Modal analysis application to estimate bony callus stiffness during fracture healing process

Università di Pisa

Scuola di Ingegneria

Laurea Magistrale in Ingegneria Biomedica

THESIS

Modal analysis application to estimate bony callus stiffness

during fracture healing process

Supervisors: Candidate:

Prof. Francesca Di Puccio Elmira Khoubanfar

Ing. Lorenza Mattei

1 Table of contents

Introduction ... 5

1. State of art ... 6

1.1 Vibration analysis ... 6

1.2 Osteoporosis ... 6

1.2.1 Effect of soft tissue ... 9

1.3 The vibrational mode of tibia ... 13

1.3.1 Impulse response ... 13

1.3.2 Impulse response method ... 13

1.4 Vibration mode of the human tibia ... 14

1.5 The influence of fracture fixation on the vibrational measurements ... 15

1.6 Relationship of resonant frequency to stiffness in an experimental fracture model ... 20

1.7 Bone healing process ... 23

1.7.1 Inflammation Stage... 23

1.7.2 Soft Callus Formation Stage ... 24

1.7.3 Hard Callus Formation Stage ... 25

1.7.4 Bone Remodelling Stage ... 25

2 Background: Experimental modal analysis ... 27

2.1 Impact testing ... 27

2.1.1 Reciprocity of the test in each session ... 29

2.2 Frequency analysis ... 29

2.2.1 FRF measurement ... 29

2.2.2 Vibration is easier to understand in terms of mode ... 30

2.3 Mode shape ... 31

2.3.1 What is a Mode Shape? ... 31

Sampled mode shapes ... 31

3 Materials and methods ... 35

3.1 Case study ... 35

3.2 Micro Hammer Dytran 5800 SL ... 35

3.3 Accelerometer Dytran 3133A1 ... 37

3.4 Accelerometer Dytran model 3035BG ... 40

3.5.1 LMS Testing Solution Software ... 42

3.5.2 LMS Test.Lab Impact Testing ... 42

3.6 Comparison between accelerometer1D and 3D: ... 43

3.7 Mode analysis: Polymax ... 43

3.8 General procedure of frequencies extraction: ... 44

4 Test in-vivo: first case study ... 48

4.1 Test case description ... 48

4.2 Set up of test І ... 50

4.2.1 Reciprocity of the test (І) in each session ... 51

4.2.2 Modes analysis І ... 57

4.3 Results and discussion І ... 59

4.3.1 Healing assessment in configuration 1 , 2 and 3 ... 59

4.4 General Osservation І ... 65

4.4.1 3D Accelerometer ... 65

4.4.2 Polymax critict ... 65

4.4.3 Verify the frequencies obtained by the software LMS in-vitro ... 66

5 Test in vivo: second case study ... 67

5.1 Breve descrizione del caso ... 67

5.2 Set up of test ІІ ... 67

5.2.1 Reciprocity of the test ІІ in each session ... 68

5.2.2 Modes analysis ІІ ... 72

5.3 Results and discussion ІІ ... 74

5.3.1 Healing assessment in configuration C1... 74

5.4 General osservation ІІ ... 79

5.4.1 Verify the frequencies obtained by the software LMS in-vivo ... 79

5.4.2 Examine the repeatability of the tests ... 79

5.4.3 Compare the tests done with the resolution at 2 Hz and the resolution at 1 Hz ... 80

6 Conclusion ... 81

5

Introduction

A correct assessment of bone fracture healing is fundamental for the successful treatment of

fractures, especially when fixation devices are used. In particular, for long bone fractures treated

with external fixator, the correct time for the dynamization and removal of the device should be set

at a proper phase of the healing process.

The aim of this study is to develop and validate an objective method, completely not invasive for the monitoring of the bone fractured during healing process based on vibrational response of the bone through the use of techniques and instruments of experimental modal analysis in in-vivo. Experimental tests have been conducted for this purpose to characterize the vibrational behavior of the fractured bone treated with external fixator.

To verify the purpose of this study, 2 patients were selected and the tests were done in several sessions for a few months.

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1. State of art

This chapter presents a series of papers in the literature, characterization and monitoring of the healing process of the fractured bone.

1.1

Vibration analysis

Vibration analysis is a promising technique in diagnosing metabolic bone diseases such as osteoporosis and monitoring fracture healing. We can observe the structural dynamic property changes of the tibia extracted from the vibration analysis data.

In one study (Bekir Bediz et.all, 2010), bone mineral density (BMD) and vibration measurements were made both in in-vivo and in-vitro conditions. The relationship between structural dynamic properties, obtained and bone mineral densities measured were investigated. Also, the effect of soft tissues on measured structural dynamic properties was analyzed.

Natural frequency of the tibia decreased with decreasing bone mineral density that presented a weak correlation with the bone mineral density values measured by dual energy X-ray densitometer of the femur. In the case of in vitro experiments, it was observed that the effect of muscles on measurement results is higher than that of the effect of the skin and the fibula which makes the modal identification procedure difficult. However, having very large percentage changes in the loss factors when mineral content and collagen are reduced is an encouraging result to believe that damping measurements may yield a promising technique in diagnosing progressing osteoporosis and monitoring fracture healing period.

1.2

Osteoporosis

Osteoporosis is a disease characterized by low bone mass and a micro-architectural deterioration of bone tissue, leading to enhanced bone fragility and a consequent increase in fracture risk (World Health Organization, 1994) with high socioeconomic impact on the society (Atik et al., 2006). Dual energy X-ray absorptiometry (DXA) and quantitative computed tomography (QCT) are the common methods to detect osteoporosis. However, these methods have their limitations since in some cases, fragility fractures occur in normal and osteopenic patients whereas it is not seen in osteoporotic patients in medical practice (Atik, 2008). Therefore, the need of diagnosing bone strength more accurately increases gradually (Arpinar et al., 2005; Özdurak et al., 2006).

Due to being non-invasive and precise, using vibration analysis as a diagnosing tool is one of the most proper choices (Akkus et al.,1998). Therefore, this method has been studied over the past few decades. According to this study, measuring mineral content of bone is not an adequate method of determining bone strength because even if there is a weak region in the bone, there is no certainty that its mineral should be low. Thus, in this study stated that the fragility of bone is related with its modulus of elasticity. In the experiments carried out, they measured the resonant

frequency of ulna and by using

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the

Later studies published by Cornelissen et al. (1986) and Van der Perre and Lowet (1994, 1996) mainly involved the assessment of natural frequencies and corresponding mode shapes of human bones, especially the tibia and the radius. Results show that the natural frequencies of bone decreases with increasing level of osteoporosis; thus a correlation may exist which can be used to determine the bone strength. Later, Lowet et al. (1992) found that bending modes and stiffness of long bones are directly related with its resonant frequencies. They also constructed a simple slender beam model in order to calculate the torsional stiffness of bones using resonant frequencies.

