Z-line) to the next centre of the I-band. This repetitive unit is the functional part of the muscle with respect to contraction and is called the sarcomeres (2,2 µm in length) [Guyton, 1996].

Figure 2.2 Skeletal muscle fiber and its intracellular structures. The mitochondria are

associated with aerobic metabolism processes

2.2 - Contraction of the Skeletal Muscle In the next section, the sliding filament theory is explained for a thorough understanding of the relationship between the muscles’ anatomy and function, i.e. the muscles’ force and power development in relation to its metabolite requirements. 2.2.1 Sliding Filament Theory

Muscle contraction is a result of shortening of the sarcomeres. The sliding-filament theory is based upon movement of the thick and thin filaments sliding past each other [Huxley, 1957]. The Lymn-Taylor mechanism (figure 2.3) describes the contraction of the sarcomeres using a biochemical process. The myosin cross-bridges attach, rotate, and detach from the actin filaments under influence of energy, provided by adenosine tri-phosphate (ATP) hydrolysis. The resulting products of this cycle are adenosine di-phosphate (ADP) and a development of force at the ends of the Z-line.

I Steady State II IVIII

Actin

Myosin

ATP ADP+Pi

ATP

AD

P+P i

Hydrolysis

I Steady State II IVIII

Actin

Myosin

ATP ADP+Pi

ATP

AD

P+P i

Hydrolysis

Figure 2.3 The Lymn-Taylor mechanism.

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The steady-state actin-myosin cross-bridge is detached as a result of ATP binding to myosin (Figure 2.3; I to II). The lose myosin head rotates into a position where it can attach to the following actin-myosin binding site (II to III); at the same moment the coupled ATP is hydrolyzed to adenosine di-phosphate (ADP). The myosin molecule attaches to the next actin-binding site to form the next cross-bridge (IV) and generates a power-stroke (IV to I). The total of active cross-bridges causes a change of size of the sarcomeres, muscle cells and the muscle. The latter transports the required force to the tendons. [Lymn & Taylor]. Hence, one ATP molecule is needed for one Lymn-Taylor cycle. Within one temporal step, a maximum of 50% of the myosin cross-bridges are connected to the actin filaments. All other myosin heads are between the coupling phases of the cycle. All single cross-bridges move independently over the filaments, resulting in a smooth shortening of the muscle and force developing process. It is also possible that the muscle generates force while remaining at a constant length (myosin heads coupling repeatedly to the same actin binding site) or even increasing length of sarcomere (myosin heads coupling to the previous actin binding site).

2.2.2 Force and ATP usage

For further understanding of the mechanisms and kinetics of force generation, the relation between developed force and ATP usage is examined. Hill [Hill, 1938] examined the dynamic properties of muscles. These properties can be modelled by a number of contractile elements, and non-linear serial and parallel viscoelastic elements. Hill described that the muscular force, generated by a contractile element, is a function of neural activation, length and contracting velocity of each contractile element. The characteristic Hill equation (equation 2.1) describes the force-velocity relationship of each individual sarcomere (=contractile element) during isotonic contraction;

( )( )m mF v cα β+ + = or ( )m m

cF

vα

β= −

+ (eq. 2.1)

with m

F (N) the sum of force generated by the contractile element (or sarcomere), α

the force for initial contracting (N), mv the contracting velocity (cm/s), β the minimum

contraction rate (cm/s) and c is a constant (N·m/s). Huxley [Huxley, 1957] used this model to link the biochemical process of ATP (discussed in section 2.2.1) to the physical process of cross-bridge attachment and detachment. Huxley estimated this relationship to be;

fg

αβ = (eq. 2.2)

with f (1/s) the ratio of myosin-actin attachments and g the rate of myosin-actin

detachments (1/s). Applying equation 2.2 to the Hill equation (2.1) reveals a linear relation between muscular force and myosin attachment-detachment;

2

,max ,max

,

,max

1( )

4

4

m m m m

m c

m

F F cv Ff

FF c g

+ −= = (eq. 2.3)

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where ,m cF is the applied muscle contraction force and ,maxmF the maximum force in N (in

case all cross-bridges are linked). It is assumed that α , β , c and mv are constant and

that α is about a fourth of ,maxmF [Huxley, 1957].

Huxley's model assumes a one-to-one relationship between the kinetics that describe the dynamics of cross-bridge attachment-detachment and the kinetics of ATP hydrolysis. A lot of debate is going on about this subject [Landesberg, 2000, Piazzesi, 2002] but a general agreement concerning a relation between ATP kinetics and force generation is evident. 2.3 - Metabolism of the Skeletal Muscle Equation 2.3 shows that muscular force is proportional to the ATP usage. To have an overview of the relation between blood supply and muscles’ force, this section deals with the relationship between ATP and the metabolites in the blood.

2.3.1 ATP re-synthesis

Skeletal muscle contraction requires energy. Within (muscle) cells, this energy is stored in the form of the high-energy compound, adenosine triphosphate (ATP). ATP is the immediate source for energy necessary for the sliding filament theory (section 2.2). The terminal phosphate bond of ATP releases high free energy when hydrolysed, and

adenosine diphosphate (ADP) and iP (inorganic phosphate) are formed (eq. 2.4)

2 iATP H O ADP P H++ + +� (eq. 2.4)

At different intensity levels of muscle contraction, the ATP should be hydrolysed proportionally [Cain, 1962]. Three different ATP re-synthesises pathways can be described; (1) the breakdown of phosphocreatine (PCr), (2) anaerobic metabolism and (3) aerobic metabolism. The breakdown of phosphocreatine results in an exchange of the high energy bond (P) between phosphocreatine and ADP to form ATP (Eq. 2.5),

PCr ADP H Cr ATP++ + +� (eq. 2.5).

Anaerobic and aerobic metabolism pathways are both initiated by glycolysis. Glycolysis is the breakdown of glucose into two pyruvate molecules forming 2 high-energy bonds available for contraction (Eq. 2.6).

22 2 2 2 2 2 2iglucose ADP P NAD pyruvate NADH H O ATP++ + + + + +� (eq. 2.6)

Subsequently, when no oxygen is available, pyruvate and NADH are converted into lactic acid, which is washed out into the blood. This breakdown of glucose is called anaerobic metabolism. On the other hand, if oxygen is available, the re-synthesis pathway is known as aerobic metabolism. After glycolysis, pyruvate molecules are subsequently converted into two Acetyl-CoA and two NADH molecules. Within the Krebs citric acid cycle the Acetyl-CoA molecules are converted into three substances, i.e. six NADH, two FADH2, and two GTP molecules. NADH degrades into three ATP molecules and the second derivative degrades into 2 ATP molecules. In total, one molecule glucose breaks down to 36 high-energy bonds (for glycogen 38 high energy bonds) available for contraction. Six molecules of oxygen are needed for this degrading process.

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2.3.2 ATP usage at different levels of exercise All three mentioned pathways are time and intensity related. In following section the usage of ATP is described as a function of time and exercise intensity. In figure 2.4 a schematic overview of ATP usage at prolonged maximum exercise is given. Each skeletal muscle cell contains a small quantity of ATP. At the early stage of the exercise, this small amount of ATP stock is used. It lasts only for about two seconds. Nevertheless, it can fulfil all needs for energy during this period.

