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SENKRON SIKIŞTIRMA DÖNÜŞÜMÜ VE DERİN ÖĞRENME KULLANILARAK FOTOPLETİSMOGRAFİ TABANLI KAN BASINCI KESTİRİMİ

Year 2024, , 243 - 255, 03.03.2024

Yeşim Hekim Tanç , Mahmut Öztürk

https://doi.org/10.17780/ksujes.1376860

Abstract

Kalp ve damar hastalıkları en ölümcül sağlık sorunlarından biridir. Hipertansiyon, kardiyovasküler hastalıkların en yaygın nedenidir. Tansiyon düzeyini kontrol altında tutmak, hipertansiyonun ölümcül sonuçlarından kurtulmanın tek yoludur. Bu nedenle, hipertansiyonu olan hastalar için kan basıncının (KB) düzenli olarak izlenmesi, tehlikeli durumların tespitini mümkün kılar. Bilgisayar ve sensör teknolojilerindeki hızlı gelişmeler ile fotopletismogram (PPG) sinyalleri kullanılarak kan basıncının sürekli olarak izlenmesi mümkün hale gelmektedir. Bu çalışmada, tek kanallı PPG sinyali kullanan invazif olmayan bir KB tahmin yöntemi sunuyoruz. PPG sinyallerinin Zaman-Frekans (ZF) görüntülerini elde etmek için Eş Zamanlı Sıkıştırma Dönüşümünü kullandık. ZF görüntüleri, önceden eğitilmiş bir derin sinir ağını beslemek için kullanıldı. KB seviyelerini 5 saniyelik aralıklarla tahmin ettik. Yöntemimiz, sistolik ve diyastolik kan basıncı (SKB ve DKB) seviyelerini sırasıyla 0,2148 mmHg ve -0,0370 mmHg ortalama hata (ME) ile tahmin eder. Yöntemimizin ME değerleri uygulanabilir seviyelerdedir. Yöntemimizin standart sapması (SS) DKB için 5.0642 mmHg, SKB için 10.9904 mmHg değerindedir. AAMI tarafından belirlenmiş olan üst limit 8 mmHg değerindedir. Ayrıca yöntemimiz BHS standardına göre A ve B sınıfları ile uyumludur.

Keywords

Fotopletismografi Arteriyel kan basıncı Konvolüsyonel sinir ağı Zaman-Frekans analizi Senkron sıkıştırma dönüşümü.

