How many 25ml measures in 70cl conversion

Dissertation Petra Margaritoff - University of Lübeck

From the Clinic for Cardiac Surgery of the universitytoLübeck

Director: Prof. Dr. med. H.-H. Sievers

Development and application of a

Bioimpedance method tor functional

Monitoring muscular

Hertonterstüttong systems

Inaugural dissertation

tor

Obtaining a doctorate

the universitytoLübeck

- From the medical faculty -

Presented by

Dipl.-Ing. Petra R. J. Margaritoff, M.Sc.

from Hamburg

Lübeck 2008


1. Rapporteur: Prof. Dr. med. Norbert W. Guldner

2. Rapporteur: Prof. Dr. rer. nat. Thorsten ButoG

Oral exam day: May 20, 2009

Approved for printing. Lübeck, May 20, 2009

signed Prof. Dr. med. Werner Solbach

- Dean of the Medical Faculty -


3

Table of Contents

1 Introduction and problem definition .............................................. .................................................. .......................................... 6

1.1 Skeletal muscles ................................................ .................................................. .................................................. ........... 7

1.1.1 Skeletal muscle structure .............................................. .................................................. .................................................. .7

1.1.2 Types of skeletal muscles .............................................. .................................................. .................................................. .... 7

1.1.3 Active electrical properties of the skeletal muscles .......................................... .................................................. .8th

1.1.4 Energy conversiontong in the skeletal muscles .............................................. .................................................. ............... 9

1.1.5 Passive electrical properties of the skeletal muscles .......................................... ................................................ 9

1.1.5.1 Electrical model of the cell structure ........................................... .................................................. .......................... 9

1.1.5.2 Anisotropy of the skeletal muscle ............................................ .................................................. ............................. 11

1.1.6 Contraction .............................................. .................................................. .................................................. ............... 12

1.1.6.1 Recruitment pattern .............................................. .................................................. ............................................ 13

1.1.6.2 External stimulation ............................................. .................................................. ............................................... 13

1.1.6.3 Diameter of the muscle fiber ............................................ .................................................. ............................... 13

1.2 Heart muscles ................................................ .................................................. .................................................. ............ 14

1.2.1 Active electrical properties of the heart muscles .......................................... .................................................. ..14

1.3 Muscular Hertonterstüttong ................................................. .................................................. ....................................... 15

1.3.1 Dynamic cardiomyoplasty ............................................. .................................................. .................................... 16

1.3.2 Dynamic aortomyoplasty ............................................. .................................................. ...................................... 17

1.3.3 Indirect myocardial revascularization ............................................. .................................................. ............................ 17

1.3.4 Cardiomyopexy with a pedicled muscle transplant ........................................... .................................................. ..... 18

1.3.5 Skeletal muscle ventricles .............................................. .................................................. ............................................... 18

1.3.6 Biomechanical heart ............................................. .................................................. ............................................... 19

1.3.7 Muscular in comparison to cellular hertonterstüttong ................................................. .......................................... 19

1.3.7.1 Cellular cardiomyoplasty ............................................. .................................................. .................................... 19

1.3.7.2 Cardiogenesis .............................................. .................................................. .................................................. ..... 19

1.3.7.3 Stem cell cardiomyopexy ............................................ .................................................. ............................... 19

1.3.8 Muscular in comparison to mechanical mantonterstüttong ................................................. .................................. 20

1.4 Basics of bioimpedance measurement .............................................. .................................................. ............................ 23

1.4.1 Measuring principle .............................................. .................................................. .................................................. .............. 23

1.4.2 Volume conductor .............................................. .................................................. .................................................. ............ 24

1.5 Problem ................................................ .................................................. .................................................. ............ 25

2 Materials and Methods .............................................. .................................................. .................................................. .26

2.1 Muscle stimulator ................................................ .................................................. .................................................. .......... 26

2.2 Electrodes ................................................ .................................................. .................................................. ..................... 26

