**Data Availability Statement:** Not applicable.

**Acknowledgments:** We thank Ph. Fernandes and F. Stocard from L3Médical for their financial support of the CAPNO2 project.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Agache, P. Carbon Dioxide Transcutaneous Pressure. In *Agache's Measuring the Skin*; Humbert, P., Maibach, H., Fanian, F., Agache, P., Eds.; Springer International Publishing: Cham, Switzerland, 2016; pp. 587–590. ISBN 978-3-319-26594-0.

2. Higgins, C. An Introduction to Acid-Base Balance in Health and Disease. 2004. Available online: https://acutecaretesting.org/en/articles/an-introduction-to-acidbase-balance-in-health-and-disease (accessed on 15 June 2022).

3. Higgins, C. Parameters That Reflect the Carbon Dioxide Content of Blood. 2008. Available online: https://acutecaretesting.org/en/articles/parameters-that-reflect-the-carbon-dioxide-content-of-blood (accessed on 15 June 2022).

4. Seifter, J.L.; Chang, H.-Y. Disorders of Acid-Base Balance: New Perspectives. *Kidney Dis.* **2016**, *2*, 170–186. [CrossRef]

5. Huttmann, S.E.; Windisch, W.; Storre, J.H. Techniques for the Measurement and Monitoring of Carbon Dioxide in the Blood. *Ann. Am. Thorac. Soc.* **2014**, *11*, 645–652. [CrossRef]

6. Hahn, C.E.W. Blood Gas Measurement. Review Article. *Clin. Phys. Physiol. Meas.* **1987**, *8*, 3–38. [CrossRef]

7. Rithalia, S.V.S. Developments in Transcutaneous Blood Gas Monitoring: A Review. *J. Med. Eng. Technol.* **1991**, *15*, 143–153. [CrossRef]

8. Severinghaus, J.W. The Current Status of Transcutaneous Blood Gas Analysis and Monitoring. *Blood Gas News* **1998**, *7*, 4–9.

9. Zosel, J.; Oelßner, W.; Decker, M.; Gerlach, G.; Guth, U. The Measurement of Dissolved and Gaseous Carbon Dioxide Concentration. *Meas. Sci. Technol.* **2011**, *22*, 072001. [CrossRef]

10. Dervieux, E.; Théron, M.; Uhring, W. Carbon Dioxide Sensing—Biomedical Applications to Human Subjects. *Sensors* **2021**, *22*, 188. [CrossRef]

11. Severinghaus, J.W.; Stafford, M.; Bradley, A.F. TcPCO, Electrode Design, Calibration and Temperature Gradient Problems. *Acta Anaesthesiol. Scand.* **1978**, *22*, 118–122. [CrossRef]

12. Thiele, F.A.J.; Kempen, L.H.J. A Micro Method for Measuring the Carbon Dioxide Release by Small Skin Areas. *Br. J. Dermatol.* **1972**, *86*, 463–471. [CrossRef]

13. Eletr, S.; Jimison, H.; Ream, A.K.; Dolan, W.M.; Rosenthal, M.H. Cutaneous Monitoring of Systemic $P_{CO2}$ on Patients in the Respiratory Intensive Care Unit Being Weaned from the Ventilator. *Acta Anaesthesiol. Scand.* **1978**, *22*, 123–127. [CrossRef]

14. Gehrich, J.L.; Lubbers, D.W.; Opitz, N.; Hansmann, D.R.; Miller, W.W.; Tusa, J.K.; Yafuso, M. Optical Fluorescence and Its Application to an Intravascular Blood Gas Monitoring System. *IEEE Trans. Biomed. Eng.* **1986**, *BME-33*, 117–132. [CrossRef]

15. Tufan, T.B.; Sen, D.; Guler, U. An Infra-Red-Based Prototype for a Miniaturized Transcutaneous Carbon Dioxide Monitor. In Proceedings of the 2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Guadalajara, Mexico, 1–5 November 2021; pp. 7132–7135.

16. Chatterjee, M.; Ge, X.; Kostov, Y.; Luu, P.; Tolosa, L.; Woo, H.; Viscardi, R.; Falk, S.; Potts, R.; Rao, G. A Rate-Based Transcutaneous $CO_2$ Sensor for Noninvasive Respiration Monitoring. *Physiol. Meas.* **2015**, *36*, 883–894. [CrossRef]

17. Ge, X.; Adangwa, P.; Lim, J.Y.; Kostov, Y.; Tolosa, L.; Pierson, R.; Herr, D.; Rao, G. Development and Characterization of a Point-of Care Rate-Based Transcutaneous Respiratory Status Monitor. *Med. Eng. Phys.* **2018**, *56*, 36–41. [CrossRef]

18. Iitani, K.; Tyson, J.; Rao, S.; Ramamurthy, S.S.; Ge, X.; Rao, G. What Do Masks Mask? A Study on Transdermal $CO_2$ Monitoring. *Med. Eng. Phys.* **2021**, *98*, 50–56. [CrossRef]

19. Grangeat, P. *Nanoscience: Nanobiotechnology and Nanobiology—Chap 13 Data Processing*; Boisseau, P., Houdy, P., Lahmani, M., Eds.; Springer: Berlin/Heidelberg, Germany, 2009; ISBN 978-3-540-88632-7.