Test in-vivo

For in vivo experiments, foremost difficulty comes from the soft tissues and joints which may result in inaccurate interpretations. Van der Perre et al. (1983), Cornelissen et al. (1986b) and Sahaand Lakes (1977) investigated the structural dynamic properties of bones under the effect of soft tissues. To eliminate or minimize the influence of soft tissue on vibration measurements, a set of solution methods were developed. For example, an attempt that was done by Soethoudt et al. (2007) revealed that the preload that is applied by holding a small cylinder metal element manually pressed at the excitation point while holding the accelerometer during the excitation of the bone via impact hammer helps to decrease the damping effect of the skin and the underlying soft tissues.

In this study, the ultimate goal is to determine structural dynamic properties, mainly the loss factor of the tibia extracted from frequency response functions (FRFs) obtained by vibration analysis both in vivo and in vitro tests. Therefore it is aimed to monitor the changes in these parameters with bone mineral density (BMD) values and develop a new approach to detect progressing osteoporosis by obtaining a correlation between these values and other properties of bone which cause osteoporosis. In vivo experiments 42 volunteers participented in this study, all of the subjects of this experiment are chosen to be female and older than 50 years of age, Vibration measurements were made in the left and the right tibiae of the participants. Excitation of each tibia was performed at a specific point, near to the middle section of the tibia along the length of the bone by an impact hammer (Dytran Instruments, type 5800B3, S/N 4354, sensitivity = 48.5 mV/lbf – Chatsworth, CA, USA) by manually pressing a small cylindrical element at the excitation point and the response of tibia was recorded using a manually pressed accelerometer (Dytran Instruments, type 3035B, S/N 2436, sensitivity = 104 mV/g – Chatsworth,CA, USA). Both signals were measured simultaneously with an instrument of Data Physics (Istanbul, Turkey), ‘‘QUATTRO”, to obtain the FRF data. The experiments were carried out with free free boundary condition by placing the leg on a soft rubber in order to minimize the physical effects coming from participants. the measurements were carried out for a frequency range of 0–100 Hz with a resolution of 1 Hz. The measurements were triggered by the input of the impact hammer’s channel and recorded only after at least five successive hits. In order to minimize the effects of leakage (occurs since the measurements are recorded for a finite length of time history), exponential windowing was used.

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From vibration tests carried out, FRFs which contain input–output relation of the measured system, are obtained. These functions are calculated simply by taking the ratio of the output signal to the given input (force) signal. Structural dynamic properties of a system such as natural frequency, loss factor, and modal constant can be extracted from these functions through modal identification (modal parameter extraction) techniques. These modal identification techniques are generally related with expressing the obtained FRF data by an analytical expression through curve fitting techniques. (Reference thesis: Antonia Longo)

Test in-vitro

In vitro experiments (modal analysis of tibia), Two fresh tibia specimens obtained from above knee amputations are used in order to extract structural modal parameters of human tibial bone in vitro (ex vivo). The specimens are selected in such a manner that they had no history of bone diseases related to tibia and they are preserved at -20 °C after the amputation process.

Measurements were made at Ankara University Faculty of Medicine Department of Anatomy, Ankara. Since the major aim of this study is to observe the changes in the structural dynamic

properties of tibia, the experiments are also carried out on a dry tibia specimen obtained from Middle East Technical University, Medical Center, Ankara. In order to analyze the effect of the soft tissues, a set of experiments are carried out on these two tibia specimens under different

conditions. These conditions can be described as:

Intact (Case I), After removal of the skin tissue (Case II), After removal of the muscle tissue (Case III), After exarticulation of the joints and detaching the fibula (Case IV).

Experiments were carried out with free–free boundary condition by placing the specimens on a soft rubber.

Measurements were recorded in order to observe the first two modes (modes of interest) of the tibia, in a frequency range of 0–800 Hz with a resolution of 1 Hz. The FRFs obtained were analyzed by using the modal identification software MODENT. Circle and line fit methods are used for the identification of modal parameters.

In this study, the results of the experiments carried out both in vivo and in vitro conditions, in order to diagnose osteoporosis by frequency response function measurements of human tibial bone are presented. In the first part of the study, a set of experiments are carried out on human female participants. vibration measurements were generally based on the observation of changes in natural frequency with progressing osteoporosis to diagnose this metabolic bone disease. these approaches are not appropriate for the assessment of osteoporosis since this parameter does not only depend on the property of bone, but also depends on the geometry, dimensions and the boundary conditions during measurement. The box plots in Fig. 1-1 shows that there is no definite discrimination between the values to diagnose osteoporosis or progressing osteoporosis.

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Fig. ‎1-1 : Natural frequency of (a) right tibia and (b) left tibia vs. state of osteoporosis (femur) (Bekir Bediz et.all, 2010)

In the study of Cornelissen et al. (1986a), correlation between the natural frequencies of the ulna and the degree of osteoporosis was also investigated and it was concluded that in the diagnosis of osteoporosis, the use of natural frequency alone has a limited value.

1.2.1 Effect of soft tissue

In the second part of this study, firstly the effect of soft tissues on the frequency response functions is investigated. As seen from Fig. 1-2, skin has a negligible effect; however, the major effect is due to the muscle group surrounding the tibia which is in agreement of the study conducted by Cornelissen et al. (1986). This influence can be explained by not only the additional heavy mass added to the system by the muscle group, but also by the heavy damping of the muscles. From the modal identification results, it is observed that another significant effect comes from the fibula and joints. As a result, the soft tissues in the system make the modal identification procedure difficult. In other words, although there occurs a considerable change in damping properties of tibia, soft tissues may suppress the effect of these changes to depict themselves in the modal loss factor of the tibia–muscle–skin system that are obtained from in vivo tests.

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Fig. ‎1-2: Cluster plot of natural frequency values vs. bone mineral density (BMD) values (Bekir Bediz et.all, 2010)

Progressing osteoporosis leads to increasing fragility in bones. Therefore, its damping properties should decrease.

In the last part of this study, a set of experiments were carried out on two fresh frozen and one dry tibia specimens. The fresh frozen ones are obtained from fresh frozen cadavers that show no history of metabolic bone disease or tibial fracture. According to the experiments carried out on fresh frozen tibiae, it was observed that some differences occur both in the natural frequencies and loss factors of different specimens. Due to the reasons mentioned above, the differences in natural frequency values were expected. However, the modal loss factors were expected to be closer to each other since DXA measurements of these specimens showed that there is no considerable difference between the mineral contents of both fresh frozen tibiae. Therefore, these measurements may imply that not only mineral content but also collagens structure of bone affects the modal loss factors of tibia. However, in this study only two fresh frozen and one dry tibia specimens were investigated, due to the difficulties in

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obtaining the specimens, and therefore more specimens need to be tested to be able to generalize this conclusion.

For comparison with the fresh frozen case, similar FRF measurements were carried out on a dry tibia. The primary reason for the differences in loss factors of tibia should be the loss in collagen structure of the bone. Having very large percentage changes in the loss factors when mineral content and collagen are reduced is an encouraging result to believe that damping measurements may yield a promising technique in diagnosing progressing osteoporosis and monitoring fracture healing period. However the major difficulty encountered in developing such a technique is extracting reliable modal properties of tibia from in vivo FRF measurements. This difficulty stems from the damping introduced by soft tissues. The effect of skin can be surmounted to a certain extent by applying a preload by holding and pressing a small cylindrical element manually at the excitation point during the excitation of the bone, while holding the accelerometer pressed as suggested in a study conducted by Soethoudt et al. (2007). Yet, the main difficulty comes from the muscles. The effect of muscles on overall damping is so pronounced that it dominates the total damping.