Figure 2.4 schematic overview of the ATP usage at prolonged maximum exercise.

Beside this process of energy release, the fast phosphocreatine (PCr) pathway delivers energy within the initial period of prolonged maximum effort. PCr is instantaneously available within the muscle cell but first has to disintegrate to form ATP. This energy release lasts for the first 10-20 seconds; the energy available from the breakdown of PCr, increases for the first 5-10 seconds and decreases for the next 5-10 seconds. After this first period the energy supply needs to be maintained by glycolysis in order to continue maximum effort. The re-synthesis of ATP is obtained by aerobic and/or anaerobic metabolism. ATP formed by anaerobic glycolysis increases incrementally from the start of exercise up to 45-60 seconds where it has its maximum of portion of energy production. The aerobic synthesis pathway is fully developed after one minute of exercise, and lasts for a long period depending on the glucose / glycogen stock. The sum of the rate of energy production is at its maximum when the cell stock ATP - and phosphocreatine ATP are used. A decline is visible during anaerobic ATP re-synthesis. A steady state is reached when the ATP usage originates solely from the aerobic pathway. The steady-state rate of energy production is much smaller in relation to the maximum rate of energy production. In this report, a maximum exercise ergometer protocol is investigated, since this is used within the clinical decision algorithm in order to determine the Ankel/Brachial index. During this test, muscle performance increase incrementally (see Ch. 4). Consequently, the ATP usage increases in proportion to the muscle performance. Therefore, the ATP-usage displays a different behaviour than shown in figure 2.7, since maximum effort exercise is necessary at the end of the test. In case of the maximum exercise test, the aerobic ATP re-synthesis pathway produces the required ATP initially. Above a certain level of exercise, this pathway is exhausted. The aerobic and anaerobic pathways contribute together to produce ATP. Since the anaerobic pathway cannot hold for a long period (approx. 60 seconds), in the end all ATP re-synthesis pathways fail. For heavy loads (or long lasting loads) the muscle gets

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fatigued (see also section 2.4). Hence, for the maximum exercise test, the ATP usages from the muscles’ stock and from the PCr pathway can be negligible. Figure 2.5 shows a schematic overview of metabolism and metabolite-blood exchange for resting -, moderate activity - and peak activity muscles.

To myofibrils to support muscle contraction

To myofibrils to support

muscle contractionTo myofibrils to support muscle contraction

To myofibrils to support

muscle contraction

Figure 2.5 Muscle metabolism during different types of exercise. Left - Resting muscle: the produced ATP is used to build energy reserves of ATP, PCr, and glycogen. A relative small amount of oxygen is needed. Middle - Moderate activity: Glucose is catabolized; the produced ATP is used to power contraction. A relative large amount of oxygen is needed . Right - Peak activity: Most ATP is produced through glycolysis, with lactic acid as a residue. No oxygen is needed, lactic acid is washed out. (Adapted from Skeletal Muscle Physiology, Jack F. Yougren).

2.4 Muscle Fatigue At a certain level of exercise intensity and after a certain time period, the muscle becomes fatigued. The definition of skeletal muscle fatigue is not fully clear, but all add up to the same result: a progressive loss of force producing capacity, leading finally to an inability to fulfil the required physical work. In general, fatigue can be divided into two origin-related categories. One is called central fatigue, which is related to the neuromuscular junction and its incompetence of sufficient metabolite delivery, required for the desired level of exercise. This type of fatigue is not discussed in this report, since this kind of fatigue has its origin in the neural activation and not in blood supply. The other type is called peripheral fatigue, which is related to the contractile apparatus and its supplying nutrients (or blood). The exact physiology of peripheral fatigue is not fully understood yet. One explanation of muscle fatigue may be that the ATP stock runs low as a result of a prolonged muscle contraction period at high intensity [www3]. However, Baldwin et. al [Baldwin 2003] were not convinced by this explanation since they measured a sufficient ATP concentration in animal tissue samples after prolonged exercise, capable of maintaining muscle contraction during intensive exercise. Another potential cause of fatigue is an imbalance between the difference in required and delivered muscle glycogen and blood glucose, resulting in a shortcoming of glycogen/glucose stocks. The metabolic processes cannot be kept running. For this study, the latter cause of peripheral fatigue is not of interest, since the time of occurrence of the imbalance (> 90 minutes [Hawley et al. 1997]) is beyond our interest (ca. 10 min) (note: Hawley et al used a moderate exercise intensity). Another essential metabolite is oxygen. Active muscles will create an O2 supply/demand imbalance. At specific exercise level, no extra oxygen can be delivered to the muscle tissue. The non-oxidative ATP production cooperates, from this point, with the oxidative ATP production to maintain the required force. At this point, waste products of anaerobic metabolism are washed out into the blood. This can cause insensibility and pain in the legs [McArdle, 1996]

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Figure 2.9 Endurance Time as a function of Maximum Voluntary Contraction

[adapted from Rohmert, 1968]

The relationship between maximum voluntary contraction (MVF) (contraction until fatigue sets in) and the duration of contraction is known as the Rohmerts’ curve (Figure 2.9). The time period a required force is maintained by a person is expressed as the percentage of the maximum force. The Rohmerts’ curve can also be described by a negative exponential function (Amstrong, 1976). At 15-20% of the maximum voluntary force, the contraction can be held for a long lasting period. However, the MVF can be sustained for approximately 4-6 seconds. The cause of the decline described by Rohmerts’ curve is caused by the occluded blood supply. If the contraction time exceeds the time as described by the curve, the muscle will become fatigued. 2.5 Oxygen Delivery The last step in determining the relation between force generation and blood supply is the oxygen delivery. Oxygen is transported in the blood in two forms. Most relevant is the transportation of O2 using haemoglobin (Hb) as transport molecule. Beside that, oxygen dissolves for a small amount in the blood plasma. Fully saturated Hb carries a limited amount of oxygen (≈ 1,31 mL O2/ 1 g Hb). The percentage of arterial Hb saturation is dependent on the oxygen pressure (PO2) and on the lung function. Assuming a perfect lung, the PO2 equals the arterial oxygen pressure (PaO2). Furthermore it is assumed that no oxygen is used along the arterial pathway to the location of interest. For PO2 > 100 mmHg (normal circumstances in the lungs) arterial hemoglobin saturation can be assumed to be constant and >95%. The oxygen delivery (O2Del) to the entire body is now modelled as;

2 1.31 [ ] %O Del CO Hb saturation= ⋅ ⋅ ⋅ (eq. 2.7).

In here, CO is cardiac output (L/min), [Hb] the concentration of haemoglobin (g/L) and the constant ≈ 1.31 (mL O2/g Hb). Since the Hb concentration and arterial Hb-saturation are constant, the O2-concentration is assumed to be constant in arteries for all aerobic exercise intensities. The amount of required blood (equivalent with CO see Ch. 3) is direct related to the O2 (and ATP) requirements during aerobic metabolism. [Law 1999]

22

2.6 An Overview: Muscular Force - Blood Flow Active muscles need more nutrients and metabolites during force generation with respect to resting muscles. A complex regulation system attempts to regulate the supply of extra blood. This chapter discusses first the increasing ATP usage during a maximum exercise protocol (section 2.3.2). The aerobic metabolism pathway requires 6 molecules of oxygen to form 36 ATP molecules and the anaerobic does not need oxygen for forming ATP molecules. During exercise, the ATP usages increases; the oxygen demands increase proportionally with the aerobic metabolism. Since the O2-concentration is assumed to be constant in arteries for all aerobic exercise intensities, the amount of supplied blood is direct related to the ATP usage. Considering the sliding filament theory, ATP is used for the detachment/attachment rate of myosin to actin filaments. This coupling and decoupling of cross-bridges is proportional to the generated force. Therefore, the blood flow to the muscles is related to the exercise level for near-maximal exercise intensities [MacIntosh B.R. 2000].