20. Marco, S.; Gutierrez-Galvez, A. Signal and Data Processing for Machine Olfaction and Chemical Sensing: A Review. *IEEE Sens. J.* **2012**, *12*, 3189–3214. [CrossRef]

21. Candy, J.V. *Model-Based Signal Processing*; Wiley-IEEE Press: Hoboken, NJ, USA, 2006; ISBN 978-0-471-73266-2.

22. Al Fahoum, A.S.; Abu Al-Haija, A.O.; Alshraideh, H.A. Identification of Coronary Artery Diseases Using Photoplethysmography Signals and Practical Feature Selection Process. *Bioengineering* **2023**, *10*, 249. [CrossRef]

23. Kalman, R.E. A New Approach to Linear Filtering and Prediction Problems. *J. Basic Eng.* **1960**, *82*, 35–45. [CrossRef]

24. Chui, C.K.; Chen, G. *Kalman Filtering with Real-Time Applications*; Springer Series in Information Sciences; Springer: Berlin/Heidelberg, Germany, 1987; Volume 17, ISBN 978-3-662-02510-9.

25. Anderson, B.D.O.; Moore, J.B. *Optimal Filtering*; Dover Publications: New York, NY, USA, 2004; ISBN 978-1-62198-604-1.

26. Haykin, S.; Widrow, B. *Least-Mean-Square Adaptive Filters*, 1st ed.; Wiley-Interscience: Hoboken, NJ, USA, 2008.

27. Piiper, J. Respiratory Gas Exchange at Lungs, Gills and Tissues: Mechanisms and Adjustments. *J. Exp. Biol.* **1982**, *100*, 5–22. [CrossRef]

28. Piiper, J.; Scheid, P. Blood—Gas Equilibration in Lung. In *Pulmonary Gas Exchange*; West, J.B., Ed.; Academic Press: New York, NY, USA, 1980; ISBN 978-0-12-744501-4.

29. Farhi, L.E. Elimination of Inert Gas by the Lung. *Respir. Physiol.* **1967**, *3*, 1–11. [CrossRef]
30. King, J.; Unterkofler, K.; Teschl, G.; Teschl, S.; Koc, H.; Hinterhuber, H.; Amann, A. A Mathematical Model for Breath Gas Analysis of Volatile Organic Compounds with Special Emphasis on Acetone. *J. Math. Biol.* **2011**, *63*, 959–999. [CrossRef]

31. Unterkofler, K.; King, J.; Mochalski, P.; Jandacka, M.; Koc, H.; Teschl, S.; Amann, A.; Teschl, G. Modeling-Based Determination of Physiological Parameters of Systemic VOCs by Breath Gas Analysis: A Pilot Study. *J. Breath Res.* **2015**, *9*, 036002. [CrossRef]

32. Piiper, J.; Scheid, P. Gas Transport Efficacy of Gills, Lungs and Skin: Theory and Experimental Data. *Respir. Physiol.* **1975**, *23*, 209–221. [CrossRef]

33. Scheuplein, R.J.; Blank, I.H. Permeability of the Skin. *Physiol. Rev.* **1971**, *51*, 702–747. [CrossRef]

34. Scheuplein, R.J. Mechanism of Percutaneous Adsorption. *J. Investg. Dermatol.* **1965**, *45*, 334–346. [CrossRef]

35. Rosli, A.; Shoparwe, N.F.; Ahmad, A.L.; Low, S.C.; Lim, J.K. Dynamic Modelling and Experimental Validation of CO₂ Removal Using Hydrophobic Membrane Contactor with Different Types of Absorbent. *Sep. Purif. Technol.* **2019**, *219*, 230–240. [CrossRef]

36. Qazi, S.; Gómez-Coma, L.; Albo, J.; Druon-Bocquet, S.; Irabien, A.; Younas, M.; Sanchez-Marcano, J. Mathematical Modeling of CO₂ Absorption with Ionic Liquids in a Membrane Contactor, Study of Absorption Kinetics and Influence of Temperature. *J. Chem. Technol. Biotechnol.* **2020**, *95*, 1844–1857. [CrossRef]

37. Darabi, M.; Pahlavanzadeh, H. Mathematical Modeling of CO₂ Membrane Absorption System Using Ionic Liquid Solutions. *Chem. Eng. Process.-Process Intensif.* **2020**, *147*, 107743. [CrossRef]

38. Al-Marzouqi, M.; El-Naas, M.; Marzouk, S.; Abdullatif, N. Modeling of Chemical Absorption of CO₂ in Membrane Contactors. *Sep. Purif. Technol.* **2008**, *62*, 499–506. [CrossRef]

39. Faiz, R.; Al-Marzouqi, M. Mathematical Modeling for the Simultaneous Absorption of CO₂ and H₂S Using MEA in Hollow Fiber Membrane Contactors. *J. Membr. Sci.* **2009**, *342*, 269–278. [CrossRef]

40. Li, X.L.; Karimi, H.; McLellan, P.J.; McAuley, K.B.; Jeffrey, C. Mathematical Model for a Point-of-Care Sensor for Measuring Carbon Dioxide in Blood. *Sens. Actuators B Chem.* **2016**, *236*, 635–645. [CrossRef]

41. Grangeat, P.; Gharbi, S.; Koenig, A.; Comsa, M.-P.; Accensi, M.; Grateau, H.; Ghaith, A.; Chacaroun, S.; Doutreleau, S.; Verges, S. Evaluation in Healthy Subjects of a Transcutaneous Carbon Dioxide Monitoring Wristband during Hypo and Hypercapnia Conditions. In Proceedings of the 2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Montreal, QC, Canada, 20–24 July 2020; pp. 4640–4643.