In conclusion, natural frequency of tibia shows a weak correlation with BMD values measured by DXA of femur in human tibia. It is observed that the correlation between the natural frequency of right tibia and the BMD measurements of femur is higher than the correlation for the left one. Still, these correlations do not seem to be sufficient to use them as a diagnosing tool. However, the experiments carried out for in vitro cases give encouraging results to believe that damping measurements may be used for diagnosing progressing osteoporosis and monitoring fracture healing period if loss factor of tibia can be accurately extracted from the total damping

measured in in vivo tests for overall system.

In Fig. 1-3, the FRF plots of these experiments are given (for the first tibia specimen). As expected, the effect of the skin is very low compared to the effect of muscles and fibula, because the skin itself has very low mass and stiffness contribution to the whole system.

The FRFs obtained from the experiments carried out on the two excised tibias and the coherence plots of the measurements are given in Fig. 1-4. The coherence plots indicate that experimental data obtained are reliable.

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Fig. ‎1-3: Effects of soft tissues on FRF of human tibia (Bekir Bediz et.all, 2010)

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1.3 The vibrational mode of tibia

The progress of healing of a fractured long bone is usually subjectively judged by the orthopedic surgeon through the use of physical and radiografic examination. A system quantitatively to access the healing of a fracture, as well as to estimate the mechanical properties of a bone would be a valuable diagnostic tool. The vibrational and ultrasonic responses of long bones have been used to objectively assess fracture healing and to evaluate the mechanical properties of bones. The use of vibrational responses can be classified into two types according to the method of the vibrational input to the bone, namely, bone resonance analysis with the impedance head mounted on a shaker and the impulse response method with hammer impactor. The impulse response method is generally simpler in its set up and also requires less testing time than the shaker method.

1.3.1 Impulse response

In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response is the reaction of any dynamic system in response to some external change. In both cases, the impulse response describes the reaction of the system as a function of time (or possibly as a function of some other independent variable that parameterizes the dynamic behavior of the system).

In all these cases, the dynamic system and its impulse response may be actual physical objects, or may be mathematical systems of equations describing such objects.

Since the impulse function contains all frequencies, the impulse response defines the response of a linear time-invariant system for all frequencies.

Analysis of the resonant frequency (RFA) of bone is a painless, non invasive and reproducible method to measure mechanical properties of bone.

1.3.2 Impulse response method

One study (Yukio Nakatsuchiet.all, 1996 ) generated in the tibia by the impact of an impulse hammer. The vibrational response along the bone was detected with a piezo-electric accelerometer with a built-in charge amplifier, each signal was transmitted to a two channel waveform-analyzer. The waveforms of impact and response in the time domain were viewed on the analyzer screen. The frequency response function, the spectrum of response divided by the spectrum of impact, was used to determine the resonant frequency of the bone because this decreases the influence of the variation in impaction forse. The FFT analyzer was set at a resolution of 5Hz with a sampling frequency of 1Hz. The magnitude of the impact generated by the impulse hammer was about 9.8N( Fig. 1-5).

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Fig. ‎1-5: Block diagram of the instrument set-up to measure the vibration of an excised human tibia by the impulse response method. Vibration are generated by the impact of an impulse hammer (input). The vibrational response is detected along the bone with an accelerometer (output). Both the input and output waveforms are transmitted to a two channel FFT-analyzer where immediate observation of their spectra is made and the response function, is calculated as the resonant frequency of the bone (Yukio Nakatsuchiet.all, 1996 )

1.4 Vibration mode of the human tibia

The characteristic of the vibration mode were studied using a dry human tibia and four wet tibias. Four sites for hammering were selected, two sites for detecting the response waveform also were chosen: the medial tibial condyle and the tibial tuberosity. The tibia nad fibula specimens were prepared by excising all soft tissues, the vibrational mode was studied first on the tibia with the fibula attached, and then without the fibula.

The vibrational mode of a dry human tibia is shown in Fig. 1-6 where the four pairs of power spectra obtained by hammering at each site along the tibia are presented. Two vibrations, one vibrating strongly in a lateral direction recorded at the medial condyle and the other vibrating weakly in antero-posterior direction recorded at the tibial tuberosity, were found.

The resonant frequency in the lateral direction was lower than that in the antero-posterior direction in the primary mode. The primary vibrational mode when the impactor was placed at the medial malleolus and the vibrations were detected at the medial condyle had a significantly larger amplitude.

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Fig. ‎1-6:The vibrational mode of a dry tibia. The four sites of impaction along the medial margine of the tibia are illustrated on the left. The power spectra at two detecting sites, the medial tibial condyle and the tibial tuberosity, are shown for each impaction site. A frequency of 612Hz defines the primary vibrational mode, 1725 Hz the secondary, and 3348 Hz the tertiary mode in the frontal plane. A frequency of 721 Hz define the primary and 3696 Hz the tertiary mode in the sagittal plane. On the right , the nodes and loops of the primary , secondary and tertiary modes in the lateral direction are illustraited (Yukio Nakatsuchiet.all, 1996 )

1.5 The influence of fracture fixation on the vibrational measurements

One of the problem that the impulse response method must overcome before clinical use is its use in fractures treated by various methods of fixation. The results suggest that the impulse response method can be useful in the quantitative assessment of fracture healing even if the various materials for fracture fixation are utilized. each construct provided a distinctive feature in its impulse response. Tower et al. who analysed 74 fractured tibias with the impulse response method, reported that resonant frequency analysis was not useful in evaluating healing in patients with interlocked intrammedually devices and that additional study is needed to determine if this technique is applicable to fractures stabilized by external fixation.

This experiment on external fixation demonstrated that evaluation of fracture healing with the impulse response method is possible. The reason why the resonant frequency was the highest in the tibia fixated by an external fixator may be that both the tibia and fixator vibrated as one body and its apparent bending rigidity increased. As long as the vibration of the bone is measured, the vibration of the fixation materials will not be detected. It was considerably difficult in vitro to find the resonant frequency of the bone itself out of the many frequencies component encountered with the vibration of the pins, the

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external fixator and the vibration of the bone in antero-posterior direction. However its easier to detect the vibration of a healing tibia treated by an external fixator in vivo.

The reason for decreased peaks of vibrations in vivo compared with in vitro is that the surrounding tissues act as a damper attenuating the vibrations caused by the fixator and pins. Even if a vibration from an external fixator is mixed into the measurments, one can confirm whether or not the vibration was derived from the external fixator by hammering on the medial malleolus and detecting the response of the external fixator by putting the pick up sensor on the fixator.

Discussion

The primary vibrational modes of the four human tibias with and without the attached fibula, on the frontal sagittal planes, are shown in Fig. 1-7.

