Determination of the difference between two complex polymer models simulating the behaviour of biological structures

biocybernetics and biomedical engineering 39 (2019) 503–511

Available online at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/bbe

Original Research Article

Determination of the difference between two complex polymer models simulating the behaviour of biological structures Barbara Kmiecik *, Magdalena Labowska, Jerzy Detyna Department of Mechanics, Materials Science and Engineering, Faculty of Mechanical Engineering, Wroclaw University of Science and Technology, WroclawPoland

article info

abstract

Article history:

This article presents research conducted on various polymer models imitating biological

Received 12 January 2019

structures. Tests were conducted using a newly developed research method described in [1].

Received in revised form

The purpose of our research was to check if the measuring system [1] is able to distinguish

2 April 2019

multilayer samples. Test materials were two different polymer models which were sub-

Accepted 3 April 2019

jected to pressure in the central point. Marked points on the external surface of the sample

Available online 10 April 2019

were followed during the measurement. The arrangement of points on the image allowed to

Keywords:

points. Measurements were repeated 10 times to ensure the representativeness (credibility)

Polymer models

of the conducted research. Statistical tests and artificial neural networks (ANN) were used to

reconstruct the 3D surface of the sample and to determine the displacement of the analysed

Hysteresis

classify the examined samples. We used 5-fold cross-validation for training and validating

Load

the ANN. The entire set of 75 cases was divided into 5 equinumerous subsets. The obtained

Displacement

results suggest that the proposed method distinguished between the tested samples on the

Biological structures

basis of results. Analysed materials react differently to the given mechanical factor. © 2019 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.

1.

Introduction

In the world of biology atoms and molecules are organized in cells, tissues, organs and individual organisms, hence gaining a complete knowledge of processes taking place in them requires a precise description of matter movement. Due to the fact that even the smallest analyzed volumes contain large numbers of atoms and molecules, it is more convenient to consider mechanics as continuum [2–7].

An engineer looking at the human body can see a mechanism which can perfectly transfer loads as a result of interactions with the external environment. The most important function of this system is the protection of internal organs enabling the body to maximally extend life. The role of tissues is to transfer loads by deformation. The knowledge of relations between these values characterizes tissues from the mechanical perspective and can be used as a basis for diagnosing and monitoring general treatment progress, or it can also be an

* Corresponding author at: Department of Mechanics, Materials Science and Engineering, Faculty of Mechanical Engineering, Wroclaw University of Science and Technology, Smoluchowskiego 25, Wroclaw 50-370, Poland. E-mail address: [email protected] (B. Kmiecik). https://doi.org/10.1016/j.bbe.2019.04.001 0208-5216/© 2019 Nalecz Institute of Biocybernetics and Biomedical Engineering of the Polish Academy of Sciences. Published by Elsevier B.V. All rights reserved.

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biocybernetics and biomedical engineering 39 (2019) 503–511

important element in the development of reconstructive surgery [8–17]. Currently scientists have access to a large number of publications describing tissues from both the biomechanical and mechanical perspective [5,18–22]. Despite this, there still are gaps in the understanding of even the simplest relations in live organisms [23–29]. The occurrence and progression of some human diseases may be related to changes in the mechanical properties of cells. Any deviation from their correct values may influence physiological functions and indicate a developing disease (e.g. malaria, neoplastic lesions) [30–35]. For instance, cancer most frequently causes structural changes which directly influence the mechanical properties (e.g. elasticity) [31] of lesions. Describing a single cell from an engineering perspective [36] will allow to better understand mechanisms leading to the development of pathological states [31,34,37,38]. Pathological states of soft tissues very often correlate with local stiffness changes, an example of which are neoplastic processes in which emerging tumours are usually very hard. There are also extremely soft changes, such as papillary carcinoma. In many pathological cases, prophylactic palpation tests are characterized by low sensitivity. Small and deep abnormal cell masses are then not detected [39]. For this reason, work is continuing on algorithms and devices that will be able to detect any type of cancer at a very early stage, which increases the chances of full recovery. Research on biological tissues is difficult to perform and interpret. For ethical reasons, in experiments materials from animals or posthumously from humans are used most often. Unfortunately, the in vitro tests do not allow for reproducible numerical results. This is probably caused by disruption of tissue continuity during sample preparation. For this reason, more and more scientists are moving towards non-invasive research in vivo [40–43]. In mechanical tests of soft tissues, biological samples are often replaced (due to bioethical reasons) with synthetic

materials of similar mechanical properties (e.g. silicone in the form of a phantom). Soft tissues and rubber materials can be described as nonlinear, anisotropic and not homogenic materials [44]. Because of these similarities in presented research we decided to use polymers instead of soft tissues. As part of the presented research, an original measurement stand was used, which, by application, should be enable to analyze in vivo the surface of biologically diverse soft tissues and initially identify possible structural changes (e.g. pathological). The aim of this work was to check whether the presented test method and measuring system is able to distinguish multilayer polymer models, without interrupting the material continuity. There are several similar setups in the world [8,42], but only proposed device is focused on the surface around the indenter.

