372 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 55, NO. 1, JANUARY 2008 whereas the stiffness decreases slowly with some delay during the sub- sequent decrease of [9]. Therefore lower values of result for the decrease of because of the delayed decrease of the stiffness. This hysteretic behaviour is in agreement with an exercise study [10], where the authors have demonstrated a reduction of the dynamic dis- tension of the carotid artery from peak exercise to early post-exercise; in addition, a constant pressure stimulus produced less distension in early post-exercise than during exercise because of the assumed active vasoconstriction. A further restriction of the SC-sensor is that the cardiovascular oscil- lations can be assessed on the superficial arteries only, as given in the case of the carotid artery. Deeper vessels can be expected to yield insuf- ficient reliability of palpating data. Of course, the correlation between and is influenced by various anatomic parameters with distinct individual variations. Lastly, it should be mentioned that the hysteretic behaviour of the SC-sensor ( over , Fig. 2(b)) is in the order of one percent and thus cannot significantly influence the aforementioned hysteretic behaviour between and . Summing up, the application of the novel skin curvature sensor on the neck over the carotid artery allows for the assessment of cardio- vascular oscillations of the artery. Multiple physiological data are re- flected, such as cardiac activity, respiratory activity, their mutual depen- dencies, and blood pressure changes. However, the assessment of car- diovascular oscillations has limitations due to the hysteretic mechan- ical behaviour of the artery wall. On the other hand, the hysteretic be- haviour may provide information regarding the autonomic control of the arterial wall stiffness, i.e., may be used as an indicator of the health of the arterial system. As an advantage, the extremely flat skin curva- ture sensor minimally disturbs the patient, which is relevant for many medical areas. REFERENCES [1] Y. W. Shau, C. L. Wang, J. Y. Shieh, and T. C. Hsu, “Noninvasive as- sessment of the viscoelasticity of peripheral arteries,” Ultrasound Med. Biol., vol. 25, no. 9, pp. 1377–1388, 1999. [2] W. R. Milnor, Hemodynamics. Baltimore, MD: Williams & Wilkins Publisher, 1989. [3] M. Sugawara, K. Niki, H. Furuhata, S. Ohnishi, and S. Suzuki, “Re- lationship between the pressure and diameter of the carotid artery in humans,” Heart Vessels, vol. 15, pp. 49–51, 2000. [4] E. Kaniusas, H. Pfützner, L. Mehnen, J. Kosel, G. Varoneckas, A. Alon- deris, T. Meydan, M. Vázquez, M. Rohn, A. M. Merlo, and B. Mar- quardt, “Magnetoelastic skin curvature sensor for biomedical applica- tions,” in Proc. IEEE Sensors, 2004, pp. 1484–1487. [5] E. Kaniusas, H. Pfützner, L. Mehnen, J. Kosel, J. C. Téllez-Blanco, G. Varoneckas, A. Alonderis, T. Meydan, M. Vázquez, M. Rohn, A. M. Merlo, and B. Marquard, “Method for continuous non-disturbing monitoring of blood pressure by magnetoelastic skin curvature sensor and ecg,” IEEE Sens. J., vol. 6, no. 3, pp. 819–828, 2006. [6] M. Elstad, K. Toska, K. H. Chon, E. A. Raeder, and R. J. Cohen, “Res- piratory sinus arrhythmia: Opposite effects on systolic and mean arte- rial pressure in supine humans,” J. Physiol., vol. 536.1, pp. 251–259, 2001. [7] A. Khasnis and Y. Lokhandwala, “Clinical signs in medicine: Pulsus paradoxus,” J. Postgrad. Med., vol. 48, no. 1, pp. 46–49, 2002. [8] H. Pfützner, E. Kaniusas, J. Kosel, L. Mehnen, T. Meydan, M. Vázquez, M. Rohn, A. M. Merlo, and B. Marquardt, “Magnetostrictive bilayers for multi-functional sensor families,” Sens. Actuators A: Phys., vol. 129, pp. 154–158, 2006. [9] T. J. Pedley, The Fluid Mechanics of Large Blood Vessels. Cam- bridge, MA: Cambridge Univ. Press, 1980. [10] P. Studinger, Z. Lenard, Z. Kovats, L. Kocsis, and M. Kollai, “Static and dynamic changes in carotid artery diameter in humans during and after strenuous exercise,” J. Physiol., vol. 550, no. 2, pp. 575–583, 2003. The Single Nerve Fiber Action Potential and the Filter Bank—A Modeling Approach Lotte N. S. Andreasen Struijk*, Metin Akay, and Johannes J. Struijk Abstract—Single fiber action potentials (SFAPs) from peripheral nerves, such as recorded with cuff electrodes, can be modelled as the convolution of a source current and a weight function that describes the recording elec- trodes and the surrounding medium. It is shown that for cuff electrodes, the weight function is linearly scaled with the action potential (AP) velocity and that it is, therefore, possible to implement a model of the recorded SFAPs based on a wavelet multiresolution technique (filterbank), where the wavelet scale is proportional to the AP velocity. The model resulted in single fiber action potentials matching the results from other models with a good- ness of fit exceeding 0.99. This formulation of the SFAP may serve as a basis for model-based wavelet analysis and for advanced cuff design. Index Terms—Cuff electrodes, filter bank, nerve signal, single fiber ac- tion potentials, wavelet. I. INTRODUCTION Electrical activity of peripheral nerves can be recorded with the use of cuff electrodes. Electroneurographic (ENG) signals thus obtained have been used as natural sensory feedback in humans for the control of functional electrical stimulation systems, such as for the correction of foot-drop or for restoration of movement in a paralyzed hand [3], [4]. An ENG signal as recorded with a cuff electrode is the superposition of many extracellular potential fields generated by single fiber action potentials (SFAPs). The performance of the cuff electrode can thus be understood using models for the SFAPs, which has prompted several experimental and theoretical modeling studies [1], [2], [5], which also have been used to improve cuff designs. Advanced signal processing methods have been used to analyze ENG signals from cuff electrodes [6]–[8], but, even though SFAPs are the building blocks of the ENG, SFAP models have never been used in those signal processing methods. Nevertheless, the idea of signal processing based on SFAP models is appealing both because of the composition of the ENG, being a superposition of SFAPs, and because of the wavelet-like properties of the SFAP, such as compact support, vanishing integral, and the near proportional dependency of the SFAP bandwidth with the velocity of the action potentials (APs). The velocity dependency of the SFAP makes it possible in principle to decompose the ENG into SFAPs at different levels (scales) of velocity, which is of great interest because of the distinct physiological functionality of fiber groups having different velocities. In the present work a first step is taken towards this model-based ENG analysis: here we focus on modeling SFAPs within the framework of a multiresolution signal representation, based on wavelets [9]–[11]. This is done by implementing a SFAP model using a filter bank struc- ture [10], [11] where the weight function as defined by the cuff elec- trode is used as the scaling function, the transmembrane action current Manuscript received March 28, 2006. This work was supported by grants from the European Commission (#QLG5-CT-2000-01372, SENS project). As- terisk indicates corresponding author. *L. N. S. Andreasen Struijk is with the Center for Sensory Motor Interaction, Aalborg University, DK-9220 Aalborg, Denmark (e-mail: naja@smi.auc.dk). M. Akay is with the Harrington Department of Bioengineering, Fulton School of Engineering, Arizona State University, Tempe, AZ 85287 USA. J. J. Struijk is with the Center for Sensory Motor Interaction, Aalborg Uni- versity, DK-9220 Aalborg, Denmark. Digital Object Identifier 10.1109/TBME.2007.903518 0018-9294/$25.00 © 2007 IEEE