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Design of a reverberant chamber for noise exposure experiments with small animals
Applied Acoustics 70 (2009) 1034–1040
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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Design of a reverberant chamber for noise exposure experiments with small animals Pedro Cobo a,*, Silvia Murillo-Cuesta b, Rafael Cediel b,c, Antonio Moreno a, Patricia Lorenzo-García b, Isabel Varela-Nieto b a
Instituto de Acústica, CSIC, Acustica Ambiental, Serrano 144, 28006 Madrid, Spain Instituto de Investigaciones Biomédicas Alberto Sols, CSIC-UAM, CIBER-ER Unit 761, Arturo Duperier 4, 28029 Madrid, Spain c Departamento de Anatomía, Facultad de Veterinaria, Universidad Complutense de Madrid, Avda. Puerta de Hierro s/n, 28040 Madrid, Spain b
a r t i c l e
i n f o
Article history: Received 29 October 2008 Received in revised form 9 March 2009 Accepted 12 March 2009 Available online 14 April 2009 Keywords: Noise exposure experiments Reverberant chamber
a b s t r a c t Previous work on the acoustic design of small reverberant chambers for studies on laboratory animals has paid, in general, more attention to the frequency response at certain points in their interior. These designs aimed to provide a frequency response as flat as possible at the receivers, thus avoiding unpleasant spectral coloration effects. However, an equally important, and frequently neglected, aspect is to set an acoustic field as spatially uniform as possible inside the zone where the animals are to be placed during the exposure to noise. Here, an optimization procedure is described to calculate the proportions of the chamber dimensions that confers the highest sound level with the minimum mean squared deviation averaged in a given area inside the chamber. In addition, new stimuli have been designed with a high-pass filtering and linear with frequency gain. These stimuli were intended to adapt the characteristics of the exposing noise to the rodent hearing spectrum, displaced toward higher frequencies than the hearing frequency band of humans. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction An important part of the investigation in audiology is made using small animals, typically rodents, as models to understand the cellular and molecular bases of hearing and deafness. Noise is an important damaging factor for the inner ear hair cells. According to the World Health Organization, exposure to excessive noise from different sources (social, environmental and occupational noise) is the major avoidable cause of permanent hearing impairment and therefore an important public health priority. Research needs to be carried out on noise pathogenic mechanisms including risk factors, individual susceptibility and interaction with other toxic agents. Diverse approaches have been taken to understand otic damage after noise exposure in animal models by using different experimental settings. In general, laboratory animals are exposed to an intense acoustic field with the aim to produce a severe hearing loss. Ngan and May [1] exposed cats to a severe sound of 108–111 dB SPL, during 2–4 h, within an anechoic chamber. Brand-Larsen et al. [2] subjected rats to a gaussian noise of 90–105 dB in the frequency band 4–20 kHz within an anechoic chamber. Fechter et al. [3] exposed rats to a noise stimulus consisting of one-octave band noise around 13.6 kHz, at a sound level of 95 dB, during two hours. Noreña and Eggermont [4] caused and acoustic trauma in cats, exposing them * Corresponding author. Tel.: +34 91 5618806; fax: +34 91 4117856. E-mail address: [email protected] (P. Cobo). 0003-682X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.03.005
to tones of 5 kHz at 120 dB during two hours in an anechoic room. Murillo-Cuesta et al. [5] used genetically modified mice to study the relationship between the pigment melanin and hearing recovery after exposure to a swept-sine noise at 90–100 dB during 12 h. Although these and other authors use in-house acoustic chambers for noise exposure, there is not standardization of their acoustic properties. A far bigger problem is the variability of effect associated with noise exposure studies. Identically exposed animals have varying hearing losses. In general, the acoustic design of the noise exposure chamber is ill-defined, with exceptions such as the work by Davis and Franks [6] that describe the design of a noise exposure chamber for chinchillas. They proposed an anechoic chamber to produce a homogeneous field as high as 130 dB, using a horn loudspeaker in the ceiling. The type of chamber, whether anechoic or reverberant, is related to the objective. An anechoic chamber provides a unique and direct sound from the source. On the contrary, each point inside a reverberant chamber will be reached by the addition of direct plus reverberant sound. Therefore, the sound level produced by a source in a receiver will be louder in a reverberant than in an anechoic chamber. Since the hearing loss induced will be directly proportional to the product of the exposure time by the sound level, the higher the level the lower the exposure time required. This is an important aspect of the design of an experimental paradigm of noise damage by using noise exposure chambers. As mentioned above, Davis and Franks [6] designed an anechoic chamber with a horn loudspeaker in the ceiling able to produce a