42. Grangeat, P.; Gharbi, S.; Accensi, M.; Grateau, H. First Evaluation of a Transcutaneous Carbon Dioxide Monitoring Wristband Device during a Cardiopulmonary Exercise Test. In Proceedings of the 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Berlin, Germany, 23–27 July 2019; pp. 3352–3355.

43. Grangeat, P.; Gharbi, S.; Accensi, M.; Grateau, H. Dispositif Portable d'Estimation de La Pression Partielle de Gaz Sanguin. Portable Device for Estimating the Partial Pressure of Blood. Gas. Patent WO 2020/249466A1, 17 December 2020.

44. Lallemand, A. Écoulement des fluides—Équations de bilans. *Tech. Ing.* **1999**, *1*, BE8153.1–BE8153.18. [CrossRef]

45. Anissimov, Y.G.; Jepps, O.G.; Dancik, Y.; Roberts, M.S. Mathematical and Pharmacokinetic Modelling of Epidermal and Dermal Transport Processes. *Adv. Drug Deliv. Rev.* **2013**, *65*, 169–190. [CrossRef]

46. Couto, A.; Fernandes, R.; Cordeiro, M.N.S.; Reis, S.S.; Ribeiro, R.T.; Pessoa, A.M. Dermic Diffusion and Stratum Corneum: A State of the Art Review of Mathematical Models. *J. Control. Release* **2014**, *177*, 74–83. [CrossRef]

47. Fick's First Law. Available online: https://www.doitpoms.ac.uk/tlplib/diffusion/fick1.php (accessed on 22 June 2023).

48. Darby, R.; Chhabra, R.P. *Chemical Engineering Fluid Mechanics*, 3rd ed.; CRC Press: Boca Raton, FL, USA, 2016; ISBN 978-1-315-37067-5.

49. Fick's Second Law. Available online: https://www.doitpoms.ac.uk/tlplib/diffusion/fick2.php (accessed on 22 June 2023).

50. Mitragotri, S.; Anissimov, Y.G.; Bunge, A.L.; Frasch, H.F.; Guy, R.H.; Hadgraft, J.; Kasting, G.B.; Lane, M.E.; Roberts, M.S. Mathematical Models of Skin Permeability: An Overview. *Int. J. Pharm.* **2011**, *418*, 115–129. [CrossRef]

51. Comsa, M.-P. Méthodes Numériques Pour Un Dispositif de Suivi Autonome Personnalisé Des Gaz Transcutanés. Numerical Methods for a Personalized Autonomous Transcutaneous Gas Monitoring Device. EEATS—Signal Image Parole Telecoms. Ph.D. Thesis, UGA—Université Grenoble Alpes, Grenoble, France, 2022.

52. Grangeat, P.; Gharbi, S.; Accensi, M.; Grateau, H. Etude d'un modèle linéaire quadratique appliqué à la mesure optique infrarouge du gaz carbonique sanguin émis par la peau. In Proceedings of the 27° Colloque sur le Traitement du Signal et des Images, Lille, France, 29 August 2019.

53. Madrolle, S.; Grangeat, P.; Jutten, C. A Linear-Quadratic Model for the Quantification of a Mixture of Two Diluted Gases with a Single Metal Oxide Sensor. *Sensors* **2018**, *18*, 1785. [CrossRef]

54. Madrolle, S.; Duarte, L.T.; Grangeat, P.; Jutten, C. A Bayesian Blind Source Separation Method for a Linear-Quadratic Model. In Proceedings of the 2018 26th European Signal Processing Conference (EUSIPCO), Rome, Italy, 3–7 September 2018; pp. 1242–1246.

55. Madrolle, S.; Duarte, L.T.; Grangeat, P.; Jutten, C. Supervised Bayesian Source Separation of Nonlinear Mixtures for Quantitative Analysis of Gas Mixtures. In Proceedings of the 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Honolulu, HI, USA, 17–21 July 2018; pp. 1230–1233.

56. Madrolle, S. Méthodes de Traitement du Signal Pour L'analyse Quantitative de Gaz Respiratoires à Partir d'un Unique Capteur MOX. Signal Processing for Quantitative Analysis of Exhaled Breath Using a Single MOX Sensor. EEATS—Signal Image Parole Telecoms. Ph.D. Thesis, UGA—Université Grenoble Alpes, Grenoble, France, 2016.

57. Vaidya, D.S.; Nitsche, J.M.; Diamond, S.L.; Kofke, D.A. Convection-Diffusion of Solutes in Media with Piecewise Constant Transport Properties. *Chem. Eng. Sci.* **1996**, *51*, 5299–5312. [CrossRef]
30. King, J.; Unterkofler, K.; Teschl, G.; Teschl, S.; Koc, H.; Hinterhuber, H.; Amann, A. A Mathematical Model for Breath Gas Analysis of Volatile Organic Compounds with Special Emphasis on Acetone. *J. Math. Biol.* **2011**, *63*, 959–999. [CrossRef]

31. Unterkofler, K.; King, J.; Mochalski, P.; Jandacka, M.; Koc, H.; Teschl, S.; Amann, A.; Teschl, G. Modeling-Based Determination of Physiological Parameters of Systemic VOCs by Breath Gas Analysis: A Pilot Study. *J. Breath Res.* **2015**, *9*, 036002. [CrossRef]