2.2.1 Phase boundary .............................................. .................................................. .................................................. .......... 26

2.2.2 Polarization .............................................. .................................................. .................................................. ............. 27

2.2.3 Equivalent circuit diagram .............................................. .................................................. .................................................. ........ 28

2.2.4 Electrodes used ............................................. .................................................. ............................................... 28

2.3 Electrode system ................................................ .................................................. .................................................. ......... 29

2.4 Impedance measuring system ................................................ .................................................. .................................................. .29

2.4.1 Methods and tools tor Development of the software .............................................. ........................................... 29

2.4.2 Measurement hardware .............................................. .................................................. .................................................. .......... 29

2.5 Carrying out and evaluating experiments ............................................. .................................................. .......................... 30

2.5.1 Animals, samples and measurements carried out ......................................... .................................................. ................ 30

2.5.2 Operation and test procedure ............................................ .................................................. ..................................... 31

2.5.2.1 Intraoperative procedure ............................................. .................................................. ...................................... 31

2.5.2.2 Muscle pre-stimulation .............................................. .................................................. ........................................... 33

2.5.2.3 Termination .............................................. .................................................. .................................................. ....... 33

2.5.2.4 Pressure measurement on the skeletal muscles ........................................... .................................................. .............. 33

2.5.3 Determination of muscle trainingtostand by the myosin heavy chain analysis ............................................ ... 33


4

2.5.3.1 Sample preparation .............................................. .................................................. .............................................. 33

2.5.3.2 Gel electrophoresis ............................................ .................................................. ................................................ 34

2.5.3.3 Silver coloring .............................................. .................................................. .................................................. ...... 34

2.5.3.4 Evaluation .............................................. .................................................. .................................................. ......... 35

2.5.4 Evaluation of the data ............................................ .................................................. .................................................. 35

2.5.5 Statistical procedures ............................................. .................................................. ................................................. 35

3 results ................................................ .................................................. .................................................. ........................ 36

3.1 Methodology and implementationtong a bioimpedance measurement on the skeletal muscles ............................................ ............. 36

3.1.1 Signal processing concept .............................................. .................................................. ....................................... 36

3.1.1.1 Analog input variables and their sampling .......................................... .................................................. ...... 37

3.1.1.2 Windowing .............................................. .................................................. .................................................. ......... 40

3.1.1.3 Discrete and Fast Fourier Transformation ......................................... .................................................. ......... 42

3.1.1.4 Calibration .............................................. .................................................. .................................................. ........ 43

3.1.1.5 Impedance determination .............................................. .................................................. .............................................. 44

3.1.1.6 Error detection .............................................. .................................................. .................................................. .46

3.1.2 Software .............................................. .................................................. .................................................. ................... 46

3.1.2.1 Use cases .............................................. .................................................. .................................................. 47

3.1.2.2 Architecture and design ............................................ .................................................. ........................................... 48

3.1.2.3 Implementation .............................................. .................................................. .................................................. 52

3.1.2.4 Evaluation software .............................................. .................................................. ................................................. 53

3.1.3 Static muscle fiber impedance measurement at multiple frequencies ........................................ .............................. 53

3.1.4 Dynamic impedance measurement ............................................. .................................................. ................................... 54

3.2 Measurement results ................................................ .................................................. .................................................. ........... 55

3.2.1 Static muscle impedance at different frequencies (frequency responses) ....................................... ................. 55

3.2.1.1 Comparison of the static muscle impedance before and after stimulation ....................................... ......................... 55

3.2.1.2 Comparison of the static muscle impedance of unstimulated and pre-stimulated muscles ................................. 56

3.2.1.3 Comparison of the static muscle impedance with the myosin heavy chain distribution ...................................... ..... 57

3.2.2 Dynamic impedance with single stimulations ........................................... .................................................. ........... 58

3.2.2.1 Impedance responses .............................................. .................................................. .............................................. 58

