## 4 Non-Contact Measurement of CPF via Cough Sounds  
### CPF Estimation Model Using Cough Sounds  
CPF was measured using various devices (Figure 2). However, some medical facilities do not provide these devices [25], and some studies have used a semiquantitative cough strength assessment method [47; 48]. Moreover, the complex setup of the device, including firm attachment of the facemask and infection control filter to the patient, imposes a burden on both patients and caregivers. In addition, the measured CPF can vary depending on the type of facemask and filter. Furthermore, the mask, which should be firmly attached to the patient's face to prevent air leakage, makes it difficult for the subject to cough naturally and voluntarily. These problems could be solved by the use of cough sounds. Several previous studies proposed methods to monitor cough frequency using a microphone [49; 50; 51], and measurements of cough frequency using cough sound were introduced by the European Respiratory Society guidelines in 2007 [9]. However, no other studies attempted to design cough sound measurements of CPF. Reportedly, the relationship between air flow and the amplitude of breath sounds is linear at high flow rates [52; 53]. It has also been reported that the sound amplitude during inspiration is proportional to the square of the air flow velocity at the mouth [54]. Moreover, recent studies have shown that cough sounds are associated with cough flow (Figure 3a) [55; 56], and a method for estimating cough strength via cough sounds has been developed using a model represented by an exponential equation [56], given as follows:  
\[CPF=\alpha\ \{exp\ (\beta\cdot CPSL)-1\}, \tag{1}\]  
where \(\alpha\) and \(\beta\) are constants, and \(CPSL\) is the cough peak sound pressure level. Figure 3b shows the relationship between CPF and CPF predicted via cough sounds (CPS) calculated using Equation (1), confirming a significant positive correlation (\(r=0.920\); \(p<0.001\)) in young healthy participants. In a previous study published in 2001, [PERSON] [57] showed that the cough sound pressure level is \(94.30\pm 1.48\) dB in patients with stroke and \(106.11\pm 0.34\) dB in nonstroke elderly patients screened for the absence of pulmonary illness. Furthermore, the loudness of the cough sound may be an indicator of the aspiration severity. Although the cough sound measurement methods used by [PERSON] et al. and [PERSON] et al. [56] differ, the cough sound range reported by [PERSON] et al. is consistent with the loud region of the cough sound-measured value reported by [PERSON] et al. Figure 4 shows examples of simultaneously measured cough flow and cough sounds. A previous study reported that the absolute error between CPFs and CPSs when the microphone distance from the participant's mouth was within 30 cm was significantly lower than that when the distance exceeded 30 cm [56]. Although cough flow and cough sounds were measured through different methods, both responded to the initiation of the participant's cough. The figure also indicates that the cough sound appears faster than the cough flow. According to the European Respiratory Society guidelines on the assessment of coughing [9], the cough sound is defined as having three phases: the explosive phase, the intermediate phase, and the voiced phase. The cough sound pattern shown in Figure 4b is a two-phase cough sound without a voiced phase. Figure 4: Examples of cough flow and cough sound in a young healthy participant [56]. (**a**) Cough flow. The green line represents the cough flow measured by a flow sensor (Mobile aeromonitor AE-100i, Minato Medical Science Co., Ltd., Osaka, Japan). (**b**) Cough sound amplitude. The grey line represents the cough sound signals measured by the microphone (AT9903, Audio-Technica Corporation, Tokyo, Japan). The digitized cough sound signals were band-pass filtered between 140 to 2000 Hz to minimize artefacts. (**c**) Cough sound pressure level. The solid purple line represents the moving average with a time window of 20 ms.