23

Ch. 3 Blood Supply and Vasculature In this chapter, an overview of the anatomy and physiology of the vascular system is given. First, the organisation of the iliac vascular system is described. Then, the blood supply during exercise and its regulation systems are discussed. In section 3.3, the vascular dynamics of the abnormal legs by use of simple model. 3.1 Anatomy of Iliac Vasculature and Related Muscles Endurance athletes suffering from a vascular disease have complaints related to abnormalities in the supplying blood vessels. In chapter 2, the muscle fatigue caused by an imbalance in O2 supply/demand is described. It is assumed that, as result of a reduced blood flow, the onset of anaerobic metabolism starts at relative lower exercise intensities. An early usage of the anaerobic pathway explains the complaints of the athletes. In this section, the anatomy of the muscle supplying vascular system in relation to the musculature is discussed.

Figure 3.1 Artery trees of the lower extremities and its nourished muscles. Left hand side: Artery tree for the lower extremities (capitals). Right hand side: Leg Muscles that are nourished by the lower extremity arteries (small letters).

24

R L

Lat. (R) Lat. (R)

R L

Lat. (R) Lat. (R)

Figure 3.2 Lower extremity muscles

In figure 3.1, a schematic representation of the lower extremity arteries and their nourished muscles is shown. Figure 3.2 shows the nourished muscles in a true-to-life representation. (In this section, capitals indicate arteries and small letters indicate muscles.) From the abdominal aorta (A) oxygenated blood is transported in the caudal direction to both the left and right common iliac artery (B). The left common iliac artery branches at the level of the fourth lumbar vertebra, from the right common iliac artery. Both common iliac arteries branch in the pelvis, on top of the psoas muscles. Here, each common iliac artery bifurcates in the internal- (C) and external iliac artery (D). The internal iliac artery and its main branch provide the pelvis and the Gluteus Maximus and Iliopsoas (a) muscles of blood. At the inguinal ligament (=region that supports the groin), the external iliac artery changes into the femoral artery. The external iliac artery takes care of the blood supply to most of the tissues in the lower extremities. One of the main branches of the femoral artery is the deep femoral artery. The deeper parts of the femoral artery supply the anterior (Adductor Magnus (b)) and medial thigh muscles and its ending branches, the Hamstring muscles (Semitendinosus, Semimembranosus (b)) with oxygenated blood. The branches of deep femoral artery, amongst others, take care of the blood supply of the Biceps Femoris (short and long head) (b). The deep femoral artery bifurcates into the lateral circumflex and medial circumflex (E). The lateral circumflex passes the Satorius (c) and the Rectus Femoris (c) and divides into (1) the transverse branch for blood supply of - among other anatomies - the Vastus Lateralis (c), (2) into the ascending branch for blood supply of Rectus Femoris (c) and (3) the descending branch for blood supply of Vastus Lateralis and Vastus Intermedius (c). The lower leg receives its required blood from the femoral artery. At the popliteal space (back of the knee), the femoral artery converts into the popliteal artery and bifurcates into the anterior tibial artery (F) (supplying the Tibialis Anterior (d)), the posterior tibial artery (G) (supplying Soleus, Gastrocnemius and Plantarflexors (e)) [www1, www2]. In each leg, two major arteries take care for the delivery of nutrients. In Table 3.1 is shown that the Rectus Femoris, Vastus lateralis Gastrocnemius, Soleus, Plantar Flexors and the Tibialis anterior are purely fed by the external iliac. The Iliacus and the Psoas are provided by blood by the internal Illiac artery. Both iliac arteries supply all other muscles.

25

Table 3.1: Lower extremity muscles categorized by blood supply and Raasch et al. muscles set (Fig. 4.1)

Muscle Internal/External Blood supply set

Medial circumflex femoral artery, inferior gluteal artery, obturator artery,

Adductor Magnus external/internal and some superior muscular branches of popliteal artery GMAX

Inferior and superior gluteal arteries and the first perforating branch

Gluteus Maximus internal/external of the profunda femoris artery

Perforating branches of profunda femoris artery, inferior gluteal artery,

Medial Hamstrings external/internal and the superior muscular branches of popliteal artery HAM

Perforating branches of profunda femoris artery, inferior gluteal artery,

Bicepsfemoris lh external/internal and the superior muscular branches of popliteal artery

Rectus Femoris external Lateral circumflex femoral artery RF

Vastus lateralis external Lateral circumflex femoral artery VAS

Gastrocnemius external Each head supplied by a sural branch of the popliteal artery GAS

Soleus external Posterior tibial, peroneal, and sural arteries SOL

plantarflexors external Sural arteries

Tibialis anterior external Anterior tibial artery TA

Perforating branches of profunda femoris artery, inferior gluteal artery,

Bicepsfemoris sh external/internal and the superior muscular branches of popliteal artery BFsh

Iliacus internal Lumbar branch of iliopsoas branch of internal iliac artery IL

Psoas internal Lumbar branch of iliopsoas branch of internal iliac artery First column represents lower extremity muscles; second column represents which artery (the internal- or external iliac artery) provides the muscle

of blood; third column shows the precise anatomy of the supplying vessel tree; and last column represents the muscle sets as declared by Raasch et

al. (see Ch. 4).

3.2 Vascular regulation system 3.2.1 Cardiac Output The extra blood needed for an increased blood flow during exercise, is supplied by an increased cardiac output (CO). CO is the amount of blood pumped by the heart. At rest, the CO is low (approx. 5 L/min). During exercise, a large amount of nutrients is needed, and therefore, a large amount of blood is pumped to the nutrient demanding tissues. The product of the heart rate and its stroke volume determines the CO. For trained subjects the cardiac output is at rest about 5 L/min (heart rate = 50 beats per minute (bpm) and the stroke volume = 100ml). If the assumption is made, that CO in each individual is approximately the same (men≈5.6 L/min woman≈ 4.5 L/min) [Guyton], it becomes clear that untrained subjects have a lower stroke volume and consequently a higher heart rate. Blood flow increases proportionally with the exercise intensity. The cardiac output increases rapidly from rest to moderate exercise, followed by a gradual increase until a steady state is reached. The maximum heart rate is equal for untrained and trained subjects. However the required blood for the activated tissues is larger in trained subjects. Consequently, the stroke volume must be the cause of the proportional increase in blood flow in trained subjects. Table 3.3 summarises CO, heart rate, stroke volume for untrained and trained subjects during rest and exercise [McArdle 1996]. Table 3.3: Heart rate, stroke volume and cardiac output at rest and exercise

Subjects Heart Rate [bpm]

Stroke Volume [ml]

Cardiac Output [L/min]

Untrained at rest 70 71 5 Trained at rest 50 100 5 Untrained at exercise 195 113 22

Trained at exercise 195 179 35

26

The increased CO is needed to fulfil the demands of the active skeletal muscles. During rest, the blood is distributed according to the needs of all tissues. Skeletal muscles at rest receive about 20% of the cardiac output. Blood flow during exercise is distributed differently and depends on the metabolic demands of the muscle during physical activity. At rest, about 4 to 7 ml of blood is delivered to each 100 g of muscle tissue, at maximum exercise this amount of blood is about 50 to 75 mL per 100 g of muscle tissue. This means that during maximal exercise about 21L of 25L blood flows through the muscles capillaries (>80%)[McArdle 1996].