32. Piiper, J.; Scheid, P. Gas Transport Efficacy of Gills, Lungs and Skin: Theory and Experimental Data. *Respir. Physiol.* **1975**, *23*, 209–221. [CrossRef]

33. Scheuplein, R.J.; Blank, I.H. Permeability of the Skin. *Physiol. Rev.* **1971**, *51*, 702–747. [CrossRef]

34. Scheuplein, R.J. Mechanism of Percutaneous Adsorption. *J. Investg. Dermatol.* **1965**, *45*, 334–346. [CrossRef]

35. Rosli, A.; Shoparwe, N.F.; Ahmad, A.L.; Low, S.C.; Lim, J.K. Dynamic Modelling and Experimental Validation of CO₂ Removal Using Hydrophobic Membrane Contactor with Different Types of Absorbent. *Sep. Purif. Technol.* **2019**, *219*, 230–240. [CrossRef]

36. Qazi, S.; Gómez-Coma, L.; Albo, J.; Druon-Bocquet, S.; Irabien, A.; Younas, M.; Sanchez-Marcano, J. Mathematical Modeling of CO₂ Absorption with Ionic Liquids in a Membrane Contactor, Study of Absorption Kinetics and Influence of Temperature. *J. Chem. Technol. Biotechnol.* **2020**, *95*, 1844–1857. [CrossRef]

37. Darabi, M.; Pahlavanzadeh, H. Mathematical Modeling of CO₂ Membrane Absorption System Using Ionic Liquid Solutions. *Chem. Eng. Process.-Process Intensif.* **2020**, *147*, 107743. [CrossRef]

38. Al-Marzouqi, M.; El-Naas, M.; Marzouk, S.; Abdullatif, N. Modeling of Chemical Absorption of CO₂ in Membrane Contactors. *Sep. Purif. Technol.* **2008**, *62*, 499–506. [CrossRef]

39. Faiz, R.; Al-Marzouqi, M. Mathematical Modeling for the Simultaneous Absorption of CO₂ and H₂S Using MEA in Hollow Fiber Membrane Contactors. *J. Membr. Sci.* **2009**, *342*, 269–278. [CrossRef]

40. Li, X.L.; Karimi, H.; McLellan, P.J.; McAuley, K.B.; Jeffrey, C. Mathematical Model for a Point-of-Care Sensor for Measuring Carbon Dioxide in Blood. *Sens. Actuators B Chem.* **2016**, *236*, 635–645. [CrossRef]

41. Grangeat, P.; Gharbi, S.; Koenig, A.; Comsa, M.-P.; Accensi, M.; Grateau, H.; Ghaith, A.; Chacaroun, S.; Doutreleau, S.; Verges, S. Evaluation in Healthy Subjects of a Transcutaneous Carbon Dioxide Monitoring Wristband during Hypo and Hypercapnia Conditions. In Proceedings of the 2020 42nd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), Montreal, QC, Canada, 20–24 July 2020; pp. 4640–4643.

42. Grangeat, P.; Gharbi, S.; Accensi, M.; Grateau, H. First Evaluation of a Transcutaneous Carbon Dioxide Monitoring Wristband Device during a Cardiopulmonary Exercise Test. In Proceedings of the 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Berlin, Germany, 23–27 July 2019; pp. 3352–3355.

43. Grangeat, P.; Gharbi, S.; Accensi, M.; Grateau, H. Dispositif Portable d'Estimation de La Pression Partielle de Gaz Sanguin. Portable Device for Estimating the Partial Pressure of Blood. Gas. Patent WO 2020/249466A1, 17 December 2020.

44. Lallemand, A. Écoulement des fluides—Équations de bilans. *Tech. Ing.* **1999**, *1*, BE8153.1–BE8153.18. [CrossRef]

45. Anissimov, Y.G.; Jepps, O.G.; Dancik, Y.; Roberts, M.S. Mathematical and Pharmacokinetic Modelling of Epidermal and Dermal Transport Processes. *Adv. Drug Deliv. Rev.* **2013**, *65*, 169–190. [CrossRef]

46. Couto, A.; Fernandes, R.; Cordeiro, M.N.S.; Reis, S.S.; Ribeiro, R.T.; Pessoa, A.M. Dermic Diffusion and Stratum Corneum: A State of the Art Review of Mathematical Models. *J. Control. Release* **2014**, *177*, 74–83. [CrossRef]

47. Fick's First Law. Available online: https://www.doitpoms.ac.uk/tlplib/diffusion/fick1.php (accessed on 22 June 2023).

48. Darby, R.; Chhabra, R.P. *Chemical Engineering Fluid Mechanics*, 3rd ed.; CRC Press: Boca Raton, FL, USA, 2016; ISBN 978-1-315-37067-5.

49. Fick's Second Law. Available online: https://www.doitpoms.ac.uk/tlplib/diffusion/fick2.php (accessed on 22 June 2023).

50. Mitragotri, S.; Anissimov, Y.G.; Bunge, A.L.; Frasch, H.F.; Guy, R.H.; Hadgraft, J.; Kasting, G.B.; Lane, M.E.; Roberts, M.S. Mathematical Models of Skin Permeability: An Overview. *Int. J. Pharm.* **2011**, *418*, 115–129. [CrossRef]

51. Comsa, M.-P. Méthodes Numériques Pour Un Dispositif de Suivi Autonome Personnalisé Des Gaz Transcutanés. Numerical Methods for a Personalized Autonomous Transcutaneous Gas Monitoring Device. *EEATS—Signal Image Parole Telecoms*. Ph.D. Thesis, UGA—Université Grenoble Alpes, Grenoble, France, 2022.