3.2.2.1.1 Isolated muscle sample ........................................... .................................................. .......................................... 58

3.2.2.1.2 Relaxed muscles, in-situ ....................................... .................................................. ................................... 58

3.2.2.1.3 Comparison of the RDI for different functional and morphological musclestostands .................... 59

3.2.2.1.4 Comparison of the RDI at different measuring locations ....................................... .................................................. 60

3.2.2.1.5 Comparison of the RDI maxima with other variables ..................................... .................................................. ....... 61

3.2.2.1.6 Comparison of the RDI with different electrode sequences ....................................... ............................. 61

3.2.2.1.7 Comparison of the RDI with flexible and blocked electrode position ..................................... .............................. 62

3.2.2.2 Dynamic impedance during fatigue tests ........................................... .................................................. .62

3.2.2.2.1 Impedance responses of the working muscle ......................................... .................................................. ...... 63

3.2.2.2.2 Comparison of impedance and pressure responses of the working muscle .................................... ................... 64

4 Discussion ................................................ .................................................. .................................................. ......................... 72

4.1 Electrodes ................................................ .................................................. .................................................. ..................... 72

4.2 Analog hardware ............................................... .................................................. .................................................. ......... 73

4.3 Goats as an experimental animal model .............................................. .................................................. ......................................... 74

4.4 Methodology and implementationtong a bioimpedance measurement on the skeletal muscles ............................................ ............. 74

4.4.1 Electrode system .............................................. .................................................. .................................................. ..... 74

4.4.2 Software and signal processing ............................................ .................................................. ................................. 75

4.4.3 Measurement direction .............................................. .................................................. .................................................. ............ 75

4.4.4 Parallel line .............................................. .................................................. .................................................. ........... 76

4.4.5 Thermally caused artifacts ............................................ .................................................. ...................................... 76

4.5 Measurement results ................................................ .................................................. .................................................. ........... 77

4.5.1 Static muscle impedance ............................................. .................................................. ........................................ 77

4.5.1.1 Acute effect of muscle stimulation on static muscle impedance ....................................... ............. 77

4.5.1.2 Effect of pre-stimulation on static muscle impedance ........................................ ............................ 78


Introduction and problem 5

4.5.2 Dynamic impedance ............................................. .................................................. ................................................ 78

4.5.2.1 Control measurements .............................................. .................................................. ............................................. 79

4.5.2.2 Single contractions .............................................. .................................................. .............................................. 79

4.5.2.2.1 Comparison of the impedance response of different functional and morphological musclestostands ........ 80

4.5.2.2.2 Effects of the measuring location on the impedance response ....................................... ........................................... 80

4.5.2.3 Fatigue tests .............................................. .................................................. ............................................ 81

4.5.3 Measurement errors and methodological errors ........................................... .................................................. ............................. 82

4.5.3.1 Parallel line effects .............................................. .................................................. .......................................... 82

4.5.3.2 Pressure measurement on the skeletal muscles ........................................... .................................................. ............... 83

4.5.3.3 Myosin heavy chain analysis ............................................ .................................................. ................................ 83

4.5.3.4 Influence of the arterial supply ........................................... .................................................. ......................... 83

4.6 ImplementtoInstructions for a permanent implantable impedance measurement ............................................ .................. 84

4.7 Clinical relevance (outlook) ............................................ .................................................. ............................................ 85

5 Conclusion ................................................ .................................................. .................................................. .......................... 86

6 Summary ................................................ .................................................. .................................................. .......... 87

7 Bibliography ................................................ .................................................. .................................................. ......... 88

8 Appendices ................................................ .................................................. .................................................. ............................. 95

List of tables ................................................. .................................................. .................................................. ........... 95

List of figures ................................................. .................................................. .................................................. ..... 96

Measurement results................................................. .................................................. .................................................. ................. 98

Static impedance measurements at different frequencies (frequency response) ........................................ ............. 98