Project Number

FBA-2022-36694

References

  • American National Standards Institute. ANSI/AAMI/ISO 81060–2:2013.Non-invasive sphygmomanometers - Part 2: clinical investigation of automated measurement type. http://webstore.ansi.org, Accessed July 15, 2017.
  • Arnold, M. A., Liu, L.,& Olesberg, J. T., (2007), Selectivity assessment of noninvasive glucose measurements based on analysis of multivariate calibration vectors, Journal of Diabetes Science and Technology, 1(4), 454–462.
  • Auger F., Flandrin P., Lin Y., et al, (2013). Time-Frequency reassignment and synchrosqueezing, IEEE Signal Processing Magazine, 30:32-41.
  • Chao, P. C. , Wu, P. C. -C. D., Nguyen, H. B. -S. Nguyen, P. -C. Huang and V. -H. Le, (2021). The Machine Learnings Leading the Cuffless PPG Blood Pressure Sensors Into the Next Stage, IEEE Sensors Journal, 21(11), 12498-12510, doi: 10.1109/JSEN.2021.3073850.
  • Daubechies, I., Lu, J., Wu, H.T., (2011), Synchrosqueezed wavelet transform: an empirical mode decomposition like tool, Appl. Comput. Harmon. Anal., 30(2), 243-261.
  • Elgendi M, Norton I, Brearley M, Abbott D, Schuurmans D. (2013), Systolic peak detection in acceleration photoplethysmograms measured from emergency responders in tropical conditions. PLoS One, 8:e76585.
  • El-Hajj, C., and Kyriacou, P.A, (2021), Cuffless blood pressure estimation from PPG signals and its derivatives using deep learning models, Biomedical Signal Processing and Control, 70, 102984.
  • El-Hajj, C., and Kyriacou, P.A., (2020), A review of machine learning techniques in photoplethysmography for the non-invasive cuff-less measurement of blood pressure, Biomedical Signal Processing and Control, 58,.
  • Esmaelpoor, J., Moradi, M. H., and Kadkhodamohammadi, A., (2020), A multistage deep neural network model for blood pressure estimation using photoplethysmogram signals, Computer in Biology and Medicine, 120, 103719.
  • He, K., Zhang, X., Ren, S., and Sun, J., (2016), Deep Residual Learning for Image Recognition, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770-778, doi: 10.1109/CVPR.2016.90.
  • Johnston, William S., (2006), Development of a Signal Processing Library for Extraction of SpO2, HR, HRV, and RR from PhotoplethysmographicWaveforms, Masters Theses (All Theses, All Years), 919, https://digitalcommons.wpi.edu/etd-theses/919.
  • Kachuee, M., Kiani, M. M., Mohammadzade, H., and Shabany, M., (2017), Cuffless Blood Pressure Estimation Algorithms for Continuous Health-Care Monitoring, IEEE Transactions on Biomedical Engineering, 64,(4), 859-869.
  • Kachuee, M., Kiani, M. M., Mohammadzade, H., and Shabany, M., (2015), Cuff-less high-accuracy calibration-free blood pressure estimation using pulse transit time, 2015 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1006-1009.
  • Kayadelen, C., Altay, G., Önal, S., & Önal, Y., (2022) Sequential minimal optimization for local scour around bridge piers, Marine Georesources & Geotechnology, 40:4, 462-472, DOI: 10.1080/1064119X.2021.1907635
  • Kim, B.S., & Yoo S. K.,(2006), Motion artifact reduction in photoplethysmography using independent component analysis, IEEE Transactions on Bio-Medical Engineering, 53 (3), 566–568.
  • Kraitl J, Ewald H (2005), Optical non-invasive methods for characterization of the human health status. In: Presented at the 21st international conference on sensing technology, Palmerston North, New Zealand.
  • Kurylyak, Y., Lamonaca, F., and Grimaldi, D., (2013), A Neural Network-based method for continuous blood pressure estimation from a PPG signal, 2013 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), pp. 280-283.
  • Lang, N., Kalischek, N., Armston, J., Schindler, K., Dubayah, R., & Wegner, J. D. (2022). Global canopy height regression and uncertainty estimation from GEDI LIDAR waveforms with deep ensembles. Remote Sensing of Environment, 268, 112760.
  • Lázaro, J., Gil, E., Vergara, J. M., & Laguna, P., (2014), Pulse rate variability analysis for discrimination of sleep-apnea-related decreases in the amplitude fluctuations of pulse photoplethysmographic signal in children. IEEE Journal of Biomedical and Health Informatics, 18(1), 240-246.
  • Liang, Y., Chen, Z., Ward, R., & Elgendi, M. (2018), Photoplethysmography and deep learning: enhancing hypertension risk stratification, Biosensors, 8(4), 101.