Fig. ‎1-7: Primary vibrational mode of the wet tibia in the frontal and sagittal plane. Abscissas normalized distance frome the distal to proximal ends of tibias. Ordinates the amplitude ratio or the peak value of the frequency response function (Yukio Nakatsuchiet.all, 1996 )

The resonant frequencies in the tibias fixed by a metal plate, ender’s intarmedullarly pins and orthofix external fixator all showed a remarkable increase during the initial phase of adhesive consolidation (Fig. 1-8).

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Fig. ‎1-8: Influence of various fracture fixation constructs on the vibration in tibia. The changes of resonant frequency with the time after the beginning of consolidation

There are two different vibrational modes in the human tibia, one in the lateral direction and the other in the antero-posterior direction, the differentiation of the two modes can be made by changing the direction of impaction on the medial malleolus (Fig. 1-9).

Fig. ‎1-9: Influence of the direction of impaction on the response waveform

It is preferable to measure the primary mode of the tibia in vivo in the lateral direction by hammering on the medial malleolus and detecting at the medial tibial condyle. This is because the soft tissue overlying both sites is relatively thin and either site corresponds to a loop in the primary mode of the

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tibia. Therefore, high amplitude vibrations can be detected on the medial tibial condyle. This is because the soft tissue overlying both sites is relatively thin and either site corresponds to a loop in the primary mode of tibia . therefore high amplitude vibrations can be detected on the medial tibial condyle.

The use of the resonant frequency of bone as a guide for estimation of fracture healing was more sensitive in the initial stages of healing than in the later stage, this tendency also was seen in the experiments of fracture healing using various fracture constructs as it discussed above.

Here is another study to measure the resonant frequency of fractured tibia that expected to change during the process of healing as stiffness increses.

They considered 74 fractured osteotomized tibia. There are different tips of fixation, different grade of fractured and different location of the fractures or osteotomies.

Resonant frequencies were analyzied by impulse frequency response (IFR).

In IFR a brief tap is delivered to the tibia by an instrumented impactor and the magnitude of the resultant response is recorded with an accelerometer , impulse responses analyzed using software (SBA 2000,pacific biomedical crop,Portland).

The resonant frequencies produced were in two major range, the lowest range is 125 Hz and the second range is 250-400 Hz.

The resonant frequency an in-vivo tibia analyzed with the patient seated and relaxed with the legs dangling to minimize the effects of the position of the patient, the sites of placement of the accelerometer and the impactor and soft tissue. The accelerometer was pressed against the anterior proximal medial tibial plateau and the impactor was placed against the anterior portion of the medial malleolus by the examiner.

The contralateral tibia was used as a control, no transmission was seen in fresh fractures or in the case when there was moderate soft tissue swelling or sever obesity.

Results of the study above

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Tips of fixation

Number of

Examination

_Results

No internal fixation

96

10% of examination of tibial progressing

to nonunion would have been falsely

classified as united by RFA examination.

Undreamed/unlocked

intramedullary

39

If there is nonunion tibia , its possible to

recognize correctly.

External fixation

46

Some

examination

were

correctly

identified as not united but some

examination would have been falsely

classified as healed.

Locked

undreamed nail

11

Six examination had RFA>0.8 and would

have been considered falsely united by

RFA.

Tab. ‎1-1:Result of test

Tibia treated by external fixation demostrated an increase in RFA as they progressed clinically and radiographically to heal.

This study demonstrated that there is a correlation between traditional parameters of tibial fracture healing and the measured resonant frequency of the healing tibia. This technology is inexpensive and easily developed, RFA may have a promising role in research to study the temporal changes in tibial stiffness as fracture healing progresses.

In another study ( S.K. Benirschke et.all, 1993) established the clinical potentioal of non invasive fracture healing assessment with resonant frequency by verifying the relationship between stiffness and measured resonance frequencies in a human tibia with varying flexural rigidity documenting the reproducibility of resonant frequency measurments over time in volunteers with intact tibia , determining if there is any difference between right and left intact tibia , and determining the relationship between resonance frequency and time to union in a group of patients with normally healing tibial fractures.

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1.6 Relationship of resonant frequency to stiffness in an experimental fracture model

For an experimental model of a tibia with a central segment of changing stiffness (to stimulate healing) five fresh intact tibia were obtained from donated cadavers. A 3 cm defect was cut from the center of each tibia and replaced by an H-shaped piece of 60 durometer solid neoprene rubber. The osteotomy ends were pressed against the center of the rubber insert and the arms of the insert were damped around the tibial shaft, the assembly was then fozen at -20 °C for 24 h, and the assembly removed fome the freezer and it was loaded in four-point bending using a servohydraulic material tester.

The net effect was that in the frozen condition , the structure approached 28,2% of the flexural rigidity of the intact tibia.

The specimen was then refrozen and its resonant frequency was tested the next day. The tibia was suspended freely from the end of the table, an accelerometer was attached on the anteromedial surface. Tibia was excited by a tap from an electronic hammer (Fig. 1-10).

Fig. ‎1-10: Picture of the instrumentation used for exciting the tibia and measuring its vibrational response

The data was analysed using software (SBA 2000) software pinpointed several peaks in the response spectrum, the lowest frequency ~ 125 Hz and the second range of frequency ~ 250 - 400Hz. This test shows resonant frequency can be used to determine stiffness of a tibia as its flexural rigidity.

Reproducibility of the method

To recognize the reproducibility, both tibia of volunteers were tested in a period of 4 months , 2 support condition of the leg: one was freely hanging vertically off the end of the examination table with the volunteer sitting. The second used a support frame in which the leg was placed horizontally.

The reproducibility was defined as the values defining the 95% confidence interval of the population. Table 1-2 shows the condition of the patients and confidence limits and figure 1-11 shows the average resonant frequency for left leg of volunteers was 293.67 Hz while for the left leg was 290.90 Hz, which were not significantly different.

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Condition

Confidence limits (95%)

Horizontally supported leg, proximal

accelerometer

98.89 101.06

Free-hanging leg, distal accelerometer

97.92 102,00

Free-hanging leg, proximal accelerometer

96.79 102.90

Tab. ‎1-2: Confidence values (95%) for tests of measurement reproducibility done at four monthly intervals

Fig. ‎1-11: First mod bending frequencies of left versus right intact tibia of volunteers

Measurements in patients

For the 24 months period patients with tibial fractures were envolved in the study, all of them were tested with their legs hanging freely over the edge of an examination table. Contralateral intact leg was as a control leg. Table 1-3 shows the data from the patients.

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Average

Age

Sex

Injured

leg

Fixation

type

25.6

M

L

URN*

16.4

M

L

URN

38.7

M

L

URN

29.7

F

R

EXF*

40.1

M

R

EXF

18.9

M

R

URN

39

M

L

EXF

21.6

M

R

EXF

30.5

F

L

URN

23.5

M

R

URN

30.3

F

L

URN

27.3

M

L

NONE

20

M

L

URN

39.4

M

L

URN

Tab. ‎1-3: Data from patients studied

*URN, undreamed nail; EXF, external fixator.