3.2.2 Vascular Resistance The second regulation system that maintains an adequate blood flow during exercise is the vascular regulation system. Vascular control of the blood flow can be achieved by changing vessel radii (vasodilation and vasoconstriction). The precise mechanisms are complex. It is assumed that the ability of the endothelium to sense chemical substances and hemodynamic loads upon physical forces applied to the vessel wall, regulate the blood flow in muscles [Murrant 1999, Delp, 1998]. Skeletal muscles in rest show a high degree of vasoconstriction, which is caused for instance by the secretion of nor-epinephrine. The effect of nor-epinephrine can be cancelled out by epinephrine. Vasoconstriction will then not be maintained, which results in an increase in vessel diameter . Hence, the vessel resistance is reduced and an increased blood flow is achieved. This relative slow regulator is called vasodilation and takes place during prolonged exercise. The resulting increased mean muscle blood flow is called active hyperaemia [Robert C. Hickner]. Besides the nor-ephedrine/ephedrine-system, a complex of other factors regulates vasodilation which is induced by muscle activity (reactive hyperaemia). It includes local metabolic control and endothelium-mediated control [Murrant 1999]. A bulk of metabolites is considered to work along in reactive hyperaemia (Granger 1984, Laughilin 1996). For example; as result of muscle contractions, changes in oxygen pressure, potassium and adenosine concentration act in order to rule out the vasoconstriction. However, more exercise induced vasodilation regulators exist; metabolic control seems to be an important factor (Delp, 1998). 3.3 Vascular Dynamics (Model) In this section a simple model for the circulation is reported. This model will describe the blood flow through the legs in which one leg is has a vascular abnormality. In general, the flow in a vessel can be described analogous to Ohm’s Law (eq. 3.1).

/Q P R= ∆ (eq. 3.1)

In here, the blood flow (Q in ml/min or m3/s) in a vessel is inversely proportional to the vascular resistance (R in MPa·s/m3) and proportional to the blood pressure gradient over the a vessel (∆P in mmHg or N·m-2). No blood will flow when the blood pressure gradient is zero. The pressure gradient is generated by the heart. Since mean arterial and venous pressure are normally maintained within narrow limits, blood flow is regulated by the fluctuation in vascular resistances [Delp 1998]. The vascular resistance is proportional to the length and radius of the vessel and to the viscosity of blood, as represented by Poiseuille’s law, in equation 3.2.

4

8 LR

r

η

π∝ (eq. 3.2),

with, R the vessel resistance, L the length of the vessel [m] and r the radius of the vessel and [m]η the viscosity of blood [Pa·s]. A fourth power dependency of the resistance to

blood is obtained by means of the vessel radius. Blood flowing near the vessel wall has a larger adherence to the vessel wall than the inner flowing blood.

27

Combining equation 3.1 and 3.2 yields a relationship between the blood flow in a vessel and the applied pressure gradient:

4P r

8Q

L

π

η

∆= (eq. 3.3)

When keeping the blood pressure gradient constant, an increasing radius result in an increasing flow with a fourth power of this radius. A case model is described in which the vascular abnormality is located between the common iliac artery and the external iliac artery. The analogous to electrical circuit is represented in figure 3.2. In this model, a constant pressure gradient is applied (∆PT). A resistance (RA) proximal to the bifurcation of abdominal aorta and both common iliac arteries is introduced. At this bifurcation, the flow split into a left (or diseased) branch and a right (or normal) branch (QD and QN). Blood experiences the same resistances in the left (L) and right (R) branch: Common Iliac Artery Resistance, External Iliac Artery Resistance and the Peripheral Resistance, RCIA, REIA and RP respectively. However, the left branch contains an extra resistance RD that represents the vascular abnormality (stenosis/kinking).

Q=Flow, ∆P=blood pressure gradient over vessel, T=Total, L=Left, R=Right, D=Diseased and N=Normal

Figure 3.2 Schematic flow circuits for left and right leg.

The heart pumps the blood with certain pressure gradient (∆PT). In patients, the blood experiences different resistances for left and right leg:

-Left leg: RA, RCIA, RD, REIA, R -Right leg: RA, RCIA, REIA, RP

The total resistance of this case model is,

1 1

/ / / / / /

1 1 1 1T A A

CIA L EIA L D P L CIA R EIA R P R D N

R R RR R R R R R R R R

− −

= + + = + + + + + + +

(eq. 3.4)

Consequently, the total flow (QT) can be represented by:

1

1 1

TT

A

D N

PQ

RR R

−=

+ +

(eq. 3.5)

Symbol Resistance of

RA Proximal of Abdominal Aorta bifurcation

RCIA Common Iliac Artery

REIA External Iliac Artery

RD Abnormality / Disease

RP Peripheral Resistance

28

And the flow for left and right leg can be represented by:

DD

D

PQ

R

∆= and NN

N

PQ

R

∆= (eq. 3.6 & 3.7)

Firstly, a flow that is distributed equal over left and right leg is assumed. In healthy subjects, this means that the pressure gradient over left and right leg is similar. However, in case of a diseased subject the RD > RN and a difference in the blood pressure gradient between the left and right leg can be observed. However, within this report it is assumed that the vascular abnormality causes a disturbed blood flow. For an easy assessment, the left and right pressure gradients are considered to be equal. This implies that the local blood flow is inversely proportional to the resistances of the left and right leg. This model gives a schematic and global interpretation to understand the basics of the vascular dynamics. The precise regulation of flow dynamics with respect to distribution between left and right leg is not described in this model. The required blood flow is determined by the peripheral resistance, but when proximal stenosis/kinking occurs, the required blood flow cannot be delivered. Thus, the hypothesis is that the origin of patients’ complaints lie in a imbalance between nutrient requirement and supply as result of a flow restriction in the painful area. As a result of a decreased vessel diameter (or increased vessel resistance) at the location of the disease the blood flow is decreased. The assumption was made that the oxygen or blood requirement increases linearly with muscle activity and that this requirement can only be achieved when the diameter of the supplying vessel is sufficiently large. It may be concluded that lesions/ kinkings reduce the flow to the goal tissue and stays behind according to eq 3.5.

( )

4

maxmax

4 4

max max

P (r r)Q Q

8 L

PQ (r r) -r

8 L

π

η

π

η

∆ + ∆+ ∆ =

∆∆ = + ∆

(eq. 3.8)

where maxQ Q+ ∆ is the required blood flow. The maximum blood flow that can be

achieved as result of stenosis/kinking is maxQ . So, the lack is Q∆ and can be derived by

eq. 3.8.

For example, if the muscle requires maxQ Q+ ∆ = 100%, and the diseased area has a

radius reduction of 25%, the deficit is Q∆ = 68%.