52. Grangeat, P.; Gharbi, S.; Accensi, M.; Grateau, H. Etude d'un modèle linéaire quadratique appliqué à la mesure optique infrarouge du gaz carbonique sanguin émis par la peau. In Proceedings of the 27° Colloque sur le Traitement du Signal et des Images, Lille, France, 29 August 2019.

53. Madrolle, S.; Grangeat, P.; Jutten, C. A Linear-Quadratic Model for the Quantification of a Mixture of Two Diluted Gases with a Single Metal Oxide Sensor. *Sensors* **2018**, *18*, 1785. [CrossRef]

54. Madrolle, S.; Duarte, L.T.; Grangeat, P.; Jutten, C. A Bayesian Blind Source Separation Method for a Linear-Quadratic Model. In Proceedings of the 2018 26th European Signal Processing Conference (EUSIPCO), Rome, Italy, 3–7 September 2018; pp. 1242–1246.

55. Madrolle, S.; Duarte, L.T.; Grangeat, P.; Jutten, C. Supervised Bayesian Source Separation of Nonlinear Mixtures for Quantitative Analysis of Gas Mixtures. In Proceedings of the 2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Honolulu, HI, USA, 17–21 July 2018; pp. 1230–1233.

56. Madrolle, S. Méthodes de Traitement du Signal Pour L'analyse Quantitative de Gaz Respiratoires à Partir d'un Unique Capteur MOX. Signal Processing for Quantitative Analysis of Exhaled Breath Using a Single MOX Sensor. *EEATS—Signal Image Parole Telecoms*. Ph.D. Thesis, UGA—Université Grenoble Alpes, Grenoble, France, 2016.

57. Vaidya, D.S.; Nitsche, J.M.; Diamond, S.L.; Kofke, D.A. Convection-Diffusion of Solutes in Media with Piecewise Constant Transport Properties. *Chem. Eng. Sci.* **1996**, *51*, 5299–5312. [CrossRef]
58. Ghasem, N. Modeling and Simulation of CO₂ Absorption Enhancement in Hollow-Fiber Membrane Contactors Using CNT-Water-Based Nanofluids. *J. Membr. Sci. Res.* **2019**, *5*, 295-302. [CrossRef]

59. Cao, F.; Gao, H.; Ling, H.; Huang, Y.; Liang, Z. Theoretical Modeling of the Mass Transfer Performance of CO₂ Absorption into DEAB Solution in Hollow Fiber Membrane Contactor. *J. Membr. Sci.* **2020**, *593*, 117439. [CrossRef]

60. Formaggia, L.; Quarteroni, A.; Veneziani, A. *Cardiovascular Mathematics*; MS&A: Modeling, Simulation and Applications; Springer: Berlin/Heidelberg, Germany, 2009; ISBN 978-88-470-1151-9.

61. Vlachopoulos, C.; O'Rourke, M.; Nichols, W.W. *McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles*, 6th ed.; CRC Press: London, UK, 2012; ISBN 978-0-429-16692-1.

62. Guyton, A.C.; Hall, J.E.; Cuculici, G.P.; Gheorghiu, A.W. *Tratat de Fiziologie a Omului. Bucureşti*; Editura Medicală; Callisto: Bucureşti, Romania, 2007.

63. Chappell, M.; Payne, S. *Physiology for Engineers*; Biosystems & Biorobotics; Springer International Publishing: Cham, Switzerland, 2016; Volume 13, ISBN 978-3-319-26195-9.

64. Agache, P. Main Skin Physical Constants. In *Agache's Measuring the Skin: Non-Invasive Investigations, Physiology, Normal Constants*; Humbert, P., Fanian, F., Maibach, H.I., Agache, P., Eds.; Springer International Publishing: Cham, Switzerland, 2017; pp. 1607–1622. ISBN 978-3-319-32383-1.

65. Severinghaus, J.W.; Stafford, M.; Thunstrom, A.M. Estimation of Skin Metabolism and Blood Flow with $TcPo_2$ and $TcPco_2$ Electrodes by Cuff Occlusion of the Circulation. *Acta Anaesthesiol. Scand.* **1978**, *22*, 9–15. [CrossRef]

66. Agache, P. Physical, Biological and General Constants of the Skin. In *Agache's Measuring the Skin: Non-Invasive Investigations, Physiology, Normal Constants*; Humbert, P., Fanian, F., Maibach, H.I., Agache, P., Eds.; Springer International Publishing: Cham, Switzerland, 2017; pp. 1623–1626. ISBN 978-3-319-32383-1.

67. Severinghaus, J.W.; Stupfel, M.; Bradley, A.F. Accuracy of Blood PH and $Pco_2$, Determination. *J. Appl. Physiol.* **1956**, *9*, 189–196. [CrossRef]

68. Lumb, A.B. *Nunn's Applied Respiratory Physiology—Chapter 10 Carbon Dioxide*; Elsevier Health Sciences: Amsterdam, The Netherlands, 2012; ISBN 978-0-7020-5416-7.

69. Itoh, S.; Yamamoto, K.; Mikami, T. [Measurement of skin conductance to gas in adults]. *Iyo Denshi Seitai Kogaku/Jpn. J. Med. Electron. Biol. Eng.* **1987**, *25*, 227–231.