The factors which influence the measurments, the support conditions of the tibia, the skin as a damped spring interposed between the tranducers and bone, the muscles influence the vibrational frequencies in two ways: first they act as additional mass decreasing the tibial resonant frequency and the second tense muscle act as additional constraints to the moving tibia and the fibula that increase the resonant frequencies.

Based on this study , based on patient tolerance, they found that freely hanging is the method of choice, locations with minimal soft-tissue coverage, patients should be encouraged to relax, the measurement from the intact leg should be used to monitor the quality of the result.

Conclusion: the vibrational resonance frequency of a healing tibia is a measure of its bending stiffness, with attention to detail the measurments are highly reproducible, there is no different between right and

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left intact tibia in human, in a patient population a significant correlation is seen between time postinjury and tibial resonant frequency as the tibia progress to the healed state.

1.7 Bone healing process

Bone is living tissue that performs several important functions. Most obviously, the bones of the skeleton are essential for protection of organs, maintenance of posture, and movement. Less obviously, the bones of the skeleton are essential for the formation of blood cells and the regulation of Calcium levels within the body. Bone is very strong, but also relatively lightweight. It is made up of microscopic channels that are surrounded by a very strong layer called the Cortex, which in turn is surrounded by a tough outer surface known as the Periosteum. When viewed in cross section the channels produce a honeycomb effect. Apart from making bones lightweight, the channels allow blood flow throughout the bone tissue which supports constant metabolic activity within the bone. This metabolic activity means that bone is constantly re-modelling itself in response to the stress it is subjected to during exercise and work activities. There are three main types of cell that are active within bone: Bone Cells, Osteoblasts and Osteoclasts. All of these are present within the dense connective tissue of bone called the Bone Matrix. Osteoblasts lay down new bone tissue and then revert to being Bone Cells that sit in the Bone Matrix, whereas Osteoclasts are constantly active, re-absorbing bone tissue. The process of 'bone modelling' occurs all the time and this ability to constantly regenerate means that bone can heal fully following a fracture. There are the four main stages of bone healing:

 Inflammation Stage

 Soft Callus Formation Stage

 Hard Callus Formation Stage

 Bone Remodelling Stage

1.7.1 Inflammation Stage

The Inflammation Stage (fig.1-12) begins the moment the bone is broken and lasts for around five days. bone has a very good blood supply due to the channels within its structure. When a fracture occurs there is massive disruption to these channels and a large amount of bleeding from the fracture fragments. This is what causes immediate swelling and bruising in the area of the broken bone. This is known as a Haematoma, which means bleeding within the tissue. The damaged bone tissue at the edges of the fracture fragments die back and the dead cells release chemicals called Cytokines which initiate the healing process. Osteoclasts work to remove the dead bone cells. However, Osteoblasts are unable to work to lay down new bone tissue at this stage because of the movement of the fracture fragments which stops Osteoblast activity.

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Fig. ‎1-1‎1-2: inflammation stage

1.7.2 Soft Callus Formation Stage

The chemical and metabolic reactions that produce the Soft Callus begin a few days after the bone is broken. Fibroblast cells that are present in the Granulation tissue begin to form Cartilage and Fibrocartilage. This is a spongy material that fills the gap between the two fracture fragments, although it remains quite weak to external stresses for around six weeks. For this reason it is important that there is not too much movement of the fracture fragments.(fig.1-13)

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After a couple of weeks, despite being quite fragile, the Soft Callus provides sufficient stability at the fracture site for new blood vessels to begin forming and for Osteoblasts at the Periosteum (the outer surface of the bone) to begin laying down what is called 'Woven bone'. This Woven bone at the margins of the fracture is a little soft and disorganised, but it's the first bone contact between the two fracture fragments.

1.7.3 Hard Callus Formation Stage

From two to three weeks onwards a process begins whereby the fragile cartilage material of the Soft Callus is transformed completely into Woven bone. This process typically continues for between six and twelve weeks, depending on the location and type of fracture. Hard Callus formation is a complex process that is guided by the release of mineral compounds such as Calcium and Phosphate into the Cartilage tissue, which subsequently transforms into a bridge of Hard Callus over the fracture site.

Fig. ‎1-1‎1-4: Hard Callus Formation Stage

Once the Hard Callus has formed at the former fracture site, then fracture Union is said to have occurred.

1.7.4 Bone Remodelling Stage

During normal bone healing the body will lay down more Hard Callus than is needed to unite the fracture fragments. As a result the fracture, site looks enlarged when viewed on x-ray. Bone Remodelling begins once the fracture has united and may continue for several years, as a continuum of normal bone function.

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Fig. ‎1-1‎1-5: Bone Remodelling stage

Over time, the normal shape of the bone is restored. Bone is laid down where it is needed by Osteoblasts and removed by Osteoclasts, depending on the stresses that are placed on the bone during every day and sports activities. At the Bone Remodelling stage of fracture healing a progression of weight bearing exercise is encouraged because it leads to an increase in bone strength.

The loosely organised Woven bone is gradually replaced by Lamellar bone, which is highly organised along lines of stress and therefore much stronger than Woven bone. Ultimately, once the fracture healing process is complete, the bone should be at least as strong as it was originally.

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2 Background: Experimental modal analysis

The mechanical behavior of a structure can be assessed by going to study its response to appropriate stresses. The experimental modal analysis allows to study the dynamic characteristics of the system, in particular resonance frequencies, modal shapes and damping, following well-known experimental and numerical procedures.

2.1 Impact testing

The use of Impact Testing is a fast, convenient and low cost method for evaluating the vibrational response of structures.

With the ability to compute FRF measurements in an FFT analyzer, impact testing was developed during the late 1970’s, and has become the most popular modal testing method used today.

Fig. ‎2-1: Impact Testing

Impact testing is depicted in Figure 2-1. The following equipment is required to perform an impact test: 1. An impact hammer with a load cell attached to its head to measure the input force.

2. An accelerometer to measure the response acceleration at a fixed point & direction. 3. A 2 or 4 channel FFT analyzer to compute FRFs.

4. Post-processing modal software for identifying modal parameters and displaying the mode shapes in animation.

A wide variety of structures and machines can be impact tested. Of course, different sized hammers are required to provide the appropriate impact force, depending on the size of the structure; small hammers for

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small structures, large hammers for large structures. Realistic signals from a typical impact test are shown in Figure 2-2 .

Fig. ‎2-2(A): Impact Force and Response Signals

Fig. ‎2-2(B): Impact APS and FRF

Roving Hammer Test

A roving hammer test is the most common type of impact test. In this test, the accelerometer is fixed at a single DOF, and the structure is impacted at as many DOFs as desired to define the mode shapes of the structure. Using a 2-channel FFT analyzer, FRFs are computed one at a time, between each impact DOF and the fixed response DOF.

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2.1.1 Reciprocity of the test in each session

Fig 2-3 shows a structure where an input-output measurement is to be made at point “i” and point “j”. Now in one measurement the force is applied at point “i” and the response is measured at point “j”. And in the second measurement, the force is measured at point “j” and the response is measured at point “i”. From the principle of reciprocity, the hij must equal hji.