29

Ch. 4 Pedal Force Measurement as a Diagnostic Tool In the previous chapter, a description of the relationship between the properties of muscle contraction and heamodynamics was given. This relationship may be used in clinical practice in order to assess the complaints of the patients. By determination of muscle contraction forces at different intensity levels, vascular abnormalities could be diagnosed. Before the latter is discussed, the different types of contraction in relation to the muscles’ inflow of blood are described. Furthermore, the use of cycling and its biomechanics in relation to the blood supply is discussed. This is essential for a thorough understanding of the individual muscle involvement during a pedal cycle by means of muscle on- and off-phasing. Finally, the influence of iliac vascular abnormalities on the outcome of the cycling tests (or pedal force measurements) is discussed. 4.1 - Muscle Contraction in Relation to Blood flow Three parameters can be used to describe muscle contraction, namely time, displacement and load. Different types of contraction are possible: (1) isometric contraction and (2) isotonic contraction, which can be subdivided into concentric contraction and eccentric contraction. Contraction while maintaining the same muscle length is called isometric contraction (1). All sarcomeres cooperate to develop a constant muscle tension while maintaining the same muscle length; some sarcomeres shorten and others lengthen [Guyton]. Isotonic contraction (2) is a term for muscles that shorten (concentric) or lengthen (eccentric) while maintaining the same tension as a result of applied load. During concentric contraction, the muscle is able to shorten under its applied load. In the case of eccentric contractions, the load is too big. Although the muscle lengthens, it contracts at maximum effort. The tensions at the tendons are larger than the load working on it for concentric contraction and smaller for eccentric contraction. Locomotion doesn’t involve one single muscle. Different muscles groups, acting at different time intervals and contraction intensities, cooperate in developing a stable movement. Besides, the type of contraction differs per muscle. For example, the contraction of the Vastus Lateralis during the downstroke phase of pedalling may be considered as a combination of eccentric, concentric and isometric contraction [Komi 1973]. Other combinations of contraction types are possible. The blood flow response as a result of isometric contractions is different during periodic rhythmic concentric contractions. At the onset of isometric contraction, the mean blood flow decreases as result of an arrested inflow, followed by a blood flow increase as result of (reactive) hyperaemia (see figure 4.1). [Brodal, P. et al, 1976]. However, during rhythmic concentric contraction cycles (fast contractions followed by relaxations) mean blood flow increases and blood flow fluctuates with respect to the contraction cycles. In the action phase (contraction) the blood flow decreases and during the relaxation phase the blood flow increases (see figure 4.1) [McArdle]. An explanation for the increasing mean muscular blood flow at the onset of dynamic exercise is the contraction itself. Muscle contraction and relaxation result in a draught of blood at the supplying blood vessel. After contraction, a sudden lowering of venous blood pressure causes an inflow of blood in the arterial side of the muscle [Hickner, McArdle]. A wide variety of combinations between contraction types exists. All have their own specific blood flow response.

30

Figure 4.1 Blood flow response to sustained (dashed) and rhythmic (solid) contractions. (adapted from McArdle and www4)

4.2 - Biomechanics of Pedalling Pedalling is a combination of complex dynamics of the ankle, knee and hip joints and muscle functioning. The total functioning of lower extremity dynamics during cycling is beyond the scope of this report. However, muscle coordination and recruitment during the pedal cycle is necessary in prospect of using pedal force measurements as a tool for diagnosing iliac artery abnormalities. 4.2.1 Muscles used for Pedalling

Cycling involves various combinations of contractions. All lower extremity muscles cooperate to exert force to the pedal. Each leg consists of 32 muscles, delivering energy within the sagittal-plane. Raasch et al. [Raasch et al., 1997] used electromyography (EMG) data to rank these muscles in functioning during maximum-speed pedalling. A total of 15 main cycling contributors were observed which were reduced to 9 muscle sets (see table 3.1 and 4.1) Figure 4.2 shows a schematic representation of these muscle sets with respect to the cycling position.

0 50 100 150 200 250 3000

20

40

60

80

100

120

140Blood Flow Response to Muscle Contraction

time [-]

Muscle

Blo

od F

low [-]

rhythmic contraction

sustained contraction

0 50 100 150 200 250 3000

20

40

60

80

100

120

140Blood Flow Response to Muscle Contraction

time [-]

Muscle

Blo

od F

low [-]

rhythmic contraction

sustained contraction

31

Figure 4.2 Main cycle contributors of the nine muscle sets with respect to the cycling position

and the phase of functioning. [Raasch, 1997]

Cycling is a repetitive movement of the leg. If the crank is in a vertical and upward position (0°), the leg is maximally flexed. The leg extents during the down stroke; the crank moves clockwise until the leg reaches maximal extension at a vertical and downward position (180°). From maximal extension, the leg flexes during the upstroke (from 180° to 360° ). Primary functions of the extensor and flexor muscles are to generate perpendicular forces (or effective forces) on the pedal by accelerating the limb. The muscle sets that extent the leg, are the VAS and GMAX. The muscles of the extensor group (E) (see figure 4.3) excite between ca. 337-134 degrees. The IL and BFsh develop force in order to flex the leg. The flexor group muscles (F) excite between ca. 149-324 degrees. No effective force (parallel to the crank) is applied to the pedal at the transition between extensions and flexion phases. During the transition regions, energy is transferred from the limb to the crank and provides propulsion. The muscle group RF works during the top transition (T) between the flexor phase and the extensor phase (ca. 241-35 degrees) and the HAM / SOL / GAS work during the bottom transition phase (B, ca. 72-228 degrees) Figure 4.2 shows these phase-controlled functional regions (T, E, B and F) [Neptune, 1997]. Other studies investigated with EMG on- and off-phasing of muscles during cycling [Brown 1997, Neptune 1997, Raasch 1997, Hull 1985, Neptune 1999, Brown 1996, Gregor 1985]. From these studies, the average crank angles, during which the defined muscles are active, were determined (figure 3.2 and appendix A).

In

In/Ex

Ex

Ex

Ex

In/Ex

In/Ex

In/Ex

Ex

Ex

Ex

In

In/Ex

Ex

Ex

Ex

In/Ex

In/Ex

In/Ex

Ex

Ex

Ex

Figure 4.3 Mean activity per muscle group distributed over the pedal cycle. In = muscle

groups nourished by the internal iliac artery. Ex= muscle groups nourished by the external iliac artery

32

The maximum generated force of the muscle groups during one individual revolution gives information about the contribution of each muscle group. Since force cannot be determined directly in EMG experiments, Raasch et al simulated the peak isometric force that the muscle can develop during maximum-speed pedalling. (table 4.1) [Raasch et al. 1997]. Table 4.1: Peak isometric force for muscle groups [Raasch et al. 1997]

Muscle Group GMAX HAM BFsh Vastus RF IL/Ps GAS SOL TA

Peak Isometiric Force (N) 1250 1300 502 2125 974 788 2225 3550 1375

From these data it can be concluded that the lower leg muscles (GAS and SOL) contribute significantly to maximum speed pedalling. Muscle groups with less significant contribution are the BFsh and IL.