70. Janssens, K.G.F.; Raabe, D.; Kozeschnik, E.; Miodownik, M.A.; Nestler, B. (Eds.) *Computational Materials Engineering*; Academic Press: Burlington, NJ, USA, 2007; p. iii. ISBN 978-0-12-369468-3.

71. Kozeschnik, E. 5.—Modeling Solid-State Diffusion. In *Computational Materials Engineering*; Janssens, K.G.F., Raabe, D., Kozeschnik, E., Miodownik, M.A., Nestler, B., Eds.; Academic Press: Burlington, NJ, USA, 2007; pp. 151–177. ISBN 978-0-12-369468-3.

72. Langtangen, H.P.; Linge, S. *Finite Difference Computing with PDEs: A Modern Software Approach*; Texts in Computational Science and Engineering; Springer International Publishing: Cham, Switzerland, 2017; Volume 16, ISBN 978-3-319-55455-6.

73. Linge, S.; Langtangen, H.P. Diffusion Equations. In *Finite Difference Computing with PDEs: A Modern Software Approach*; Langtangen, H.P., Linge, S., Eds.; Texts in Computational Science and Engineering; Springer International Publishing: Cham, Switzerland, 2017; pp. 207–322. ISBN 978-3-319-55456-3.

74. Scherer, P.O.J. *Computational Physics: Simulation of Classical and Quantum Systems*; Springer: Berlin/Heidelberg, Germany, 2010; ISBN 978-3-642-13989-5.

75. Scherer, P.O.J. Advection. In *Computational Physics: Simulation of Classical and Quantum Systems*; Scherer, P.O.J., Ed.; Graduate Texts in Physics; Springer International Publishing: Cham, Switzerland, 2017; pp. 427–454. ISBN 978-3-319-61088-7.

76. Scherer, P.O.J. Diffusion. In *Computational Physics: Simulation of Classical and Quantum Systems*; Graduate Texts in Physics; Scherer, P.O.J., Ed.; Springer International Publishing: Cham, Switzerland, 2017; pp. 479–491. ISBN 978-3-319-61088-7.

77. Crank, J.; Crank, J. *The Mathematics of Diffusion*, 2nd ed.; Oxford University Press: Oxford, UK; New York, NY, USA, 1979; ISBN 978-0-19-853411-2.

78. Comsa, M.-P.; Phlypo, R.; Grangeat, P. Inverting the Diffusion-Convection Equation for Gas Desorption through an Homogeneous Membrane by Kalman Filtering. In Proceedings of the 2022 30th European Signal Processing Conference (EUSIPCO), Belgrade, Serbia, 28 August–2 September 2022; pp. 1318–1322.

79. Amarah, A.A.; Petlin, D.G.; Grice, J.E.; Hadgraft, J.; Roberts, M.S.; Anissimov, Y.G. Compartmental Modeling of Skin Transport. *Eur. J. Pharm. Biopharm.* **2018**, *130*, 336–344. [CrossRef]

80. Dias, D.; Paulo Silva Cunha, J. Wearable Health Devices—Vital Sign Monitoring, Systems and Technologies. *Sensors* **2018**, *18*, 2414. [CrossRef]

81. Jin, H.; Abu-Raya, Y.S.; Haick, H. Advanced Materials for Health Monitoring with Skin-Based Wearable Devices. *Adv. Healthc. Mater.* **2017**, *6*, 1700024. [CrossRef]

82. Kireev, D.; Sel, K.; Ibrahim, B.; Kumar, N.; Akbari, A.; Jafari, R.; Akinwande, D. Continuous Cuffless Monitoring of Arterial Blood Pressure via Graphene Bioimpedance Tattoos. *Nat. Nanotechnol.* **2022**, *17*, 864–870. [CrossRef]

83. Akinwande, D.; Kireev, D. Wearable Graphene Sensors Use Ambient Light to Monitor Health. *Nature* **2019**, *576*, 220–221. [CrossRef]

84. Tricoli, A.; Nasiri, N.; De, S. Wearable and Miniaturized Sensor Technologies for Personalized and Preventive Medicine. *Adv. Funct. Mater.* **2017**, *27*, 1605271. [CrossRef]
58. Ghasem, N. Modeling and Simulation of CO₂ Absorption Enhancement in Hollow-Fiber Membrane Contactors Using CNT-Water-Based Nanofluids. *J. Membr. Sci. Res.* **2019**, *5*, 295-302. [CrossRef]

59. Cao, F.; Gao, H.; Ling, H.; Huang, Y.; Liang, Z. Theoretical Modeling of the Mass Transfer Performance of CO₂ Absorption into DEAB Solution in Hollow Fiber Membrane Contactor. *J. Membr. Sci.* **2020**, *593*, 117439. [CrossRef]

60. Formaggia, L.; Quarteroni, A.; Veneziani, A. *Cardiovascular Mathematics*; MS&A: Modeling, Simulation and Applications; Springer: Berlin/Heidelberg, Germany, 2009; ISBN 978-88-470-1151-9.

61. Vlachopoulos, C.; O'Rourke, M.; Nichols, W.W. *McDonald's Blood Flow in Arteries: Theoretical, Experimental and Clinical Principles*, 6th ed.; CRC Press: London, UK, 2012; ISBN 978-0-429-16692-1.