2.

Materials and methods

Previous studies show that designed device and research methods (presented in [1]) can distinguish similar polymers (NBR, SBR and silicone [45]). In this study we wanted to check if measurement method can distinguish similar, complex polymer models.

2.1.

Materials

In presented studies polymers materials such as silicone and nitrile rubber (with diverse thick) were used to build multilayer polymer models, such as these in Fig. 1. Analyzed materials were glue together by silicone. Points were marked on the external surface of each sample and their movement was observed during mechanical extortion. (1)

Fig. 1 – Pictures of the analyzed polymer models.

biocybernetics and biomedical engineering 39 (2019) 503–511

505

MSS (multilayer silicone silicone): pumice 20 mm thick – polyurethane sponge 10 mm thick – silicone 2 mm thick – silicone 1 mm thick – silicone 0.5 mm thick; (2) MSN (multilayer silicone nitrile rubber): pumice 20 mm thick – polyurethane sponge 10 mm thick – NBR 2 mm thick - NBR 1 mm thick – silicone 0.5 mm thick.

2.2.

Measurement setup

The measuring stand consists of two high-speed cameras, the uArm arm and a set of microcontrollers with sensors (Fig. 2). Parameters of the devices used were selected in accordance with the literature and according to the expected measurement possibilities. The designed measuring system aims at deforming the sample at its central point and analyzing the changes occurring on its surface during mechanical forces. Then, based on the position of the tracked points, its external surface (3D) is reconstructed. This allows the determination of the real displacement (in all dimensions X, Y and Z) and the creation of a graph of the dependence of applied force on the displacement of a single point. The field of the resulting hysteresis is a measure of the energy absorbed by the material during mechanical extortion. It magnitude may suggest potential local stiffness changes.

2.3.

Methods

2.3.1.

Testing a new research method

The observation of the displacement of the points located on the surface of the tested material allows to establish the response of the sample to mechanical extortion. Such an observation (displacement recording) allows to determine the mechanical hysteresis area for a given measurement point, which can also be one of the parameters characterizing the mechanical properties of the sample. It is possible to generate graph representing the distribution of hysteresis area values for the set of all measurement points on the sample surface. In a situation when material continuity is broken, in the area surrounding this discontinuity a distinguishable disruption should occur. As a result of local rigidity changes, the dispersed energy of this place should be characterized by a different value (a diagram charactering the method is presented in Fig. 3).

Fig. 2 – The photo of measurement setup.

Fig. 3 – Diagram characterizing used research method.

Before the measurements of a sample, the points whose position will be analyzed during mechanical extortion, are marked on its surface (as it was mentioned). The measurements are taken using the specially constructed measurement setup (a spherical tipped indenter loaded the sample and cameras recorded its response) [1] and a programme developed in the LabVIEW environment, apart from this an optical flow algorithm was used to follow the determined points. Application of this method allowed to register a position of the point in every recorded image. First the point was marked manually, next optical flow was tracking it on the rest pictures. After that, the recorded data was processed by MATLAB software, which altogether allowed to determine the total displacement of a point during a measurement. Under the influence of mechanical extortion, the analyzed points could change their location (in a cartesian coordinate system X, Y, Z). The described point displacement D was calculated using Eq. (1):

D¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðXi X0 Þ2 þ ðYi Y 0 Þ2 þ ðZi Z0 Þ2

(1)

where X0, Y0, Z0 – position of an analyzed point at first image; Xi, Yi, Zi – position of an analyzed point at i image.

3.

Results and discussion

3.1.

Research results

In Fig. 4 we present photos were transfer to materials reconstructed 3D surfaces of the analyzed polymer models. It can be observed that the tested surfaces at the initial state are not ideally smooth, which may make their observation during loading and unloading slightly more difficult. Fig. 5 presents the dependence of displacement on the applied force for one set of measurement points (located 10 mm away from sample centre). It can be easily observed that during both loading and unloading the analyzed models reacted differently. This is confirmed by the determined parabolic curve factors, presented in Table 1. Both coefficients B and C represent different numerical values. It was also observed that larger differences occurred during loading than unloading (Table 2). Next, Fig. 6 presents the dependence of displacement as a function of the applied force for another set of

506

biocybernetics and biomedical engineering 39 (2019) 503–511

Fig. 4 – Reconstructed 3D surfaces (initial state) of analyzed models MSS and MSN.