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maximum sound field of 130 dB. However, these horns radiate in a frequency band (100 Hz, 10 kHz) which is rather below the hearing spectrum of rodents. Zheng et al. [7] established a reference for hearing ability of commonly used mice based upon the auditory brainstem response (ABR) thresholds of 80 inbred strains of mice. Although these mice can hear over a range of frequencies between 0.5 and 120 kHz, normal mice are most sensitive to frequencies of 8–24 kHz [7]. Tweeters are loudspeakers with a higher frequency band response, and therefore more appropriated for rodent noise exposure experiments. Here we show the acoustic basis for the design of a reverberant chamber, which should allow more controlled noise exposure, using tweeters as noise sources. Some improvements concerning linearity of reverberation time and sound diffusion inside the room can be obtained in non rectangular chambers. However, this does not improve the distribution of natural frequencies. On other hand, the chamber normally contains a rectangular cage. Furthermore, it will be placed in a laboratory which is, in general, also rectangular. Therefore, for practical reasons, we decide to focus our attention on the design of a rectangular reverberant chamber. As pointed out by Bolt [8], the spectral response in each point inside a rectangular reverberant chamber is largely determined by its dimensions. He proposed a chart to choose the proportions between the room dimensions that provides a homogeneous distribution of normal frequencies inside the chamber. More specifically, the Bolt’s chart, Fig. 1, provides the relative dimensions of a small rectangular room giving the smoothest frequency response. In this chart, the dimension ratios c:b:1 are normalized to the smaller one (see Section 3). Thus, rectangular chambers with spectrally homogeneous sound field have dimension proportions which should lie within the white area of Fig. 1. The original design chart of Bolt has been further updated by other authors [9–11] emphasizing its universal character in the whole frequency range, by using a new
assessing equation with strictly statistical meaning and not far from Bolt’s equation. The new chart restricts some zones inside, and adds some other outside, the Bolt’s area. The Bolt’s criterion seeks to provide even frequency response at a point inside the room or chamber. This avoids unwanted coloration effects on the sound, mainly at low frequencies, which influence the quality of sound perception. In noise exposure experiments with small animals, in order to ensure a proper dose-effect correlation, it is even more important to avoid the spatial variation of sound levels along the zone where the animals are to be located than the spectral coloration at each point. Hence, a new criterion is formulated to calculate the dimensions of the room or chamber considering the spatial uniformity of the sound field inside it. This criterion has also been harmonised with the spectral uniformity proposed by Bolt. In summary, in this work: (i) the normal mode approach to model the acoustic field in a reverberant chamber is re-examined; (ii) the dimensions of the chamber are optimised so that the acoustic field is as homogeneous as possible both in the frequency and space domains; and (iii) two sound stimuli are proposed as an standardized paradigm for noise exposure studies. Experimental results, regarding the measurement of the sound field inside the chamber, are presented. 2. Sound in a reverberant chamber The acoustic pressure, at the frequency x, in a point r = {x, y, z} inside a lightly damped rectangular chamber with dimensions (L1, L2, L3), damping factor n, wall surfaces S1, S2, and S3, and volume V, is [12]
pðr; xÞ ¼
1 X
an ðr; xÞwn ðrÞ;
ð1Þ
n¼0
where
wn ðrÞ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
en1 en2 en3 cos
n 1 px n2 py n3 pz cos cos ; L1 L2 L3
ð2Þ
is the nth normal mode, which satisfies the orthogonality condition
Z V
wn ðrÞwm ðrÞdV ¼ Vdnm ;
ð3Þ
dnm being the Kronecker function,
eni ¼
1 if ni ¼ 0 ; 2 if ni > 0
ð4Þ
{n1, n2, n3} are integer numbers,
an ðr; xÞ ¼
q0 c20 An ðxÞ V
Z V
wn ðrÞqv ol ðrÞdVm;
ð5Þ
is the nth modal coefficient,
An ðxÞ ¼
x
; 2nn xn x þ jðx2 x2n Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 n1 n2 n3 xn ¼ c0 p þ þ L1 L2 L3
ð6Þ ð7Þ
is the frequency of the nth mode,
en S1 þ en2 S2 þ en3 S3 nn ¼ n 1 2ðS1 þ S2 þ S3 Þ
Fig. 1. Bolt’s chart for choosing dimension ratios of rectangular enclosures with homogeneous spacing of normal frequencies.