4.2.2 Pedalling and Blood Supply

In chapter 3, the anatomy of the artery tree with respect to the lower extremity muscles was discussed. A distinction was made between muscles nourished by the external iliac artery and by the internal iliac artery. Combining the muscle on- and off-phasing during a pedal cycle (figure 4.3) and the vessel anatomy (figure 3.1), it can be possible to predict which muscles are affected by kinking/stenosis in one of the arteries. The contribution of the muscles nourished by the internal iliac artery is distributed over the whole pedal cycle. However, the contribution of these muscles to the exerted pedal force is expected to be larger during the upstroke phase with respect to the contribution of the muscles nourished by the external iliac artery. It must be noted that the iliacus, the psoas (upper leg muscle) and the Tibialis Anterior (lower leg muscle) cover most of the upstroke phase. Most of the muscles fed by the external iliac artery are distributed over the whole pedal cycle, but again there is a significant contribution during the downstroke phase of the pedal. According to Raasch, muscles nourished by the internal iliac artery are most active within the F and T phase. However, muscles fed by the external iliac artery show most activity within the E and B phase. 4.3 Pedal Force Measurement In this section, the setup for measuring pedal force is described. 4.3.1 Cycle Ergometry

Cycle ergometry is based upon the principle that subjects conquer enforced power by varying resistances applied to the flywheel of the ergometer by use of pedalling. Figure 5.1 shows a schematic representation of cycle ergometry.

Flywheel Subject

flw flw flwP Rv I αω= + P

Fr

τω

τ

=

=

R

F

Flywheel Subject

flw flw flwP Rv I αω= + P

Fr

τω

τ

=

=

R

F

Figure 4.4 Schematic visualisation ergometry

33

The power of the flywheel (Pflw [W]) is described by equation 4.1:

flw flw flwP Rv Iτω αω= = + (eq. 4.1)

with, τ = torque [Nm], ω = the angular velocity of the flywheel [ -1rad s⋅ ], vflw = the

velocity of the flywheel [-1rad s⋅ ] at the applied breaking resistance R [N], Iflw = the

moment of inertia [2kg m⋅ ] and α = the angular velocity [ 2rad s−⋅ ].

A subject can conquer the power of the flywheel by delivering force (F) perpendicular to the pedals. The produced power of the subject is described by equation 4.2,

subP F rτω ω⊥= = (eq. 4.2)

In here, Psub = the power of the subject [W], F⊥ = the force perpendicular tot the crank

[N], r the crank length [m] and ω = angular velocity [ -1rad s⋅ ] (Revolutions per Minute, RPM is more often used). Both rotational systems are coupled rigidly: the produced power of the subject is equal to

the enforced powersub flwP P= . By varying the breaking resistance of the flywheel, the

power needed to rotate the flywheel can be controlled. Consequently, the power exertion (or the applied pedal force with respect to the RPM) of the subject can be determined. 4.3.2 Pedal Force Measurement The force exerted by the subject, to overcome the breaking resistance of the ergometer, can be measured by several applications: applications on the pedal crank, rear hub, crank spindle, chain or at the bracket (Shimano). In the Máxima Medical Centre an Excalibur (Sport) Ergometer of Lode BV Medical Technology, The Netherlands, is used. This cycle ergometer measures pedal force by use of so-called strain gauges. In this set-up the strain gauges were fixed on both cranks (figure 4.5).

Figure 4.5 (A) Schematic representation of the strain gauge. (B) Strain gauges in unloaded

(left), elongated (middle) and compressed state (right) and the corresponding reactive resistance change (lower). (C) Positioning of the strain gauges (at the pedal cranks

Strain gauges are sensors using electrical resistance changes as result of deformation of the sensor. Within two polymer foil sheets, a long electricity conducting wire with a diameter of ca. 0,0025 cm is wound in a parallel configuration (figure 4.5A). If this conductive metal wire is exposed to an outwards orientated force parallel to the configuration, the wire will decrease in diameter and increase in length. Hence, the resulting electrical resistance is larger than in the resting configuration. A compressive

34

force decreases the length and increases the diameter of the wire and decreases the electrical resistance. If the applied deformation is kept within elastic material properties of the foil sheets and wire, the resistance is linearly proportional to the applied force. Hence, the coil can be used as a sensor for measuring force (figure 4.5 B). The strain gauge resistance can vary from 30Ω to 3 kΩ. Strain gauges implemented in a Wheatstone bridge circuit result in a system that can be used to measure small changes in resistance. The strain gauges are glued to the inner side of both pedal cranks. Deformation of the pedal crank as result of applied force, corresponds with the deformation of the strain gauge. The precise positioning and orientation of the strain gauges are not known since this is confidential. A calibration process is needed to obtain the linear force-resistance relationship. 4.3.3 Calibration

Lode B.V. uses a calibration technique for their ergometer by adjusting the flywheel load

such that the error beneath 100 Watt is 100Wε<

35

4.4.1 Cycle Ergometry Test Protocols Pedal power protocols can vary in different duration and intensity. A Maximum exercise intensity test is an ergometry protocol in which the ergometer load increases incrementally with time. The increment of flywheel load is individually adjusted, so that the maximum power of the subject is reached within 8 to 10 minutes. The subject exerts force to the pedals, resulting in a torque. The mean delivered torque should increase incrementally until the subject is exhausted and cannot conquer the ergometer load. However, the subject should maintain a constant pedal frequency. It is essential, that the ergometer load increases linearly, so that it can be used as a reference. 4.4.2 Pedal Force Interpretation – Pedal Force per Revolution

Figure 4.6 shows the exerted force of one leg for one revolution at different intensity loads. The pedal force graphs are shown for three subjects. Positive forces (or cooperating forces) are obtained during the downstroke of the cycle and negative forces (or counteracting forces) during the upstroke of the cycle.

Figure 4.6 Pedal Force Graphs of left leg for a healthy subject and two patients at 100W, 150W and 200W

No force is measured at a crank angle of zero degrees (the crank is orientated in a vertical upward position = Top Transition state). Although the limb applies force to the pedal (gravitational forces), this is not measured because the force vector that is orientated perpendicular to the active direction of the strain gauges. Maximum force is applied at a crank angle of approximately 90°. During the bottom transition state (B), again no force is measured for the same reason as discussed for the top transition state. Within the upstroke phase (F) negative forces are measured as result of gravitational and inertia effects. A person can cancel this negative force, by lifting the leg with the same velocity as the opposite leg pushes its downstroke. Since this is relatively hard and difficult to control, most subjects fail to completely neutralise the gravitational forces. Hence, negative forces are the consequence. In figure 4.6, in spite of similar appearance, relevant differences can be seen. At 150W of ergometer load, three different distributions of the pedal force can be observed. All tend to have sinusoidal curves. Relatively large forces within the downstroke phase result in relatively large negative forces within the upstroke phase (patient 1). Relatively small forces within the downstroke phase result in relatively small negative forces with in the upstroke phase (control). This relationship between downstroke and upstroke phase is the result of a fixed ergometer load. The summation of the applied forces during the revolution is linearly related to the ergometer load when constant angular velocity is assumed. At higher loads, less variations between subjects can be seen.

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Figure 4.7 shows the sinusoidal pedal force courses for left and right leg. Because of the crank positioning a phase difference of 180 degrees between left and right legs exists. The pedal force measurements are performed independently (see figure 4.5). However, the legs are connected to each other by a rigid crank-axis-crank system. The consequence of this mechanical connection is that the performances of the left and right leg are dependent of each other.