  • Liu Z, Zhou B, Li Y, Tang M, Miao F. (2020), Continuous Blood Pressure Estimation From Electrocardiogram and Photoplethysmogram During Arrhythmias. Front Physiol. Sep 9;11:575407. doi: 10.3389/fphys.2020.575407. PMID: 33013491; PMCID: PMC7509183.
  • McDuff D., Gontarek S. & Picard R. W., (2014), Remote detection of photoplethysmographic systolic and diastolic peaks using a digital camera, IEEE Transactions on Biomedical Engineering, 61(12), 2948-2954.
  • O’brien E., Waeber B., Parati G., Staessen J., Myers M.G. (2001), Blood pressure measuring devices: Recommendations of the European Society of Hypertension. BMJ.; 322:531–536.
  • Oğuz, F.E., Alkan, A. & Schöler, T. (2023), Emotion detection from ECG signals with different learning algorithms and automated feature engineering. SIViP, 17, 3783–3791. https://doi.org/10.1007/s11760-023-02606-y
  • Pour Ebrahim, M., Heydari, F., Wu, T. et al. (2019), Blood Pressure Estimation Using On-body Continuous Wave Radar and Photoplethysmogram in Various Posture and Exercise Conditions. Sci Rep 9, 16346.
  • Rodríguez, Juan C.R., et al. (2013), Innovative continuous non-invasive cuffless blood pressure monitoring based on photoplethysmography technology. Intensive Care Medicine 39.9: 1618-1625.
  • Saeed, M., Villarroel, M., Reisner, A.T., Clifford, G., Lehman, L., Moody, G.B., Heldt, T., Kyaw, T.H., Moody, B.E., Mark, R.G.. (2011 May), Multiparameter intelligent monitoring in intensive care II (MIMIC-II): A public-access ICU database. Critical Care Medicine, 39(5):952-960; DO: 10.1097/CCM.0b013e31820a92c6.
  • Salehizadeh, S. M., Dao, D. K., Chong, J. W., McManus, D., Darling, C., Mendelson, Y., & Chon, K. H.,(2014), Photoplethysmograph signal reconstruction based on a novel motion artifact detection-reduction approach. Part II: Motion and noise artifact removal, Annals of Biomedical Engineering, 42(11), 2251–2263.
  • Shin H. S., Lee C., & Lee M., (2009), Adaptive threshold method for the peak detection of photoplethysmographic waveform, Computers in Biology and Medicine, 39(12), 1145-1152.
  • Silva, I, Moody, G. (2014), An Open-source Toolbox for Analysing and Processing PhysioNet Databases in MATLAB and Octave. Journal of Open Research Software 2(1):e27 [http://dx.doi.org/10.5334/jors.bi].
  • Slapničar G, Mlakar N, Luštrek M. (2019), Blood Pressure Estimation from Photoplethysmogram Using a Spectro-Temporal Deep Neural Network. Sensors (Basel). Aug 4;19(15):3420. doi: 10.3390/s19153420.
  • Sun, X., Zhou, L., Chang, S., & Liu, Z. (2021), Using CNN and HHT to predict blood pressure level based on photoplethysmography and its derivatives, Biosensors, 11(4), 120.
  • Sunnetci, KM, Kaba, E, Beyazal Çeliker, F, Alkan, A. (2023), Comparative parotid gland segmentation by using ResNet-18 and MobileNetV2 based DeepLab v3+ architectures from magnetic resonance images. Concurrency Computat Pract Exper. ; 35(1):e7405. doi:10.1002/cpe.7405
  • Suzuki, T., Kameyama, K.,& Tamura, T., (2009), Development of the irregular pulse detection method in daily life using wearable photoplethysmographic sensor, Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Annual International Conference, 6080-6083.
  • Tanveer, M.S., Hasan, M.K. (2019), Cuffless blood pressure estimation from electrocardiogram and photoplethysmogram using waveform based ANN-LSTM network, Biomedical Signal Processing and Control, 51, 382-392.
  • Tazarv, A. and Levorato, M., (2021), A deep learning approach to predict blood pressure from ppg signals, in 2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 5658–5662, Mexico.
  • Teng, X. F., and Y. T. Zhang. (2003), Continuous and noninvasive estimation of arterial blood pressure using a photoplethysmographic approach, Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No. 03CH37439). Vol. 4. IEEE.
  • Tjahjadi, H., Ramli, K., & Murfi, H. (2020). Noninvasive classification of blood pressure based on photoplethysmography signals using bidirectional long short-term memory and time-frequency analysis. IEEE Access, 8, 20735-20748.
  • World Health Organization [2022-05-22]. Hypertension. https://www.who.int/news-room/fact-sheets/detail/hypertension
  • Xing, X., & Sun, M. (2016). Optical blood pressure estimation with photoplethysmography and FFT-based neural networks. Biomedical Optics Express, 7(8), 3007-3020.
  • Yousef Q., Reaz M. B. I., Ali, M. A. M., (2012), The analysis of PPG morphology: investigating the effects of aging on arterial compliance, Measurement Science Review, 12(6), 266-271.