62. Guyton, A.C.; Hall, J.E.; Cuculici, G.P.; Gheorghiu, A.W. *Tratat de Fiziologie a Omului. Bucureşti*; Editura Medicală; Callisto: Bucureşti, Romania, 2007.

63. Chappell, M.; Payne, S. *Physiology for Engineers*; Biosystems & Biorobotics; Springer International Publishing: Cham, Switzerland, 2016; Volume 13, ISBN 978-3-319-26195-9.

64. Agache, P. Main Skin Physical Constants. In *Agache's Measuring the Skin: Non-Invasive Investigations, Physiology, Normal Constants*; Humbert, P., Fanian, F., Maibach, H.I., Agache, P., Eds.; Springer International Publishing: Cham, Switzerland, 2017; pp. 1607–1622. ISBN 978-3-319-32383-1.

65. Severinghaus, J.W.; Stafford, M.; Thunstrom, A.M. Estimation of Skin Metabolism and Blood Flow with $TcPo_2$ and $TcPco_2$ Electrodes by Cuff Occlusion of the Circulation. *Acta Anaesthesiol. Scand.* **1978**, *22*, 9–15. [CrossRef]

66. Agache, P. Physical, Biological and General Constants of the Skin. In *Agache's Measuring the Skin: Non-Invasive Investigations, Physiology, Normal Constants*; Humbert, P., Fanian, F., Maibach, H.I., Agache, P., Eds.; Springer International Publishing: Cham, Switzerland, 2017; pp. 1623–1626. ISBN 978-3-319-32383-1.

67. Severinghaus, J.W.; Stupfel, M.; Bradley, A.F. Accuracy of Blood PH and $Pco_2$ Determination. *J. Appl. Physiol.* **1956**, *9*, 189-196. [CrossRef]

68. Lumb, A.B. *Nunn's Applied Respiratory Physiology—Chapter 10 Carbon Dioxide*; Elsevier Health Sciences: Amsterdam, The Netherlands, 2012; ISBN 978-0-7020-5416-7.

69. Itoh, S.; Yamamoto, K.; Mikami, T. [Measurement of skin conductance to gas in adults]. *Iyo Denshi Seitai Kogaku/Jpn. J. Med. Electron. Biol. Eng.* **1987**, *25*, 227-231.

70. Janssens, K.G.F.; Raabe, D.; Kozeschnik, E.; Miodownik, M.A.; Nestler, B. (Eds.) *Computational Materials Engineering*; Academic Press: Burlington, NJ, USA, 2007; p. iii. ISBN 978-0-12-369468-3.

71. Kozeschnik, E. 5.—Modeling Solid-State Diffusion. In *Computational Materials Engineering*; Janssens, K.G.F., Raabe, D., Kozeschnik, E., Miodownik, M.A., Nestler, B., Eds.; Academic Press: Burlington, NJ, USA, 2007; pp. 151–177. ISBN 978-0-12-369468-3.

72. Langtangen, H.P.; Linge, S. *Finite Difference Computing with PDEs: A Modern Software Approach*; Texts in Computational Science and Engineering; Springer International Publishing: Cham, Switzerland, 2017; Volume 16, ISBN 978-3-319-55455-6.

73. Linge, S.; Langtangen, H.P. Diffusion Equations. In *Finite Difference Computing with PDEs: A Modern Software Approach*; Langtangen, H.P., Linge, S., Eds.; Texts in Computational Science and Engineering; Springer International Publishing: Cham, Switzerland, 2017; pp. 207–322. ISBN 978-3-319-55456-3.

74. Scherer, P.O.J. *Computational Physics: Simulation of Classical and Quantum Systems*; Springer: Berlin/Heidelberg, Germany, 2010; ISBN 978-3-642-13989-5.

75. Scherer, P.O.J. Advection. In *Computational Physics: Simulation of Classical and Quantum Systems*; Scherer, P.O.J., Ed.; Graduate Texts in Physics; Springer International Publishing: Cham, Switzerland, 2017; pp. 427–454. ISBN 978-3-319-61088-7.

76. Scherer, P.O.J. Diffusion. In *Computational Physics: Simulation of Classical and Quantum Systems*; Graduate Texts in Physics; Scherer, P.O.J., Ed.; Springer International Publishing: Cham, Switzerland, 2017; pp. 479–491. ISBN 978-3-319-61088-7.

77. Crank, J.; Crank, J. *The Mathematics of Diffusion*, 2nd ed.; Oxford University Press: Oxford, UK; New York, NY, USA, 1979; ISBN 978-0-19-853411-2.

78. Comsa, M.-P.; Phlypo, R.; Grangeat, P. Inverting the Diffusion-Convection Equation for Gas Desorption through an Homogeneous Membrane by Kalman Filtering. In Proceedings of the 2022 30th European Signal Processing Conference (EUSIPCO), Belgrade, Serbia, 28 August–2 September 2022; pp. 1318–1322.