Dynamic measurements in the time domain .............................................. .................................................. ............................. 105

Measurements of the relative dynamic bioimpedance on the non-contracting muscle ........................................ ...... 105

Measurements of the relative dynamic bioimpedance on the contracting muscle .......................................... ............. 106

Fatigue tests with measurements of the relative dynamic bioimpedance ........................................... .............................. 107

Pressure-associated impedance measurements ................................................ .................................................. ......................... 110

Myosin heavy chain analysis ............................................... .................................................. ............................................. 114

Thanksgiving................................................. .................................................. .................................................. ..................... 115

Curriculum vitae................................................. .................................................. .................................................. ........................ 116

Publications, lectures and prizes ............................................. .................................................. ..................................... 118

Declaration on animal experiments ................................................ .................................................. .................................................. .... 119


Introduction and problem 6

1 Introduction and problem definition

The heart failure is toTogether with coronary artery disease, it is the leading cause of death in

the western industrialized countries (Table 1). In 1993 there were 218,000 treatment cases in Germany

registered [116], 12 years later more than 300,000 inpatients were treated [132],

[131]. The economic consequences of heart failure are significant across Germany

In 2002 almost 3 billion euros for her treatment

issued [39].

Heart failure will be today tonext conservative

medication (diuretics, cardiac strength enhancers, β-

Blockers, ACE inhibitors) or surgically (implantable

Cardioverter / defibrillator - ICD, dilation,

Pacemaker) [64]. About a third of that

heart failure patient is in the

Terminal stage of the disease [83]. This medicinally

refractory patients for whom all usual

indicated surgical interventions have been performed as

last therapy options the heart transplant (HTX)

and the definitive therapy with mechanical

Hertonterstüttong systems (Destination Therapy), mostly

left ventricular assistance systems (LVAD).

The International Society for Heart and Lung

Transplantation (ISHLT) carries out worldwide statistics

done heart transplants that are numbers

mainly from the large agencies for organ donation from Central Europe,

Great Britain, Scandinavia, Australia / New Zealand and the USA contributed sinceto come

Contributions from individual transplant centers in the Middle East, Asia, and Central / South America [63].

Probably the vast majority will

worldwide transplants in the ISHLT

Statistics recorded (Table 2). The number of

Heart transplants include due to the

improved road safety todeclined

[126], in 2005 there were only around 3100

Registered heart transplants in adults

[141]. Due to the lack of donor organs

A heart transplant can only be done for

less than 5% of patients realize it.

In the waiting lists for donor hearts of the above

In the period from 2005 to 2007, there were almost 4,000 patients [5], [37], [130], [148],

[149] registered. The discrepancy is mainly due to the scarce supply

Donor hearts extremely restrictive waiting list policy, toabout 1/3 of the patients die during this

the waiting time [28]. In Germany alone there are between 700 and 800 new registrations each year

on the waiting list for donor hearts, while the number of available hearts is around 400 p. a.

stagnates [29]. Only about 40% of the available donor hearts are currently being transplanted [126],

The primary reason is concern about dysfunction, which, however, presumably comes from careful

Donor organ preparation could be prevented [126].

Despite more than 40 years of technical development [87], LVADs bring serious problems

itself, such as B. the risk of infection of percutaneous feedthroughs for extracorporeal elements. The

American Interagency Registry for Mechanically Assisted Circulatory Support

(INTERMACS) has 292 implantations nationally for the period 10/2006 to 9/2007

mechanical supporttong systems, 17% of them for Destination Therapy [73]. Though

INTERMACS only keeps records of FDAtosystems left and only about 80% took part

of the centers in the US, but the number shows that despite the theoretically high availability only

few systems are implanted. Therefore and also because of

monetary considerations it is desirable to biological

and biomechanical alternatives to develop.

The global number of deaths from ischemic heart disease

(Table 3), according to WHO forecasts from today 7

Million to almost 10 million cases in 2030 [154].