Figure 4.7 Inter-leg compensation factors (1 and 2) and Intra leg-compensation factor (3).

First, let’s consider the hypothesis that both legs perform equally and that exactly the same power is exerted. If more power is exerted during a specific phase in one leg, the other leg can exert less force, since the total exerted force of left and right leg must conquer the ergometer load. Now consider a patient in whom one leg cannot fulfil its tasks during a specific phase of the revolution. The other leg fills this gap of force. It may be concluded that the other leg compensates to generate sufficient power. For example, in figure 4.7-1 a small increase in force during the upstroke phase (negative forces) for one leg can be observed (at the location of the arrow at about a crank angle of 70 degrees). As a reaction on this increase, a lower force is observed within the downstroke phase of the other leg. In other words, a leg compensates the shortcoming of the other leg. In patients, this compensation could be used for diagnostic purposes. From now on, this phenomenon is referred to as inter-leg compensation. The inter-leg compensation factors are also revealed within a larger angle of the revolution. Figure 4.7-2 show within a crank angle of 0-180 degrees relative larger forces within the downstroke phase of one leg together with relative larger negative forces for the other leg with respect to the 180-360 phase. Possible explanations can be; a leg that is not able to conquer the enforced load, a leg that rests during the specific phase or a leg that is relatively inactive. Beside the inter-leg compensation factor, another compensation factor can be introduced, namely the intra-leg compensation factor. Figure 4.7-3 shows such a compensation factor. Since the total exerted force of both legs per revolution are used to conquer the applied ergometer load, a deficit of one leg in exerted force during a specific phase of the revolution may be compensated by an excess of the same leg in exerted force within another phase of the revolution. It must be noted that inter-leg and intra-leg compensations may occur interchangeably, and are therefore not distinguishable.

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4.4.3 Pedal Force Interpretation - Pedal Power as a function of Ergometer Load The ergometer power and the subject power must be linearly related ( ergometer subjectP P= ),

since they are tightly coupled (figure 4.4). Both legs generate the power of the subject. The summation of both left and right leg power must equal the ergometer power. It is assumed that healthy subjects distribute the power equally over both legs, and that patients distribute the power differently. The pattern of left and right leg power per revolution can be different; however, the sum of both must equal the ergometer load. The courses of the mean power data may be represented by the slopes of the data. Consequently, when a superposition theory is applied, the summation of the slopes of the power as a function of the ergometer load must equal one. More specific, the slopes of exerted powers during arbitrary chosen segments of the revolution, satisfy also the superposition theorem, on condition that the chosen segments do not overlap and all segments together equal one complete revolution (eq 4.5).

1 2 ... 1total na a a a= + + + = (eq. 4.5 )

With totala [-] the slope of the total power exerted by the subject, and na [-] the partial

slope of the power per specific phase. Since the ergometer load can be used as reference, the pedal powers over a specific phase may be an ideal parameter to investigate abnormalities in patients.

Figure 4.8 An example of the power as a function of ergometer load. Mean power for left (A),

right (B) and the difference of left and right leg (C) as a function of ergometer load

Figure 4.8 represents a typical example of mean power for left leg (A), right leg (B) and the difference between left and right leg (C) as a function of ergometer load. In healthy subjects, a similar linear increase in power for the left and right leg is assumed. Therefore, the mean power of the left and right leg can be described by a linear function with similar slopes (

La = Ra =0.5). In patients, disturbances in these slopes

are expected (for example La < Ra ; La + Ra =1).

In figure 4.8 (A) and (B), it is difficult to observe differences between the left and right leg. The slopes are nearly identical (≈0.5). A closer look at the difference between left and right leg as a function of ergometer load reveals this difference more clearly in figure 4.8 (C). At the start of the test, the right leg exerts more power than the left leg. This continues until 60% of the maximum test. From this point onwards, the difference is minimal.

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Figure 4.9 An example of the power as a function of ergometer load. Mean power for left (A),

right (B) and the difference of left and right leg (C) as a function of ergometer load

In the introduction, it was stated that patients can suffer from iliac artery diseases after a certain intensity level. At the start of the test, a normal and equal course of the mean power of the left and right leg is expected. Therefore, the slopes are expected to be ≈0.5. The hypothesis is that after a certain point in exercise level a change in slope occurs, caused by a shift in force exertion. By assessing the course of the mean power of the left and right leg, an inflection point (IP) may be identified. An un-published study [Klerkx, 2003] suggested that an inflection point might be related to a subjective point of patients’ complaints (PCP). Figure 4.9 represents a data set with inflection points. At an intensity level of 200W, a different slope in mean pedal power is observed. The mean power of the right leg compensates for the left leg (inter-leg compensation). This is most clearly seen in figure 4.9 C. For patients the assumption is made: The mean power of the left and right leg can be described by two linear functions, one before- and one after the IP. Since the superposition theorem can be applied for any ergometer load, the two slopes of these linear functions can characterize the course. 4.4.4 Parameter Analysis

Pedal power/force measurements as a function of the revolution and/or during an incremental maximal test may reveal pattern changes. This may be a possible indication of a vascular abnormality. Appropriate pedal force parameters must be chosen for assessing inter- and intra-leg compensation factors with the purpose of identifying iliac artery abnormalities. Table 4.2 represents the parameters that may identify the vascular abnormalities.

For a clear overview, see Chapter 5. An extensive description is given of the expected courses of the tabulated pedal force parameters in relation to healthy subjects and patients.

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Table 4.2 Pedal Force parameters as a function of a revolution or as a function of ergometer load. Analysis of these parameters may reflect vascular abnormalities.

Parameter Function of Analysis Differentiating

Maximum Force Revolution L,R Abnormal Leg

Minimum Force Revolution L,R Abnormal Leg

∆ Pedal Force Revolution L-R Abnormal Leg

Maximum Force Ergo. Load L,R, L-R, L/R Abnormal Leg

Minimum Force Ergo. Load L,R, L-R, L/R Abnormal Leg

Crank angle of Maximum Force Ergo. Load L,R Abnormal Leg

Crank angle of Minimum Force Ergo. Load L,R Abnormal Leg

Mean Power Ergo. Load L,R,L-R Abnormal Leg

Mean Power per 90 Degrees Phase Ergo. Load L,R Abnormal Leg

Mean Power per Muscle Set Ergo. Load L, R, L-R Abnormal Leg

∆ Mean Power Internal nourished phase Ergo. Load L-R Location of Abnormality

∆ Mean Power External nourished phase Ergo. Load L-R Location of Abnormality L = Left Leg, R = Right Leg, Ergo. Load = Ergometer Load

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41

Ch. 5 Materials and Methods

In the first part of this chapter (section 5.1) the study group is described. In next sections, the used materials and the post-processing are discussed.