Fig. 5 – Displacement of points located 10 mm away from sample centre during loading (A) and unloading (B) for MSS and MSN. Approximation of points displacement using function type: y = A + Bx + Cx2.

Table 1 – Statistics describing function matching: y = A + Bx + Cx2 type for each point located 10 mm from the place of applied force, where SEn – standard deviations; R2 – coefficient of determination; Chi2 – result of Chi-squared test. Process

No.

A

SEA

B

SEB

C

SEC

Chi 2

R2

Loading

MSS MSN MSS MSN

0.145 0.148 0.062 0.396

0.042 0.047 0.097 0.078

4.938 6.45 2.099 2.535

0.114 0.192 0.173 0.231

0.882 1.369 0.347 0.929

0.053 0.129 0.06 0.117

0.027 0.042 0.028 0.039

0.996 0.993 0.991 0.992

Unloading

Table 2 – Statistics describing function matching: y = A + Bx + Cx2 type, for points located 20 mm from the place of applied force, where SEn – standard deviations; R2–coefficient of determination; Chi2 – result of Chi-squared test. Process

No.

A

SEA

B

SEB

C

SEC

Chi 2

R2

Loading

MSS MSN

0.104 0.118

0.035 0.048

10.022 15.432

0.189 0.425

3.681 8.784

0.178 0.603

0.018 0.045

0.997 0.993

Unloading

MSS MSN

0.173 0.419

0.111 0.072

4.564 7.304

0.387 0.477

1.071 1.543

0.263 0.511

0.035 0.041

0.989 0.992

measurement points (located 20 mm from sample centre). Again, it can be observed that analyzed samples react differently to the applied mechanical extortion. The difference between the responses of the analyzed models

was larger during loading (Table 3). In the case of the analyzed points, probably coefficient B, whose values are more differentiated than in the case of coefficient C, plays a more important role.

507

biocybernetics and biomedical engineering 39 (2019) 503–511

Fig. 6 – Displacement of points located 20 mm from sample centre during loading (A) and unloading (B) for MSS and MSN. Approximation of points displacement using function type: y = A + Bx + Cx2.

Table 3 – Statistics describing function matching: y = A + Bx + Cx2 type for each point located 30 mm from the place of applied force, where SEn – standard deviations; R2 – coefficient of determination; Chi2 – result of Chi-squared test. Process

No.

A

SEA

B

SEB

C

SEC

Chi 2

R2

Loading

MSS MSN

0.1 0.345

0.03 0.074

19.564 42.16

0.321 1.597

13.64 63.97

0.609 5.643

0.015 0.09

0.998 0.986

Unloading

MSS MSN

0.21 0.691

0.126 0.086

8.782 21.901

0.862 1.381

4.716 2.005

1.154 3.675

0.043 0.045

0.986 0.991

Fig. 7 – Displacement of points located 30 mm from sample centre during loading (A) and unloading (B) for MSS and MSN. Approximation of points displacement using function type: y = A + Bx + Cx2.

Fig. 7 illustrates the dependence of the displacement on the applied force for another set points locates 30 mm from the centre of polymer samples. A significant discrepancy between the obtained responses for the tested samples can be observed, which is confirmed by the generated coefficients of approximated curves (Table 3). In the case of the analyzed points they are significantly different. The next figure, Fig. 8 presents the dependence of the displacement on the applied force for another set points locates 40 mm from the sample centre. It is clearly seen that the MSS model was more difficult to measure in comparison with MSN. The approximated curve for MSS during the loading process, probably does not present the actual model response

to the applied mechanical extortion. It can be also observed that the generated curve coefficients (Table 4), in the case of the MSS model are probably wrong.

3.2. Sample classification using artificial neural networks (ANN) After the experiment, it was decided to also verify the possibility of using neural networks to classify (differentiate between) the analysed samples [45-48]. In the presented work single-direction Multi-Layered Perceptron (MLP) network was used. We used 5-fold cross-validation for training and validating the ANN. The entire set of 75 cases was divided

508

biocybernetics and biomedical engineering 39 (2019) 503–511

Fig. 8 – Displacement of points located 40 mm from sample centre during loading (A) and unloading (B) for MSS and MSN. Approximation of points displacement using function type: y = A + Bx + Cx2.

Table 4 – Statistics describing function matching: y = A + Bx + Cx2 type for points located 30 mm from the place of applied force, where SEn – standard deviations; R2 – coefficient of determination; Chi2 – result of Chi-squared test. Process

No.