Even in defined cases of coronary heart disease, e.g. B. the

Small Vessel Disease and other non-bypassable

Coronary disease, can be muscular

Hertonterstüttonew approaches to optimize blood circulation

There are therapeutic options [7], [90].

Numbers off

2003 - 2007

Prevalence, absolute

Deaths p.a.

HTX adults

worldwide, p. a. [141]

HTX pediatric

worldwide, p. a. [12]

Reporting Centers

worldwide [141]

Deaths p.a.

Numbers off

2004 - 2007

Heart failure

ICD10 I11, I13, I50

worldwide 22.5 million [83]

EU-wide 14 million [110], [69]

Germany-wide 1.6 *) - 3 million [127]

worldwide> 500,000 [83]

EU-wide 211,396 [155]

Germany-wide 47,079 [135], [134]

Table 1: Prevalence and deaths of the

Heart Failure by Region.

*) Calculation based on an assumed

Prevalence of 2% [24], [133]

1994 2005 change

4439 3094 -30 %

approx. 390 approx. 400 approx. + 2%

approx. 255 approx. 195 approx. -24%

Table 2: Heart Transplants

ischemic

Heart disease

ICD10 I20-I25

7,195 million worldwide [153]

EU-wide 729,273 [155] -

740.998 [36]

Germany-wide 225,279 [133]

Table 3: Ischemic deaths

Heart Diseases by Region


Introduction and problem 7

1.1 skeletal muscles

The aim of this thesis is to determine the degree of transformation and the contractility of one for muscular

Hertonterstüttong systems used muscle to monitor around thereby

Muscle destruction to avoid. As a rule, the latissimus muscle is used for these systems

dorsi (MLD, also Latissimus Dorsi Muscle, LDM) is used. He belongs to the skeletal muscles,

the properties of which are discussed below.

1.1.1 Skeletal muscle structure

The skeletal muscle is made up of a shell, the epimysium and the muscle fascia lying on the outside

edged. It consists of a series of muscle fiber bundles, each covered by a perimysium

are. Each of these bundles contains long, predominantly parallel muscle fibers, the

Skeletal muscle cells that are embedded in the endomysium. While Epimysium, Perimysium

and endomysium show connective tissue-like structures, the skeletal muscle cells form the

functional fabric.

Every skeletal muscle cell is made up of

numerous, arranged in parallel

Myofibrils, which are the contractile apparatus

of the muscle cell, and is made up of their

Membrane, the sarcolemma, encased.

The contractile apparatus of the muscle cell is

in the myofibrils in repetitive

Structures, the sarcomeres, arranged,

their light microscopic observation

this type of musculature also got the name

striated muscles. In the

Sarcomere are actin and

Myosin filaments running through

Discs are stabilized (Figure 1).

During the contraction, push each other

these Z-disks and actin filaments

along the myosin filaments towards

the M washer. The myosin heads as

Figure 1: sarcomere uncontracted / contracted (according to [111])

active elements bend, pull

barbed the actin in the direction of M-

Disc and release the actin again (cross-bridge cycle). The faster the myosin head

can kink, the faster the muscle contracts.

Human skeletal muscle fibers are approx. 10-100 µm thick and up to to 20cm long [27], [61], [80].

Depending on the length, the number of approx. 2 µm in each filament varies

Sarcomeres [61], [125].

1.1.2 Types of skeletal muscles

In terms of protein structure, the myosin head, neck and shaft make up the myosin heavy chain (myosin

Heavy Chain, MHC). According to the current state of knowledge, there is in the human skeletal muscle

at least three different forms of MHC: MHC I is the slowest contracting one

Variant, MHC IIa contracts faster, MHC IIx the fastest.

After birth, different muscles develop for different tasks

Types of muscle fibers, each containing different forms of MHC. Depending on the main share

of the MHC types, the fiber becomes one type toorderly.