Fig. ‎2-3: Schematic for Reciprocity Measurement

2.2 Frequency analysis

2.2.1 FRF measurement

The Frequency Response Function (FRF) is a fundamental measurement that isolates the inherent dynamic properties of a mechanical structure. Experimental modal parameters (frequency, damping, and mode shape) are also obtained from a set of FRF measurements.

The FRF describes the input-output relationship between two points on a structure as a function of frequency, as shown in Figure 2-4 Since both force and motion are vector quantities, they have directions associated with them. Therefore, an FRF is actually defined between a single input DOF (point & direction), and a single output DOF.

An FRF is a measure of how much displacement, velocity, or acceleration response a structure has at an output DOF, per unit of excitation force at an input DOF.

Figure 2-4 also indicates that an FRF is defined as the ratio of the Fourier transform of an output response ( X(w) ) divided by the Fourier transform of the input force ( F(w) ) that caused the output.

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Fig. ‎2-4

:

2.2.2 Vibration is easier to understand in terms of mode

Figure 2-5 points out another reason why vibration is easier to understand in terms of modes of vibration. It is a plot of the Log Magnitude of an FRF measurement (the solid curve), but several resonance curves are also plotted as dotted lines be low the FRF magnitude. Each of these resonance curves is the structural response due to a single mode of vibration. The overall structural response (the solid curve) is in fact, the summation of resonance curves. In other words, the overall response of a structure at any frequency is a summation of responses due to each of its modes. It is also evident that close to the frequency of one of the resonance peaks, the response of one mode will dominate the frequency response.

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2.3 Mode shape

2.3.1 What is a Mode Shape?

A mode shape (figure 2-6) is a deflection-pattern associated with a particular modal frequency or pole location. It is neither tangible nor easy to observe. It is an abstract mathematical parameter which defines a deflection pattern as if that mode existed in isolation from all others in the structure. The actual physical displacement, at any point, will always be a combination of all the mode shapes of the structure.

With harmonic excitation close to a modal frequency, 95% of the displacement may be due to that particular mode shape, but random excitation tends to produce an arbitrary "shuffling" of contributions from all the mode shapes. Nevertheless, a mode shape is an inherent dynamic property of a structure in "free" vibration (when no external forces are acting). It represents the relative displacements of all parts of the structure for that particular mode.

Sampled mode shapes

The mode shape vector: Mode shapes are continuous functions which, in modal analysis, are sampled with a "spatial resolution" depending on the number of DOFs used. In general they are not measured directly, but determined from a set of FRF measurements made between the DOFs. A sampled mode shape is represented by the mode shape vector {Ψ}r, where r is the mode number.

Modal displacement

The elements Ψir of the mode shape vector are the relative displacements of each DOF (i). They are usually complex numbers describing both the magnitude and phase of the displacement.

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Fig. ‎2-6:Mode shape

Normal modes

These are characterized by the fact that all parts of the structure are moving either in phase, or 180° out of phase, with each other. The modal displacements Ψir are therefore real and are positive or negative. Normal mode shapes can be thought of as standing waves with fixed node lines.

Complex modes

Complex modes can have any phase relationship between different parts of the structure. The modal displacements Ψir are complex and can have any phase value. Complex mode shapes can be considered as propagating waves with no stationary node lines (Figure 2-7).

Where to expect normal/complex modes

The damping distribution in a structure determines whether the modes will be normal or complex. When a structure has very light or no damping, it exhibits normal modes. If the damping is distributed

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in the same way as inertia and stiffness (proportional damping), we can also expect to find normal modes.

Structures with very localized damping, such as automobile bodies with spot welds and shock absorbers, have complex modes.

Warning: The mode shapes derived from poor measurements can indicate complex modes on structures where normal modes exist.

Fig. ‎2-7:Normal and complex modes

What Does the Modal Description Assume?

• Linearity : We have to assume that the systems we test behave linearly so that the response is always proportional to the excitation. This assumption has three implications for Frequency Response Function (FRF) measurements.

• Superposition : A measured FRF is not dependent on the type of excitation waveform used. A swept sinusoid will give the same result as a broadband excitation.

• Homogeneity : A measured FRF is independent of the excitation level.

• Reciprocity : In a linear mechanical system a particular symmetry exists which is described by Maxwell's Reciprocity Theorem. This implies that the FRF measured between any two DOFs is independent of which of them is used for excitation or response.

Two Kinds of Modes are further characterized as either rigid body or flexible body modes. All structures can have up to six rigid body modes, three translational modes and three rotational modes. If the structure merely bounces on some soft springs, its motion approximates a rigid body mode.

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Fig. ‎2-8: Flexible Body Modes

Many vibration problems are caused, or at least amplified by the excitation of one or more flexible body modes. Figure 2-8 shows some of the common fundamental (low frequency) modes of a plate. The fundamental modes are given names like those shown in Figure 2-8, The higher frequency mode shapes are usually more complex in appearance, and therefore don’t have common names.

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3 Materials and methods

This chapter describes the measurement setup developed for experimental tests in order to characterize the vibrational response of the bone in different configurations.

3.1 Case study

Case number one, a 19 years old girl in the outcome of right femoral diaphysis fracture, had surgical operation for correction of sagittal and coronal plane deformities with osteotomy and abdominal wedge and then lengthening started after 10 days of intervention, lengthening performed for 24 days with distraction of external fixator.

Case number two, It was a complicated case, a 53 years old man, he had several fractures in his right leg, fractured ankle and fibula, starting tests 3 days after stopping the lengthening process (lengthening started 10 daye after surgery, for 30 days)., the doctor's aim was lengthening of tibia about 3 cm, treated with external fixation.

3.2 Micro Hammer Dytran 5800 SL

The micro hammer Dytran 5800SL is an impulse micro hammer with technology IEPE (Integral Electronic Piezo-Electric) produced by Dytran Instruments. The micro hammer is equipped with a quartz force sensor mounted on the tip and an IC miniature amplifier aboard (Fig. ‎3-1).

The instrument has a sensitivity of 100 mV / Lbf, a measurement range of 50 lbf (0:22 kN) and a maximum force of 200 Lbf (0.9 kN).

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Fig. ‎3-1: Micro hammer Dytran 5800SL with strength and extensible head sensor (dimensions in inches)

The small size of the hammer and the reduced weight of the head and the handle allow to reduce the overall inertia of the instrument being able to transfer to the structures impulsive forces with frequency band up to 300 kHz. In Tab.3-1 will bring the technical specifications of the impact hammer.

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Tab. ‎3-1: Specifications of the instrumented hammer Dytran 5800SL

3.3 Accelerometer Dytran 3133A1

The accelerometer 3133A1 model Dytran Instrument is a triaxial piezoelectric accelerometer with ICP technology. The instrument has a sensitivity of 10 mV / g, a resonant frequency greater than 35 kHz and a frequency band ranging from 0.25 to 7000 Hz for the x and y axes and from 0.25 to 10000 Hz for the z-axis. The RMS noise acceleration value estimated from the value of Spectral Noise (Tab.3-2), is then 0.02 g so accelerations below this value are not resolvable. The maximum value of measured acceleration is 500 g.