PHOTOPLETHYSMOGRAPHY BASED BLOOD PRESSURE ESTIMATION USING SYNCHROSQUEEZING TRANSFORM AND DEEP LEARNING

Year 2024, , 243 - 255, 03.03.2024

Yeşim Hekim Tanç , Mahmut Öztürk

https://doi.org/10.17780/ksujes.1376860

Abstract

Cardiovascular diseases are one of the deadliest health problems. Hypertension is the most common reason for cardiovascular diseases. Keeping the blood pressure (BP) level under control is the only way to protect against the deadly results of hypertension. Therefore, monitoring BP regularly makes it possible to detect dangerous conditions in patients with hypertension. With the rapid developments in computers and sensor technologies, it is becoming possible to monitor BP levels continuously by using photoplethysmogram (PPG) signals. This work presents a non-invasive BP prediction method using one channel PPG signal. We employed the Synchrosqueezing Transform to obtain Time-Frequency (TF) images of the PPG signals. The TF images were used to feed a pre-trained deep neural network. We estimated the BP levels inside the 5-second intervals. Our method estimates BP levels with a mean error (ME) of 0.2148 mmHg and -0.0370 mmHg in the systolic and diastolic blood pressure (SBP and DBP) respectively. The ME values of our method are in the applicable levels. The standard deviation (SD) of our method is 5.0642 mmHg for DBP and 10.9904 mmHg for SBP. The upper limit specified by the AAMI is 8 mmHg. Also, our method is coherent with grades A and B according to the BHS standard.

Keywords

Photoplethysmography Arterial blood pressure Convolutional neural network Time-Frequency analysis Synchrosqueezing transform.

Supporting Institution

Scientific Research Projects Coordination Unit of Istanbul University - Cerrahpasa

Project Number

FBA-2022-36694

Thanks

This work was supported by Scientific Research Projects Coordination Unit of Istanbul University - Cerrahpasa with project number FBA-2022-36694.