Type I fibers (slow fibers) show up in both singletoas well as tetanic

Contractions a low force of contraction with a slow increase in force. Since this

Muscle fiber type works aerobically and is well supplied with blood, it is historically also called red or

called oxidative muscles. Due to the aerobic working method (see chapter 1.1.4)

the force of contraction can be maintained for a long time.

Type IIa fibers (fast, fatigue-resistant fibers) develop in both

singlestoAs well as tetanic contractions, a medium contraction force with very

rapid increase in force. This type of muscle fiber works in a mixed aerobic and anaerobic manner. He is called

called oxidative-glycolytic muscles. Due to the predominantly aerobic way of working

(see Chapter 1.1.4) he can maintain the contraction force for a long time [120].

Type IIx fibers (fast, quickly tiring fibers) develop in both singletocautions

as well as with tetanic contractions a high contraction force with very fast

Increase in force. Since this type of muscle fiber works anaerobically and has less blood supply, it will

historically referred to as white muscles (or glycolytic muscles). Due to the


Introduction and problem definition 8

Anaerobic working method tires very quickly, as the glycogen reserves are quickly exhausted

are.

Fiber type Type-I Type-IIa Type-IIx

Color red red / pink white

Capillary supply [27], [68] tight tight little

Metabolism aerobic predominantly aerobic anaerobic

Fatigue low medium high

Increase in singletockung [ms] [120] 58-110 30-55 20-47

Duration of the singletockung [68] long short short

Muscle fiber diameter [68], [14], [122] thinner medium thick

approx. 2x diameter type I [61]

tetanic fusion frequency [Hz] [27] 10-20 50-200

tetanic force development [mN] [120] 10-130 50-550 300-1300

Size of the motor units [68] small medium large

Recruitment [68] early, medium late

Table 4: Overview of properties of the skeletal muscle fiber types

Hopkins and Guytons [68] name the relative diameters of the shown in Table 4

differently typed muscle fibers. Campbell [14] found 1999 to be different

structured muscles put togethertosizes and muscle fiber diameters, the Hopkins and

Support Guyton's statement. Salmons showed that muscle mass increased as a result of

Fiber transformations from type II to type I were significantly reduced [122], which was also indicated indirectly

smaller muscle fiber diameters of type I muscles.

1.1.3 Active electrical properties of skeletal muscles

The skeletal muscle fiber itself is not electrically active. But it does interact with the electric

active motor neurons of the muscle in order to contract to can.

In a natural situation, each muscle cell is made up of an axon branch of a motor neuron

innervated. Each motor neuron innervates many muscle fibers at the same time, and the number varies depending on the number

of the muscle type. The functional unit made up of a motor neuron and those innervated by it

Muscle fibers are called a motor unit. It is the smallest that can be stimulated individually

Size.

In order for a skeletal muscle to contract, it must have one from the motor neuron of its motor unit

Experience stimulus. A motor end plate (specialized synapse) of the motor neuron lies

contactless over the sarcolemma of the muscle cell. If a motor neuron becomes supra-threshold

when electrically stimulated, the end plate releases the messenger substance acetylcholine, which stimulates the synaptic

Overcomes gap and connects to receptors on the sarcolemma. There he changes them

Permeability of the postsynaptic membrane for small ions. Cation channels open through

which Na + can flow in and K + out. A generator potential is created (end plate potential,

EPP), which is electrotonic (by ion currents, in contrast tor spread through

Action potentials) spreads and a muscle action potential leads to it. That electrotonic

transmitted endplate potential activated on the entire muscle membrane outside the

Endplate region of voltage-gated Na + channels. The sodium ion channels of the sarcolemma

open, Na + follows the chemical gradient, flows into the cell and the sarcolemma becomes

depolarized. With equipotential bonding, the Na + channels close again. Shortly after the opening of the

Sodium channels also open the potassium channels, and K + flows chemically out of the cell

and repolarization sets in. When the resting membrane potential is restored, K + close

Channels again.