79. Amarah, A.A.; Petlin, D.G.; Grice, J.E.; Hadgraft, J.; Roberts, M.S.; Anissimov, Y.G. Compartmental Modeling of Skin Transport. *Eur. J. Pharm. Biopharm.* **2018**, *130*, 336–344. [CrossRef]

80. Dias, D.; Paulo Silva Cunha, J. Wearable Health Devices—Vital Sign Monitoring, Systems and Technologies. *Sensors* **2018**, *18*, 2414. [CrossRef]

81. Jin, H.; Abu-Raya, Y.S.; Haick, H. Advanced Materials for Health Monitoring with Skin-Based Wearable Devices. *Adv. Healthc. Mater.* **2017**, *6*, 1700024. [CrossRef]

82. Kireev, D.; Sel, K.; Ibrahim, B.; Kumar, N.; Akbari, A.; Jafari, R.; Akinwande, D. Continuous Cuffless Monitoring of Arterial Blood Pressure via Graphene Bioimpedance Tattoos. *Nat. Nanotechnol.* **2022**, *17*, 864–870. [CrossRef]

83. Akinwande, D.; Kireev, D. Wearable Graphene Sensors Use Ambient Light to Monitor Health. *Nature* **2019**, *576*, 220–221. [CrossRef]

84. Tricoli, A.; Nasiri, N.; De, S. Wearable and Miniaturized Sensor Technologies for Personalized and Preventive Medicine. *Adv. Funct. Mater.* **2017**, *27*, 1605271. [CrossRef]
85. Zhang, C.; Zhang, S.; Zhang, D.; Yang, Y.; Zhao, J.; Yu, H.; Wang, T.; Wang, T.; Dong, X. Conductometric Room Temperature NOₓ Sensor Based on Metal-Organic Framework-Derived Fe₂O₃/Co₃O₄ Nanocomposite. *Sens. Actuators B Chem.* **2023**, *390*, 133894. [CrossRef]

86. Tomasic, I.; Tomasic, N.; Trobec, R.; Krpan, M.; Kelava, T. Continuous Remote Monitoring of COPD Patients-Justification and Explanation of the Requirements and a Survey of the Available Technologies. *Med. Biol. Eng. Comput.* **2018**, *56*, 547–569. [CrossRef]

87. Mochalski, P.; King, J.; Unterkofler, K.; Hinterhuber, H.; Amann, A. Emission Rates of Selected Volatile Organic Compounds from Skin of Healthy Volunteers. *J. Chromatogr. B Analyt. Technol. Biomed. Life Sci.* **2014**, *959*, 62–70. [CrossRef]

88. Arakawa, T.; Suzuki, T.; Tsujii, M.; Iitani, K.; Chien, P.-J.; Ye, M.; Toma, K.; Iwasaki, Y.; Mitsubayashi, K. Real-Time Monitoring of Skin Ethanol Gas by a High-Sensitivity Gas Phase Biosensor (Bio-Sniffer) for the Non-Invasive Evaluation of Volatile Blood Compounds. *Biosens. Bioelectron.* **2019**, *129*, 245–253. [CrossRef] [PubMed]

89. Ohkuwa, T.; Mizuno, T.; Kato, Y.; Nose, K.; Itoh, H.; Tsuda, T. Effects of Hypoxia on Nitric Oxide (NO) in Skin Gas and Exhaled Air. *Int. J. Biomed. Sci.* **IJBS 2006**, *2*, 279–283. [PubMed]

90. Sekine, Y.; Nikaido, N.; Sato, S.; Todaka, M.; Oikawa, D. Measurement of Toluene Emanating from the Surface of Human Skin in Relation to Toluene Inhalation. *J. Skin Stem Cell* **2019**, *6*, e99392. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
85. Zhang, C.; Zhang, S.; Zhang, D.; Yang, Y.; Zhao, J.; Yu, H.; Wang, T.; Wang, T.; Dong, X. Conductometric Room Temperature NOₓ Sensor Based on Metal-Organic Framework-Derived Fe₂O₃/Co₃O₄ Nanocomposite. *Sens. Actuators B Chem.* **2023**, *390*, 133894. [CrossRef]

86. Tomasic, I.; Tomasic, N.; Trobec, R.; Krpan, M.; Kelava, T. Continuous Remote Monitoring of COPD Patients-Justification and Explanation of the Requirements and a Survey of the Available Technologies. *Med. Biol. Eng. Comput.* **2018**, *56*, 547–569. [CrossRef]

87. Mochalski, P.; King, J.; Unterkofler, K.; Hinterhuber, H.; Amann, A. Emission Rates of Selected Volatile Organic Compounds from Skin of Healthy Volunteers. *J. Chromatogr. B Analyt. Technol. Biomed. Life Sci.* **2014**, *959*, 62–70. [CrossRef]

88. Arakawa, T.; Suzuki, T.; Tsujii, M.; Iitani, K.; Chien, P.-J.; Ye, M.; Toma, K.; Iwasaki, Y.; Mitsubayashi, K. Real-Time Monitoring of Skin Ethanol Gas by a High-Sensitivity Gas Phase Biosensor (Bio-Sniffer) for the Non-Invasive Evaluation of Volatile Blood Compounds. *Biosens. Bioelectron.* **2019**, *129*, 245–253. [CrossRef] [PubMed]

89. Ohkuwa, T.; Mizuno, T.; Kato, Y.; Nose, K.; Itoh, H.; Tsuda, T. Effects of Hypoxia on Nitric Oxide (NO) in Skin Gas and Exhaled Air. *Int. J. Biomed. Sci.* **IJBS 2006**, *2*, 279–283. [PubMed]

90. Sekine, Y.; Nikaido, N.; Sato, S.; Todaka, M.; Oikawa, D. Measurement of Toluene Emanating from the Surface of Human Skin in Relation to Toluene Inhalation. *J. Skin Stem Cell* **2019**, *6*, e99392. [CrossRef]

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.