References

  • American National Standards Institute. ANSI/AAMI/ISO 81060–2:2013.Non-invasive sphygmomanometers - Part 2: clinical investigation of automated measurement type. http://webstore.ansi.org, Accessed July 15, 2017.
  • Arnold, M. A., Liu, L.,& Olesberg, J. T., (2007), Selectivity assessment of noninvasive glucose measurements based on analysis of multivariate calibration vectors, Journal of Diabetes Science and Technology, 1(4), 454–462.
  • Auger F., Flandrin P., Lin Y., et al, (2013). Time-Frequency reassignment and synchrosqueezing, IEEE Signal Processing Magazine, 30:32-41.
  • Chao, P. C. , Wu, P. C. -C. D., Nguyen, H. B. -S. Nguyen, P. -C. Huang and V. -H. Le, (2021). The Machine Learnings Leading the Cuffless PPG Blood Pressure Sensors Into the Next Stage, IEEE Sensors Journal, 21(11), 12498-12510, doi: 10.1109/JSEN.2021.3073850.
  • Daubechies, I., Lu, J., Wu, H.T., (2011), Synchrosqueezed wavelet transform: an empirical mode decomposition like tool, Appl. Comput. Harmon. Anal., 30(2), 243-261.
  • Elgendi M, Norton I, Brearley M, Abbott D, Schuurmans D. (2013), Systolic peak detection in acceleration photoplethysmograms measured from emergency responders in tropical conditions. PLoS One, 8:e76585.
  • El-Hajj, C., and Kyriacou, P.A, (2021), Cuffless blood pressure estimation from PPG signals and its derivatives using deep learning models, Biomedical Signal Processing and Control, 70, 102984.
  • El-Hajj, C., and Kyriacou, P.A., (2020), A review of machine learning techniques in photoplethysmography for the non-invasive cuff-less measurement of blood pressure, Biomedical Signal Processing and Control, 58,.
  • Esmaelpoor, J., Moradi, M. H., and Kadkhodamohammadi, A., (2020), A multistage deep neural network model for blood pressure estimation using photoplethysmogram signals, Computer in Biology and Medicine, 120, 103719.
  • He, K., Zhang, X., Ren, S., and Sun, J., (2016), Deep Residual Learning for Image Recognition, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770-778, doi: 10.1109/CVPR.2016.90.
  • Johnston, William S., (2006), Development of a Signal Processing Library for Extraction of SpO2, HR, HRV, and RR from PhotoplethysmographicWaveforms, Masters Theses (All Theses, All Years), 919, https://digitalcommons.wpi.edu/etd-theses/919.
  • Kachuee, M., Kiani, M. M., Mohammadzade, H., and Shabany, M., (2017), Cuffless Blood Pressure Estimation Algorithms for Continuous Health-Care Monitoring, IEEE Transactions on Biomedical Engineering, 64,(4), 859-869.
  • Kachuee, M., Kiani, M. M., Mohammadzade, H., and Shabany, M., (2015), Cuff-less high-accuracy calibration-free blood pressure estimation using pulse transit time, 2015 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1006-1009.
  • Kayadelen, C., Altay, G., Önal, S., & Önal, Y., (2022) Sequential minimal optimization for local scour around bridge piers, Marine Georesources & Geotechnology, 40:4, 462-472, DOI: 10.1080/1064119X.2021.1907635
  • Kim, B.S., & Yoo S. K.,(2006), Motion artifact reduction in photoplethysmography using independent component analysis, IEEE Transactions on Bio-Medical Engineering, 53 (3), 566–568.
  • Kraitl J, Ewald H (2005), Optical non-invasive methods for characterization of the human health status. In: Presented at the 21st international conference on sensing technology, Palmerston North, New Zealand.
  • Kurylyak, Y., Lamonaca, F., and Grimaldi, D., (2013), A Neural Network-based method for continuous blood pressure estimation from a PPG signal, 2013 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), pp. 280-283.
  • Lang, N., Kalischek, N., Armston, J., Schindler, K., Dubayah, R., & Wegner, J. D. (2022). Global canopy height regression and uncertainty estimation from GEDI LIDAR waveforms with deep ensembles. Remote Sensing of Environment, 268, 112760.
  • Lázaro, J., Gil, E., Vergara, J. M., & Laguna, P., (2014), Pulse rate variability analysis for discrimination of sleep-apnea-related decreases in the amplitude fluctuations of pulse photoplethysmographic signal in children. IEEE Journal of Biomedical and Health Informatics, 18(1), 240-246.
  • Liang, Y., Chen, Z., Ward, R., & Elgendi, M. (2018), Photoplethysmography and deep learning: enhancing hypertension risk stratification, Biosensors, 8(4), 101.
  • Liu Z, Zhou B, Li Y, Tang M, Miao F. (2020), Continuous Blood Pressure Estimation From Electrocardiogram and Photoplethysmogram During Arrhythmias. Front Physiol. Sep 9;11:575407. doi: 10.3389/fphys.2020.575407. PMID: 33013491; PMCID: PMC7509183.
  • McDuff D., Gontarek S. & Picard R. W., (2014), Remote detection of photoplethysmographic systolic and diastolic peaks using a digital camera, IEEE Transactions on Biomedical Engineering, 61(12), 2948-2954.