The membrane resting potential can be calculated using the Goldmann equation:

= kT q ⋅ln P K [K] o P Na [Na] o P Cl [Cl] i

P K

[K] i

P Well

[Na] i

P Cl

[Cl] o

(1.1.1)

Φ Resting membrane potential [V] (= [J / C])

K Boltzmann constant [J / K]

T absolute temperature [K]

q ion charge [C]

P K permeability for potassium [cm / s]

K potassium concentration [mmol / l]

P Na permeability for sodium [cm / s]

Na sodium concentration [mmol / l]

P Cl permeability for chloride [cm / s]

Cl chloride concentration [mmol / l]

For the natural environment, this results in a membrane resting potential of approx. -90mV. While

the depolarization not only creates a potential equalization in the muscle, but also through

Excess a positive membrane potential of approx. 130mV (muscle action potential). An ATP-driven

Charge pump (ATPase, Figure 2) supports repolarization and takes care of the

Maintaining the membrane resting potential (see Chapter 1.1.4).The muscle action potential

subsided again after approx. 10 ms [27]. From the time the electrical


Introduction and problem definition 9

Membrane potential exceeds the stimulus threshold until toWhen the contraction begins, it goes away

also about 10ms [27]. Fiber-specific times could not be determined in the literature.

1.1.4 Energy conversiontong in the skeletal muscles

Like all cells, muscle cells need energy to move to

live and their work to perform. The human

Body gains energy from glucose (chemically

C 6 H 12 O 6), which either go directly from the small intestine into the

Blood enters or from the liver as glycogen

can be cached.

Serves as the energy carrier of the cells

Adenosine triphosphate (ATP), the most energetic

Molecule that humans store and synthesize

can. The ion pump that the resting potential in the

Maintaining nerve and muscle cells is e.g. ATP-powered.

With the help of one ATP molecule, three can

Sodium ions from the cell into the extracellular space

and two potassium ions are transported into the cell,

so that is necessary for actions

Concentration gradient remains (Figure 2).

Figure 2: Sodium-Potassium ATPase

Muscle cells get the glucose with the bloodstream

or from the cell's own store (then in the form of glycogen) and use it to get out

Adenosine diphosphate (ADP) adenosine triphosphate to synthesize. The conversion of glucose

in ATP can be done aerobically or anaerobically. In aerobic ATP synthesis, glycose is oxidized,

this process can take place over long periods of time if the tissue is adequately oxygenated

takes place and is used by the endurance-oriented type I muscle fibers.

The balance of aerobic ATP synthesis is

C 6H 12O 6 + 6 O 2 → 6 CO 2 + 6 H 2O + 36 ATP

The balance of anaerobic ATP synthesis is

C 6 H 12 O 6 → 2 C 3 H 6 O 3 → CO 2 + C 2 H 6 O + 2 ATP

The significantly faster anaerobic ATP synthesis produces lactic acid (chemically C 3H 6O 3), which

cannot be used by the skeletal muscle, but can be passed on to other organs

must so that the muscle does not become overly acidic. From the balance equation it can be seen that the anaerobic

ATP synthesis is far more inefficient than the aerobic form. For these reasons, the anaerobic

ATP synthesis only from fast, short-term stressed muscle fibers, the type II fibers used.

Type I fibers synthesize ATP aerobically.

1.1.5 Passive electrical properties of skeletal muscles

While only a few types of tissue are electrically active, all biological tissues are passive

Electrical Properties. Since measurements of these passive properties are not laborious

Needing sensor technology, it is an obvious approach to these properties to determine and from that

Conclusions about the physiological tissue properties to pull.

When an external electrical stimulus is applied, biological tissue behaves, too

the skeletal muscles, like passive electrical networks. That is, the fabric has one

electrical impedance property, the so-called bioelectrical impedance or short

Bioimpedance (BI) Z.