5.1 Subjects Patients suffering from iliac artery diseases were retrospectively selected from a group of patients diagnosed with vascular abnormalities in the period 2003-2006 in the Máxima Medical Centre (MMC). All patients were diagnosed using the diagnosis algorithm developed by Schep et. al (see CH. 1). The Ethics Committee of the MMC approved the study. All patients gave an informed consent. All patients were selected from a database containing data of (ex-) national and regional competitive cyclists, speed skaters and tri-athletes with iliac artery abnormalities. Only patients with a unilateral diagnosis of lesions or kinkings within the iliac artery region were selected. Thirty-four patients were included. Nine subjects without iliac artery diseases were included to form the control group. The cycle experience of the control group was comparable with the patient groups. Selected patients were divided into specific groups related to the location of the iliac artery abnormality. An overview is given in table 5.1. Group LC consists of patients suffering from abnormalities (vascular kinking or intravascular lesions) in the left common iliac artery. Group RC consists of patients that are diagnosed to have vascular abnormality in the right common iliac artery. Group LCE suffers from both problems in the left common and external iliac artery. The group RCE has vascular abnormalities in both right common and external iliac artery. Groups LE and RE consist of patients that suffer only from abnormalities in the left or right external iliac artery, respectively. Table 5.1 Volunteering groups of patients with vascular kinkings or intravascular lesions and controls

Location Disease (Group) n [-]

age [years]

σ(age) [years]

km cycled [km]

σ(km) [km]

Left Communnis (LC) 5 25.2 2.75 118750 79935

Right Communis (RC) 1 28 - 240000 -

Left Communis and Externa (LCE) 7 42.7 14.11 229090 106115

Right Communis and Externa (RCE) 1 30 - 190000 -

Left Externa (LE) 16 33.6 9.61 176973 61606

Right Externa (RE) 4 48.5 10.5 325555 221851

Normal (Controls) 9 39.8 12.3 165000 Ω 135208 Ω µ=mean, σ=SD, Ω=two controls were not included

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5.2 Materials All patients and controls were asked to participate in a maximum intensity ergometry test (section 4.4.1). The Diagnosis Algorithm procedure, as described in section 1.2, was performed. After a warm-up of several minutes at an ergometer load 0 Watt, the ergometer load increases incrementally until the maximum voluntary intensity of the subject after approximately ten minutes is reached. The voluntary exercise level was estimated prior to the test, based on the person’s cycling history. The LODE® Excalibur Sport (925900) cycle ergometer with pedal force measurement was used to collect raw data; namely workload- and averaged RPM as a function of number of revolution; time ergometer load as a function of time; and pedal torque data. The torque, exerted by both legs, was measured every two degrees of crank angle using a crank of 0.17m. The time, average RPM and average workload was measured for every revolution. During the incremental maximum intensity test, subjects were asked to indicate a the onset of complaints. The data was analysed with Matlab® (The MathWorks, Inc., version 6.1.0.450 release 12.1, 2001).

5.3 General Post Processing 5.3.1 Determination of Pedal Force and Workload

Raw pedal torque data was used to determine the pedal force as a function of revolution (and ergometer load)(eq. 4.3). Further, pedal torque data and average rpm data were used to determine workload (power) of the subject as a function of the ergometer load (eq. 4.4). 5.3.2 Inflection Points (IP)

In section 4.4.3, the inflection point (IP) and a way to describe pedal force data sets by partial slopes, was introduced. Three routines (IP-Routine 1, 2 and 3) in order to determine the inflection point and two linear functions (or partial slopes) are assessed. IP-Routine 1 Figure 5.1 represents the mean power for left (A) and right leg (B) and the difference between the mean power of left and right leg (C). The two lines can be found by using a least square fitting technique [Mizuno, 2004]. This approach determines the minimal residual error of the two linear fits. First, a linear fit can be determined by

IP IPy a x b= + (eq. 5.1)

With, sIP the (partial) slope, bIP the offset, x represents the ergometer load and y the parameter (in this case the power). The best fit can be determined by using a least squared approach of the slope and the offset. Consider a dataset of n points (n≈1000) (see in figure 5.1). The first and last 25 points are discarded from the data because of accumulation related phenomena. A point (nIP) moves through this data set, starting at n=2 and ending at n=n-1. At each nIP the slope and the offset are determined before and after the nIP. The sIP and bIP are determined for the first function (from i=1 to i=nIP) by;

1 1 1

2

1 1 1

1( ) ( ) ( ) ( )

( )1

( ) ( ) ( )

IP IP IP

IP IP IP

n n n

i i iIPIP IP n n n

i i iIP

x i y i y i x in

a n

x i x i x in

= = =

= = =

−

=

−

∑ ∑ ∑ ∑

∑ ∑ ∑ (eq. 5.2)

and,

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2

1 1 1 1

2

1 1 1

1 1( ) ( ) ( ) ( ) ( )

( )1

( ) ( ) ( )

IP IP IP IP

IP IP IP

n n n n

i i i iIP IPIP IP n n n

i i iIP

y i x i x i x i y in n

b n

x i x i x in

= = = =

= = =

−

=

−

∑ ∑ ∑ ∑

∑ ∑ ∑ (eq. 5.3).

The second fit can be determined in exactly the same way, but than from i=nIP to i=n-1. For each data set of aIP and bIP of the first function and second function, the summed squared error (SSE) is determined. The SSE can be determined by,

( )( )2

1

( ) ( ) ( ) ( )IP

IP

n

IP data IP IP IP

n

SSE n y n a n x b n=

= − +∑ (eq. 5.2)

With ydata(nIP) the power at the ergometer load. The best fit of the data is deterimed by the minimal of the sum of SSEfirst fit and SSEsecond fit. The IP is set on this point.

IP1 - IP2 ≈ -75W

Leap in fits

Change in

course

Change in

course

A B C

IP1 - IP2 ≈ -75W

Leap in fits

Change in

course

Change in

course

A B C

Figure 5.1 Mean power of left (A) and right leg (B), and the difference in mean power between

left and right leg (C). The inflection points are determined by IP routine 1. The course of the mean power is assessed with a first linear line (green) and a second linear line (red).

In figure 5.1, the linear fits are represented. A green line represents the begin-fit (first line) and the red lines the end-fit (second line). The point between the last point of the begin-fit and the first point of the end-fit represents the IP (in figure 5.1: marked as IP1). The transition can be discontinuous, because of a small leap between the two fits.

IP-Routine 2 The second approach of determination of the inflection point is based upon the same principle as IP-routine 1. However, IP-routine 2 is a continuous approach. The inflection point is determined by the intersection of the begin-fit and the end-fit (in figure marked as IP2). IP-routine 2 describes the data by two linear equations with the intersection of the both fits as the inflection point. Using this approach there may be no inflection point within the data domain, since parallel lines have no intersection point. In figure 5.1, a difference between IP1 and IP2

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IP-Routine 3 The third approach of determining the IP embeds routines 1 and 2. IP-Routine 3 uses the same method as IP-routine 2 for determination of the fits, but an extra condition is imposed. The last data point of the begin-fit and the first point the second fit must be equal. Therefore, an assessment of the data is acquired using two linear fits and a forced intersection. Again, a moving point (nIP) is introduced. At nIP the origin of the coordinate system is defined (0,0). The dataset before and after the moving point nIP can now be assessed by

to linear fits ( begin fity a x−= and end fity a x−= ). The mean slopes for these two functions are

determined (similar to IP-routine 1). For each nIP the summed squared error for both lines is determined and analogous to IP-routine 1, the IP is set at n(x), where the summation of the summed squared error of both fits is minimal. The IP is used for further analysis. It is necessary to find out which IP-routine determines the inflection point best. Two methods may be used to define the best IP-routine, namely an approach based on the least squared error (i), and an approach based on the analogy between the poin