Simulasi Numerik dan Analisis Sensitivitas Model Kinetika Urea pada Proses Hemodialisis
DOI:
https://doi.org/10.30605/proximal.v9i1.8336Keywords:
Hemodialisis, Model Matematika, Kinetika Urea, Simulasi Numerik, Analisis SensitivitasAbstract
Gagal ginjal merupakan kondisi ketika ginjal tidak mampu menjalankan fungsinya secara optimal dalam menyaring zat sisa metabolisme dari darah. Salah satu metode terapi yang digunakan untuk menggantikan fungsi ginjal adalah hemodialisis, yaitu proses pembersihan darah dari zat-zat sisa metabolisme seperti urea menggunakan mesin dialisis. Penelitian ini bertujuan untuk menganalisis dinamika konsentrasi urea dalam tubuh pasien gagal ginjal ketika proses hemodialisis, menggunakan model matematika kinetik urea satu kompartemen. Model yang digunakan dinyatakan dalam bentuk persamaan diferensial yang menggambarkan perubahan konsentrasi urea dan volume cairan tubuh terhadap waktu. Analisis yang dilakukan meliputi penentuan titik kesetimbangan, analisis kestabilan sistem menggunakan pendekatan nilai eigen, simulasi numerik, serta analisis sensitivitas parameter model. Hasil analisis menunjukkan bahwa sistem memiliki satu titik kesetimbangan yang bersifat stabil asimtotik sehingga solusi sistem akan menuju kondisi keseimbangan seiring bertambahnya waktu. Hasil simulasi numerik menunjukkan bahwa konsentrasi urea dan volume cairan tubuh mengikuti perilaku yang konsisten dengan hasil analisis teoritis. Selain itu, analisis sensitivitas parameter menunjukkan bahwa parameter laju produksi urea memiliki hubungan positif dengan konsentrasi urea, sedangkan parameter clearance dialisis dan laju perubahan volume cairan tubuh memiliki hubungan negatif dengan konsentrasi urea. Simulasi numerik juga menunjukkan adanya nilai optimum parameter perubahan volume cairan tubuh yang menghasilkan dinamika konsentrasi urea yang lebih stabil. Secara klinis, hasil penelitian ini menunjukkan bahwa efektivitas proses hemodialisis dipengaruhi oleh keseimbangan antara laju produksi urea, kemampuan eliminasi urea melalui dialisis, serta pengaturan volume cairan tubuh pasien.
References
Aguiar, M., Anam, V., Blyuss, K. B., Estadilla, C. D. S., Guerrero, B. V., Knopoff, D., ... & Stollenwerk, N. (2022). Mathematical models for dengue fever epidemiology: A 10-year systematic review. Physics of life reviews, 40, 65-92.
Bani, A., Kasbawati, Toaha, S., Mardawati, E., Suhartini, S., Natsir, H., & Aris, N. (2025). Kinetic analysis of central metabolic regulation in Debaryomyces hansenii for enhanced xylitol and ethanol production from oil palm empty fruit bunches. Chemical Engineering Communications, 1-25.
Bani, A., & Toaha, S. (2021). Stability analysis of SCPUR mathematical model for the spread of COVID-19 (corona virus disease-19). J. Math. Comput. Sci., 11(4), 4082-4103.
Francis, A., Harhay, M. N., Ong, A. C., Tummalapalli, S. L., Ortiz, A., Fogo, A. B., ... & International Society of Nephrology. (2024). Chronic kidney disease and the global public health agenda: an international consensus. Nature Reviews Nephrology, 20(7), 473-485.
Hontelez, J. A., Goymann, H., Berhane, Y., Bhattacharjee, P., Bor, J., Chabata, S. T., ... & Bärnighausen, T. W. (2025). The impact of the PEPFAR funding freeze on HIV deaths and infections: a mathematical modelling study of seven countries in sub-Saharan Africa. EClinicalMedicine, 83.
Iziana, W. V., Widyantara, A. B., & Solikah, M. P. (2024). Hubungan Kadar Ureum dan Kreatinin dengan Elektrolit Pada Penderita Gagal Ginjal Kronik. Innovative: Journal Of Social Science Research, 4(6), 8902-8911.
Jadoul, M., Aoun, M., & Imani, M. M. (2024). The major global burden of chronic kidney disease. The Lancet Global Health, 12(3), e342-e343.
Kalantar-Zadeh, K., Jafar, T. H., Nitsch, D., Neuen, B. L., & Perkovic, V. (2021). Chronic kidney disease. The lancet, 398(10302), 786-802.
Layton, A. T. (2013). Mathematical modeling of kidney transport. Wiley Interdisciplinary Reviews: Systems Biology and Medicine, 5(5), 557-573.
Liftyowati, R., Widowati, R., & Camin, Y. R. (2022). Analisis Kadar Ureum dan Kreatinin pada Pasien Rawat Jalan Diabetes Melitus Tipe 2. Jurnal Penelitian Kesehatan" SUARA FORIKES, 13(4), 979-982.
Makmur, S. A., Madania, M., & Rasdianah, N. (2022). Gambaran interaksi obat pada pasien gagal ginjal kronik dalam proses hemodialisis. Indonesian Journal of Pharmaceutical Education, 2(3), 218-229.