In Fig. 3-2 An accelerometer scheme is shown.

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Tab. ‎3-2: Specifiche tecniche dell'accelerometro Dytran 3133A1

Accelerometer Types 4507 and 4508 (fig.3-3) are specifically designed to withstand rough environments. A combination of high sensitivity, low mass and small physical dimensions makes them ideal for modal measurements such as automotive body and power-train ones as well as for modal analysis on aircraft, trains and satellites. The main difference between the Types 4507 and 4508 is the position of the coaxial connector, which is on the top surface perpendicular to the main axis for Type 4508 (top-mounted connector) and on the side surface parallel to the main axis for Type 4507 (side-mounted connector). Technical specifications is shown in Tab.3-3 and Tab.3-4.

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Fig. ‎3-3: CCLD Accelerometer

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Tab. ‎3-4: Technical specifications of accelerometer type 4508

3.4 Accelerometer Dytran model 3035BG

The Dytran model 3035BG is a miniature IEPE accelerometer, with a 100 mV/g sensitivity, an overall height of just 0.33 inches (8.3 millimeters) and a total weight of 2.5 grams. Sensors feature a rugged stainless steel construction, an adhesive mount and 5-44 radial connector. (Fig. 3-4, Tab.3-5)

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Tab. ‎3-5: Technical specifications of accelerometro type 3035BG

3.5 LMS SCADAS mobile SCM01

LMS SCADAS is an integrated hardware system in LMS Test.Lab package used for the acquisition of experimental modal analysis data. The system is constituted by an input module and a control module (Fig. 3-5).

The input module consists of 8 channels that can be expanded through a master-slave configuration. Each channel has a sampling frequency of up to 204.8 kHz with a voltage input mode or type of ICP. Within the system has an integrated 24-bit ADC technology.

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Fig. ‎3-5: LMS SCADAS mobile type SCM01

3.5.1 LMS Testing Solution Software

For the present work it has been used the LMS Test.Lab Structures software that includes an internal Test.Lab Impact Testing and Test.Lab Spectral Testing, used respectively in the case of experimental tests conducted with an instrumented hammer . The software includes within itself the Test.Lab Modal Analysis package useful for extracting modal parameters of the structure such as resonant frequencies, damping and mode shapes.

3.5.2 LMS Test.Lab Impact Testing

LMS Test.LabImpact Testing is a software that allows you to do vibrational mechanical tests on structures through the use of instrumented hammers. The software has several sections.

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3.6 Comparison between accelerometer1D and 3D:

Higher is the sensitivity of the accelerometer so lower is the measuring range.

As we found in this study, accelerometer 3D has a high frequency range (0.25-10000 Hz) but has low sensitivity (10 mv/g) therefore it does not solve well the low frequencies and has the low coherence and noisy FRF in the range of low frequencies.

While accelerometer 1D has a low frequency range compared to accelerometer 3D but has a high sensitivity so it can resolve the low frequencies.

3.7 Mode analysis: Polymax

In the Polymax section, modal structure parameters can be extracted using curve fitting techniques. The Stabilization Subsection (Fig.3-6 ) shows the stability diagram, the result of the curve fitting, with its estimated poles. By selecting stable poles, it is possible to extrapolate the resonance frequencies of the structure and its damping. The display of the Mode Indicator Function (MIF) in the Fig.3-6 on the stability diagram allows to detect adjacent poles; Each minimum point on the graph of the MIF corresponds to a stable pole.

Once the resonance frequencies are detected, in the Shapes section you can see the structure deformation modes associated with each frequency. (Reference thesis: Antonia Longo)

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3.8 General procedure of frequencies extraction:

Once you have defined the geometry and set the data save files, you can configure SCADAS acquisition channels and then connect the various transducers to the front end. In the Channel Setup section (Fig.3-7, 3-8) you must define for each connected transducer:

 The physical channel of the SCADAS to which it is connected (PhysicalChannelId).  Reference, active when the transducer is the reference.

 ChannelGroupId (vibrational or acoustic).  Point of Direction.

 InputMode, whether ICP or Charge.

 MeasuredQuantity: force for the instrument hammer and acceleration for the accelerometer.  Sensitivity.

(Reference thesis: Antonia Longo)

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Fig. ‎3-8: channel set up section

To begin our analysis after assembling accelerometers on the patient we need to do impact testing through the LMS software, the use of Impact Testing is a fast, convenient and low cost method for evaluating the vibrational response of structures. The excitation techniques used in experimental modal analysis are Impact Testing. In the case of Impact Testing, the output is fixed and the matrix of the FRF is measured, considering different inputs on the structure. This test is typically called roving hammer ,the accelerometer is considered as a reference. (Reference thesis: Antonia Longo)

To calibrate the system in the Impact Scope (Fig.3-9) section, it is possible to set the input range by automatically setting the range input of the measurement. In the same section you can define the various acquisition parameters such as frequency band, spectral points number, frequency resolution and observation period of the acquired signal.

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From the Impact Scope section (Fig 3-10) Trigger subassembly it is possible to give some test hammers to automatically set a pre-trigger for the impulse input signal to the software.

Fig. ‎3-10: Impact Setup Section

In the Measure Section (Fig 3-11), the input and output channels (Points) can be associated with the position and direction of impact and accelerometer so that they coincide with the position and SDR of the geometry nodes (if defined) . In the same section you can set the number of measurements to be used to mediate the data. By setting explicit accept mode the operator can accept the measure; The signal is accepted if the input PSD is flat in the frequency range of interest, if the coherence is good and if there are not multiple impacts.

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After this phase through the LMS (modal analysis, Fig. 3-12) software we can process the data to extract the frequencies for each configuration. An important parameter to check is reciprocity, after which we must find and evaluate the best entry and exit in upstream and downstream of fracture so to have a fracture in the middle of the input and output because they have better coherence and they have the cleanest Polymax, we avoided in / out that they are close together because in this case the accelerometers go in to over load and as a result drops the Coherence.

Fig. ‎3-12: modal analysis section

Then make the FRF matrix and evaluate the noisy measurements and then eliminate them, choose frequencies in the polymax part in the range of frequence that we considered for example in our study 0-1200 Hz . (Reference thesis: Antonia Longo)

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4 Test in-vivo: first case study

4.1 Test case description

The first case study was a 19 years old girl in the outcome of right femoral diaphysis fracture, had surgical operation for correction of sagittal and coronal plane deformities with osteotomy and abdominal wedge with the purpose of the right femur lengthening and then lengthening started after 10 days of intervention, lengthening performed for 24 days with distraction of external fixator.