A

SEA

B

SEB

C

SEC

Chi 2

R2

Loading

MSS MSN

0.181 0.192

0.25 0.114

30.818 70.796

16.99 4.071

816.35 191.9

227 21.48

0.705 0.233

0.891 0.964

Unloading

MSS MSN

1.792 0.700

0.592 0.093

115.7 33.45

22.63 2.19

1999 1.224

192.2 8.726

0.292 0.058

0.908 0.988

Table 5 – Evaluation of the classification quality (2 classes) Yes Yes No

True positive(TP) False negative(FN)

No False Positive(FP) True negative(TN)

into 5 equinumerous subsets [49-53]. Construction and chosen of the MLP network parameters was carried out in the Statistica program. There is no universal rule which defines exactly what should be the proportion of the neurons number in the input, hidden and output layer. For most of our studies, the rule introduced by Andrea et al. gave good results [54]. This rule defines ratio of the training cases number to the total number of network parameters adjusted during training, described by the following formula (2):

Table 6 – Properties of the neural network used in the analyzed polymer models. Network name Quality (training) Quality (testing) Quality (validation) Learning algorithm Error function Activation (hidden) Activation (initial)

Quality of the classification depends on the correct assignment of objects to individual classes Table 5 [55-57]. Efficiency (quality of classification) is the fraction of correctly classified cases (shortcuts as in Table 5) was calculated by using equation (3):

Efficiency ¼ r¼

T ðI þ 1HþÞðH þ 1OÞ

(2)

where: T it means the number of training cases, while I, H and O respectively the number of neurons in the input, hidden and output layer.In order for the network to work properly, in opinion of the article authors [53], the values of coefficient should be in range from 1.8 to 2.2. Models for which the value of is higher than 3, generally do not have the ability to learn all the relevant characteristics of the training set, while the close to 1 indicates the excessive complexity of the model, which may give the opportunity to match the training set too closely and thus results in loss of the ability to generalize knowledge.

MLP 4-4-2 86.67 100 100 BFGS 9 Entropy Linear Softmax

TP þ TN TP þ FN þ FP þ TN

(3)

Table 6 presents the selected neural network in the case of which the results were the best. Calculation were carried out by STATISTICA 12.0. The presented data indicate over 85% efficiency of the learning process, which is a very good result. In the analysed network the activation function was linear. The input function was an exponential Softmax function, and the learning algorithm was the BFGS gradient method. Table 7 shows the summarized results obtained after processing input data by a selected neural network MLP 4-4-2. The presented results allow to classify the tested polymer models with over 85% accuracy. Simultaneously, it can be observed that the identification of multilayer structures

biocybernetics and biomedical engineering 39 (2019) 503–511

Table 7 – Summary of the classification of the analyzed polymer models.

Total Correct Incorrect Correct (%) Incorrect (%)

MSN

MSS

All samples

7 6 1 85.71 14.29

8 7 1 87.5 12.5

15 13 2 86.67 13.33

connected with an intermediate layer (liquid silicone connected particular layers) is very difficult and it has a negative effect on measurement repeatability (Fig. 8).

4.

Conclusions

During the tests of multilayer polymer models, different responses to the set mechanical extortion of the analyzed samples were observed. The generated coefficients of approximated curves not only differentiate, but also indicate the type of materials used to make given models. In the case of the MSS model the coefficients had lower values than in the case of MSN, similarly to silicone plates and NBR discussed in another publication [58]. The materials used in the presented research simulate the behaviour of biological tissues under the influence of mechanical extortion. However, in the future it is necessary to conduct similar tests on biological tissues. This type of research will make it possible to clearly establish whether the developed research method allows to differentiate between biological structures and if so to what extent, then such structures could be used in medical diagnostics. The research results described above indicate that the designed and structured system is able to distinguish materials with the same mechanical characteristics (viscoelastic), in different combinations (layered polymer models). However, the research was done on relatively few materials, and the production process of these materials is not fully known (each company has its own different methods used in the production of silicone and rubber boards). Therefore, in order to correctly generalize the results to the population, it would be necessary to repeat the tests on a larger number of samples (perspective). In addition, the measurements performed showed some problems that were initially difficult to identify, and which should be solved before the next tests (analysis of the results by means of several programmes, a large area of analysis, lack of research on a living alive). This work presents results for a new measuring system that focuses on surface analysis around an indenter. It is probably one of the first publications that considers material behaviour beyond the point of pressure. On the basis of the presented results we can suggest methods and the potential applicability of the medical device. It seems to fill the gap in the early diagnosis of some cancers (skin, breasts, liver, sarcomas). In this work, the results were presented using three programmes, but in the future only one of them will be used for this purpose, which additionally (or after a few seconds) will present the final result.

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