Narsa, A. C., Maulidya, V., Reggina, D., Andriani, W., & Rijai, H. R. (2022). Studi Kasus: Pasien Gagal Ginjal Kronis (Stage V) dengan Edema Paru dan Ketidakseimbangan Cairan Elektrolit. Jurnal Sains Dan Kesehatan, 4(SE-1), 17-22.
Nasyafa, S. F., Saputra, O., & Zuraida, R. (2024). Homeostasis Tubuh. Medical Profession Journal of Lampung, 14(2), 249-253.
Nofiyanti, A., Nurhayati, A., Junita, D. E., & Wati, D. A. (2025). Asupan Protein Dengan Kadar Ureum Dan Kreatinin Pasien Gagal Ginjal Kronik Hemodialisa Rsud Pringsewu: Protein Intake Urea and Creatinine in Chronic Kidney Hemodialysis Patients at Pringsewu Hospital. Media Gizi Pangan, 32(1), 88-93.
Nuroini, F., & Wijayanto, W. (2022). Description Of Urea and Creatinine Levels in Chronic Renal Failure Patients at Wiradadi Husada Hospltal. Jambra Journal, 4(2), 538.
Pangestika, D. W., Sriyati, S. K., & Harun, S. (2023). Hubungan volume ultrafiltrasi dengan perubahan tekanan darah pada pasien chronic kidney disease (CKD) di ruang hemodialisa RSUD Kota Yogyakarta (Doctoral dissertation, Universitas' Aisyiyah Yogyakarta).
Pangkey, B. C. A., Klaping, A. A., Lote, A. C. K., Wariso, P. A., & Silaban, W. (2024). Faktor-Faktor yang Berhubungan dengan Perubahan Tekanan Darah pada Pasien Hemodialisis. Jurnal'Aisyiyah Medika, 9(2).
Pervyshin, N. A. (2024). Mathematical modeling of the chronic kidney disease progression rate in patients with type 2 diabetes mellitus. Science and Innovations in Medicine, 9(2), 88-94.
Purba, A. G., Sagala, D. S. P., Hasibuan, A. S., & Lubis, Y. S. (2024). Effectiveness of Intradialytic Exercise on Muscle Strength and Fatigue Score in Chronic Kidney Failure (CKF) Patients in the Grandmed Hemodialysis Room. Jurnal Keperawatan Dan Fisioterapi (JKF), 7(1), 15-20.
Rahayu, C., Permana, A., & Seprima, F. (2022). Studi Gambaran Kadar Asam Urat, Ureum dan Kreatinin Pada Pasien Gagal Ginjal Kronik. Anakes: Jurnal Ilmiah Analis Kesehatan, 8(1), 1-10.
Safitri, R., & Sutanto, A. (2025). Continuous Ambulatory Peritoneal Dialysis (CAPD) sebagai Terapi Pengganti Ginjal. Medical Profession Journal of Lampung, 15(3), 603-607.
Sari, P., Nurdini, L., Perdana, S. M., & Sayuti, S. (2022). Edukasi pencegahan penyakit tidak menular melalui gerakan masyarakat sehat. Jurnal Pengabdian Harapan Ibu (JPHI), 4(2), 36-43.
Suparmo, S., & Hasibuan, M. T. D. (2021). Hubungan kepatuhan pembatasan cairan terhadap terjadinya edema post hemodialisa pada pasien gagal ginjal kronik di Rumah Sakit Aminah Kota Tangerang. Indonesian trust health journal, 4(2), 522-528.
Takahashi, J., Tanaka, Y., Sato, Y., Hashimoto, H., Ueno, T., Kojima, S., ... & Mano, H. (2026). Spatial multiomic analyses reveal carcinogenic pathways in end-stage renal disease. Cancer Discovery, 16(3), 478-496.
Tolomeo, P., Butt, J. H., Kondo, T., Campo, G., Desai, A. S., Jhund, P. S., ... & McMurray, J. J. (2024). Independent prognostic importance of blood urea nitrogen to creatinine ratio in heart failure. European journal of heart failure, 26(2), 245-256.
Wahidin, M. (2023). Beban penyakit dan program pencegahan dan pengendalian penyakit tidak menular di indonesia. Jurnal Epidemiologi Kesehatan Indonesia, 6(2), 8.
Wang, Y., Gao, S., Hong, L., Hou, T., Liu, H., Li, M., ... & Zhang, Y. (2023). Prognostic impact of blood urea nitrogen to albumin ratio on patients with sepsis: a retrospective cohort study. Scientific reports, 13(1), 10013.
Yip, W., Ng, S. H. X., Kaur, P., George, P. P., Guan, J. H. C., Lee, G., ... & Hum, A. Y. M. (2024). Risk factors for short-term all-cause mortality in patients with end stage renal disease: a scoping review. BMC nephrology, 25(1), 71.
Yuwono, D. N. A., & Danial, D. (2025). Gambaran Pasien Penyakit Ginjal Kronik di RSUD Abdoel Wahab Sjahranie Samarinda pada Tahun 2022: Overview of Chronic Kidney Disease Patients at Abdoel Wahab Sjahranie Regional Hospital, Samarinda, in 2022. Jurnal Medika: Karya Ilmiah Kesehatan, 10(1), 7-28.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Alvioni Bani, Nur Rahmah Yunita Abar
This work is licensed under a Creative Commons Attribution 4.0 International License.
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
License and Copyright Agreement
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