Fig. ‎4-1: Session 1 (0 wks)

In this case there are three configuration that we considered "C0","C1" (Fig. 4-3(a)) which there is fixation with 6 pins, the difference of C0 and C1 is that in configuration C0 we are still in lengthening process and "C2 " (Fig. 4-3(b)) which there is fixation with 4 pins (Removing two pins, pins 3 and 4 because of infection) with dynamized fixation and in the end "C3" (Fig. 4-3(c)) there are just 4 pins without fixation. We misured in three boundary conditions: "l1" which patient lying with rubber just below the ankle and "l2" as the same l1 but rubbers are below both ankle and knee, anyway we prefered to continue the measures using twice rubber, the last one "s" that patient is standing with a broken leg "suspended" (foot off the ground, full support of healthy leg).

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Fig. ‎4-3 a) first configuration (C1)

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c)The last configuration (C3)

4.2 Set up of test І

The technique chosen was roving hammer “Roving hammer” , In the case of impact testing generally the output is fixed and the matrix of the FRF is measured by considering different inputs on the structure. This test is typically called roving hammer test. The accelerometer is considered as a reference.

As explained in the previous chapter, before starting the tests, you need to define the set-up in TestLab, that means:

1) Define the geometry of the structure that you are going to analyze and set the data saving files 2) Configure SCADAS acquisition channels and then connect the various transducers to the front-end.

In the Channel Setup section.(figure 4-4(a,b))

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Fig. ‎4-4 b) section of channel set up for session 5 to 7

In the Measure Section, the input and output channels (Points) can be associated with the position and direction of impact and accelerometer so that they coincide with the position and SDR of the geometry nodes (if defined) . In the same section you can set the number of measurements to be used to mediate the data. Our purpose is to extract frequencies from measurements made for each explained configurations above to analyze the healing process, we made the measurements in 7 sessions for this patient with three different configurations, having hammered several points then we read the measurements made using accelerometers 1D and 3D, at this point the software LMS convert the measurements in frequency and by this software we can control the reciprocity, coherence and FRF for choosing the best input and output in order to extract the best frequencies for each configuration. comparison is made only between the same configuration.

We found the best in put and out put in upstream and downstream of fracture so to have a fracture in the middle of input and output, because they have better coherence and they have the cleanest Polymax, we avoided in / out that they are close together because in this case the accelerometers go in to over load and as a result drops the coherence.

Fig. ‎4-6: General configuration and number pins

4.2.1 Reciprocity of the test (І) in each session

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Fig. ‎4-8: Rreciprocity of session 1, configurationC0

Fig. ‎4-9: Rreciprocity of session 2, configuration C1

1500.00 0.00 Hz 1.00 1.00e-3 Log g /N 1.00 0.00 A m p lit u d e / Y1 FRF fem_dx:4:-Z/fem_dx:3:+Z Y1 FRF fem_dx:3:+Z/fem_dx:4:+Z Y2 Coherence fem_dx:4:-Z/fem_dx:3:+Z Y2 Coherence fem_dx:3:+X/fem_dx:4:+Z 1500.00 0.00 Hz 1.00 0.10e-3 Log g /N 1.00 0.03 A m p lit u d e / Y1 FRF fem_dx:4:-Z/fem_dx:3:+Z Y1 FRF fem_dx:3:+Z/fem_dx:4:+Z Y2 Coherence fem_dx:4:-Z/fem_dx:6:+Z 3-4 Y2 Coherence fem_dx:3:+Z/fem_dx:6:+Z 4-3

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Fig. ‎4-10: Rreciprocity of session 3, configuration C1

Fig. ‎4-11: Rreciprocity of session 4, configuration C1

1500.00 0.00 Hz 1.00 0.10e-3 Log g /N 1.00 0.01 A m p lit u d e / Y1 FRF fem_dx:3:+Z/fem_dx:4:+Z Y1 FRF fem_dx:4:-Z/fem_dx:3:+Z Y2 Coherence fem_dx:3:+Z/fem_dx:4:+Z Y2 Coherence fem_dx:4:-Z/fem_dx:3:+Z 1500.00 0.00 Hz 1.00 0.10e-3 Log g /N 1.00 0.02 A m p lit u d e / Y1 FRF f em_dx:3:+Z/f em_dx:4:+Z Y1 FRF f em_dx:4:-Z/f em_dx:3:+Z Y2 Coherence f em_dx:4:-Z/f em_dx:3:+Z Y2 Coherence f em_dx:3:+Z/f em_dx:4:+Z

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Fig. ‎4-12: Rreciprocity of session 5, configuration C1

Fig. ‎4-13 :Reciprocity of session 6, configuration C2

1000.00 0.00 Hz 1.00 0.10e-3 Log g /N 1.00 0.00 A m p lit u d e / Y1 FRF fem_dx:1:-Z/fem_dx:6:+Z Y1 FRF fem_dx:6:-Z/fem_dx:1:+Z Y2 Coherence fem_dx:1:-Z/fem_dx:6:+Z Y2 Coherence fem_dx:6:-Z/fem_dx:1:+Z

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Fig. ‎4-14: Reciprocity of session 6, configuration C3 (lying)

Fig. ‎4-15: Reciprocity of session 6, configuration C3 (standing)

1000.00 0.00 Hz 1.00 0.01e-3 Log g /N 1.00 0.00 A m p lit u d e / Y1 FRF fem_dx:1:-Z/fem_dx:6:+Z Y1 FRF fem_dx:6:-Z/fem_dx:1:+Z Y2 Coherence fem_dx:1:-Z/fem_dx:6:+Z Y2 Coherence fem_dx:6:-Z/fem_dx:1:+Z 1000.00 0.00 Hz 1.00 0.10e-3 Log g /N 1.00 0.00 A m p lit u d e / Y1 FRF fem_dx:1:-Z/fem_dx:6:+Z Y1 FRF fem_dx:6:-Z/fem_dx:1:+Z Y2 Coherence fem_dx:1:-Z/fem_dx:6:+Z Y2 Coherence fem_dx:6:-Z/fem_dx:1:+Z

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Fig. ‎4-16: Reciprocity of session 7, configuration C3 (lying)

Fig. ‎4-17: Reciprocity of session 7, configuration C3 (standing)

1000.00 0.00 Hz 1.00 0.01e-3 Log g /N 1.00 0.00 A m p lit u d e / Y1 FRF fem_dx:1:-Z/fem_dx:6:+Z Y1 FRF fem_dx:6:-Z/fem_dx:1:+Z Y2 Coherence fem_dx:1:-Z/fem_dx:6:+Z Y2 Coherence fem_dx:6:-Z/fem_dx:1:+Z 1000.00 0.00 Hz 1.00 0.10e-3 Log g /N 1.00 0.00 A m p lit u d e / Y1 FRF fem_dx:1:-Z/fem_dx:6:+Z Y1 FRF fem_dx:6:-Z/fem_dx:1:+Z Y2 Coherence fem_dx:6:-Z/fem_dx:1:+Z Y2 Coherence fem_dx:1:-Z/fem_dx:6:+Z

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4.2.2 Modes analysis І

To extract the frequencies we used the LMS software, after choosing the best input and output, in Polymax we excluded the worst input and output and we chose the stable poles in the range of around 0-1200 Hz to extract the frequencies.