  • O’brien E., Waeber B., Parati G., Staessen J., Myers M.G. (2001), Blood pressure measuring devices: Recommendations of the European Society of Hypertension. BMJ.; 322:531–536.
  • Oğuz, F.E., Alkan, A. & Schöler, T. (2023), Emotion detection from ECG signals with different learning algorithms and automated feature engineering. SIViP, 17, 3783–3791. https://doi.org/10.1007/s11760-023-02606-y
  • Pour Ebrahim, M., Heydari, F., Wu, T. et al. (2019), Blood Pressure Estimation Using On-body Continuous Wave Radar and Photoplethysmogram in Various Posture and Exercise Conditions. Sci Rep 9, 16346.
  • Rodríguez, Juan C.R., et al. (2013), Innovative continuous non-invasive cuffless blood pressure monitoring based on photoplethysmography technology. Intensive Care Medicine 39.9: 1618-1625.
  • Saeed, M., Villarroel, M., Reisner, A.T., Clifford, G., Lehman, L., Moody, G.B., Heldt, T., Kyaw, T.H., Moody, B.E., Mark, R.G.. (2011 May), Multiparameter intelligent monitoring in intensive care II (MIMIC-II): A public-access ICU database. Critical Care Medicine, 39(5):952-960; DO: 10.1097/CCM.0b013e31820a92c6.
  • Salehizadeh, S. M., Dao, D. K., Chong, J. W., McManus, D., Darling, C., Mendelson, Y., & Chon, K. H.,(2014), Photoplethysmograph signal reconstruction based on a novel motion artifact detection-reduction approach. Part II: Motion and noise artifact removal, Annals of Biomedical Engineering, 42(11), 2251–2263.
  • Shin H. S., Lee C., & Lee M., (2009), Adaptive threshold method for the peak detection of photoplethysmographic waveform, Computers in Biology and Medicine, 39(12), 1145-1152.
  • Silva, I, Moody, G. (2014), An Open-source Toolbox for Analysing and Processing PhysioNet Databases in MATLAB and Octave. Journal of Open Research Software 2(1):e27 [http://dx.doi.org/10.5334/jors.bi].
  • Slapničar G, Mlakar N, Luštrek M. (2019), Blood Pressure Estimation from Photoplethysmogram Using a Spectro-Temporal Deep Neural Network. Sensors (Basel). Aug 4;19(15):3420. doi: 10.3390/s19153420.
  • Sun, X., Zhou, L., Chang, S., & Liu, Z. (2021), Using CNN and HHT to predict blood pressure level based on photoplethysmography and its derivatives, Biosensors, 11(4), 120.
  • Sunnetci, KM, Kaba, E, Beyazal Çeliker, F, Alkan, A. (2023), Comparative parotid gland segmentation by using ResNet-18 and MobileNetV2 based DeepLab v3+ architectures from magnetic resonance images. Concurrency Computat Pract Exper. ; 35(1):e7405. doi:10.1002/cpe.7405
  • Suzuki, T., Kameyama, K.,& Tamura, T., (2009), Development of the irregular pulse detection method in daily life using wearable photoplethysmographic sensor, Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Annual International Conference, 6080-6083.
  • Tanveer, M.S., Hasan, M.K. (2019), Cuffless blood pressure estimation from electrocardiogram and photoplethysmogram using waveform based ANN-LSTM network, Biomedical Signal Processing and Control, 51, 382-392.
  • Tazarv, A. and Levorato, M., (2021), A deep learning approach to predict blood pressure from ppg signals, in 2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 5658–5662, Mexico.
  • Teng, X. F., and Y. T. Zhang. (2003), Continuous and noninvasive estimation of arterial blood pressure using a photoplethysmographic approach, Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat. No. 03CH37439). Vol. 4. IEEE.
  • Tjahjadi, H., Ramli, K., & Murfi, H. (2020). Noninvasive classification of blood pressure based on photoplethysmography signals using bidirectional long short-term memory and time-frequency analysis. IEEE Access, 8, 20735-20748.
  • World Health Organization [2022-05-22]. Hypertension. https://www.who.int/news-room/fact-sheets/detail/hypertension
  • Xing, X., & Sun, M. (2016). Optical blood pressure estimation with photoplethysmography and FFT-based neural networks. Biomedical Optics Express, 7(8), 3007-3020.
  • Yousef Q., Reaz M. B. I., Ali, M. A. M., (2012), The analysis of PPG morphology: investigating the effects of aging on arterial compliance, Measurement Science Review, 12(6), 266-271.
There are 41 citations in total.

Details

Primary Language English
Subjects Image Processing, Pattern Recognition, Deep Learning
Journal Section Electrical and Electronics Engineering
Authors

Yeşim Hekim Tanç 0000-0001-8029-4253

Mahmut Öztürk 0000-0003-2600-7051

Project Number FBA-2022-36694
Publication Date March 3, 2024
Submission Date October 16, 2023
Acceptance Date November 7, 2023
Published in Issue Year 2024

Cite

APA Hekim Tanç, Y., & Öztürk, M. (2024). PHOTOPLETHYSMOGRAPHY BASED BLOOD PRESSURE ESTIMATION USING SYNCHROSQUEEZING TRANSFORM AND DEEP LEARNING. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 27(1), 243-255. https://doi.org/10.17780/ksujes.1376860