Bioimpedance behaves nonlinearly at high voltages or currents [50]. In alive

Tissue, the voltage / current ratio is linear when the applied fields are below the

The non-linearity threshold remains [40]. It is commonly believed that opening and

Closing the ion channels [152] in the cell membrane is responsible for such nonlinear effects

Behavior: At resttoThe cell membrane stood at approx. 10 kV / mm (voltage difference

polarized between intra- and extracellular space in the range of a few tens of millivolts) [50]. If

When an electric field is superimposed, the protein structure of the cell membrane changes its configuration

and changes the conductivity of the membrane or, in extreme cases, induces ion redistribution,

which inverts the membrane polarity (action potential). Since the in the present work for the

Measurements used currents and voltages (not the stimulation pulses) less than that

Are stimulus thresholds, the system is considered linear here.

1.1.5.1 Electrical model of the cell structure

Figure 3 shows a simple cell model showing the origin of passive electrical

Tissue properties illustrated. Since it considers intra- and extracellular parts separately, it becomes

referred to as the Bidomain model. The capacitive part of the tissue impedance Z is largely due to


Introduction and problem statement 10

caused the cell membrane, whose double lipid layers like a capacitor with the capacitance C M '

Act. The exact electrical properties of the membrane are determined by its dimensions,

Put togethertong and structure determined. Due to the influence of the cell membrane, the

Total tissue impedance Z complex and capacitive in nature.

R E

R I

C M '

R M '

extracellular resistance [Ω]

intracellular resistance [Ω]

Membrane capacity [F]

Membrane resistance [Ω]

Figure 3: Illustration of the electrical cell properties

The intra- and extracellular fluid (modeled by R I and R E) carries the largest part tor

resistive component of Z. Their specific properties are primarily determined by the

Ion concentrations in the respective liquids are determined. They control a smaller proportion

Cell membrane ion channels (represented by R M ') at.

With direct current the capacitive component behaves like an interruption, with infinite

high frequency like a short circuit. The direct current impedance therefore enables predominantly

Conclusions about the extracellular parts, while at high frequencies the intracellular

proportion of totakes.

The above model can be rewritten to the model shown in Figure 4:

Figure 4: simplest electrical cell model

R E extracellular resistance [Ω]

R I intracellular resistance [Ω]

C M membrane capacitance [F], C M = C M '/ 2

Figure 4 can again be simplified to the model shown in Figure 5:

R 2

R 1

C 1

serial resistance [Ω]

parallel resistance [Ω]

parallel capacitance [F]

Parameter order of magnitude Note

Extracellular more specific

Resistance ρ [33]

Specific resistance of blood ρ blood

Figure 5: equivalent electrical cell model

approx. 80-300 Ω cm

approx. 150 Ω cm

R = ⋅A

I.

Specific membrane resistance approx. 10 1 ... 10 5 Ω cm 2 ohmic resistance per membrane area

Specific membrane capacity approx. 1µF / cm 2 capacity per membrane area

Table 5: Orders of magnitude of specific electrical tissue properties

It has been found that biological tissue with the model shown above or with

other linear passive RLC networks cannot be modeled exactly. The reasons for this include

molecular relaxation processes after electrical changes. It is therefore customary to do so

called Constant Phase Element (CPE) for more precise modeling to use that

1928 as the first from K.S. Cole has been described and validated [22], [21]. A CPE models the non-linear

Behavior of biological tissue. CPEs are theoretical models, they are not considered

physical components available. The CPE according to Fricke [50] (Eq. 1.1.2) is one of the most common

used models:


Introduction and problem statement 11

R = 1

Z CPE

=

j⋅⋅ (1.1.2)

R ωτ = 1 resistance at ωτ = 1 [Ω]

Z CPE modeled impedance [Ω]

ω signal angular frequency [Hz]

τ frequency scaling factor [s]

α power operator (without units), with 0 ≤ α ≤ 1