ð8Þ
is the modal damping coefficient in the chamber walls, qvol is the complex strength of the sources inside the room volume, and q0 and c0 are the mass density and sound speed of the air, respectively. Eqs. (1)–(8) allow the calculation of the acoustic field in any point inside the chamber provided that its dimensions, wall
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damping, and distribution of sound sources are known. Thus, m sources located in rm with strengths, qm, produce a sound field given by
pðr; xÞ ¼
q
2 0 c0
V
xX n
X wn ðrÞ q w ðrm Þ: 2nn xn x þ jðx2 x2n Þ m m n
ð9Þ
Eq. (9) yields the sound field as the sum of an infinite number of modes. Therefore, to calculate the sound field at each point in the room or chamber, this sum must be truncated to include just a finite number of modes. The number of modes to attain an acceptable approach to the exact solution depends on the frequency. The lower the frequency, the smaller the number of modes required. 3. Optimization of the reverberant chamber dimensions Since Bolt [8] many criteria have been suggested to optimise the proportions of the room dimensions so that the spectral response at each point inside it is as even as possible. The Bolt’s criterion is based on the uniformity of the natural frequencies along the low frequency range of the spectral response. Cox et al. [10] proposed an optimization method based on finding the room dimensions with the flattest possible modal frequency response. This optimization procedure uses a cost parameter which is the sum of the squared deviation of the modal response from a least squares fitted straight line drawn through the spectra. In this paper, the aim is to design a chamber with the flattest possible spatial room response in a small area where the animals are to be placed. Thus, following the proposal of Cox, we will define a cost function that will contain the squared deviation of the sound field in the cage from a flat sound field. The characteristics of the reverberant chamber to be optimised are the following (Fig. 2):
Table 1 Coordinates of the sources and receivers inside the room. Source
Coordinates rm
Coordinates r
1 2 3 4 5
(L1/2, L2/2, L3) (L1/2 dx, L2/2, L3) (L1/2 + dx, L2/2, L3) (L1/2, L2/2 dx, L3) (L1/2, L2/2 + dx, L3)
x 2 ½L21 dy cm; L21 þ dy cm y 2 ½L22 dy cm; L22 þ dy cm z = dz cm
a symmetrical cross centred at the ceiling of the chamber (plane (x, y, zmax)).The separation between sources, dx, will be a variable of the model. The acoustic field at the square (L1/2 ± dy, L2/2 ± dy, dz) (Fig. 2) will be considered. The square is at a height dz from the floor (height of the animal heads) centred in the point (L1/2, L2/2). Both the half-width of the cage, dy, and the height of the plane, dz, will be variables of the model. Table 1 summarises the coordinates of the sources and receivers inside the room. If all the sources radiate with the same volume velocity, q, the acoustic pressure normalized by such volume velocity, at frequency x, is 5 X pðr; xÞ q0 c20 x X wn ðrÞwn ðrm Þ ¼ : q V m¼1 n 2nn xn x þ jðx2 x2n Þ
ð10Þ
Sound pressure levels, instead of spectra, will be used. Eq. (10) can be used for calculating the sound pressure in each frequency band (one-third-octave bands, for instance) L1/3 octave,i. The sound pressure level will be
Lp ¼ 10 log
" X
#
0:1L1=3octav e;i
10
:
ð11Þ
i
A number of tweeters are located in the ceiling, in a centred symmetrical cross. Several sound sources inside the chamber are used in order to overcome the rather limited sound power of a unique source and therefore to have a better control of sound level, a key parameter in noise exposure experiments. In free field, two incoherent sources radiating the same sound pressure level, Lp, produce a level 6 dB superior, i.e. Lp + 6. In a reverberant field, the reinforcement will depend on the relative location of the sources. Therefore, for a target level of about 120 dB, and assuming that each source radiates about 90 dB, we will consider 5 point omnidirectional sources, with equal volume velocity q, located in
Low frequency restriction. The frequency band of the calculation determines the number of modes to be used. Thus, this design procedure guarantees the homogeneity at low and medium frequencies. High frequency uniformity can be expected due to the room diffusivity [13]. Therefore, the cut off frequency, fc, is another variable of the model. In the following, a cut off frequency slightly higher than the Schroeder frequency of the room will be used. For instance, fc = 3000 Hz for a chamber with dimensions (L1, L2, L3) = (0.59 m, 0.53 m, 0.4 m). The number of modes of a room of volume V, below the cut off frequency fc is [14]
N
3 4pV fc : 3 c0
ð12Þ
For the above referred chamber, N = 350. Coherent or incoherent sum. This parameter relates to how the five tweeters are driven. If the five tweeters are driven with the same signal, then the sound pressures at the receiver add to each other coherently, and the total pressure can be calculated with Eq. (10). On the other hand, if the signal driving each tweeter comes from a different generator, the sum will be incoherent, and the total sound pressure at each point should be
8 2 91=2 = 5 X pðr; xÞ q0 c20 x
Fig. 2. Reverberant chamber to be optimised. Five tweeters are located in the ceiling with inter-separation dx. During exposition the animals are placed in a cage on the floor with dimensions (dy, dy, dz).
Fig. 3 shows the acoustic field in a plane (L1/2 ± 10 cm, L2/ 2 ± 10 cm, 2 cm), produced by five tweeters in the ceiling of a room with dimensions (L1, L2, L3) = (59 cm, 53 cm, 40 cm), with a
P. Cobo et al. / Applied Acoustics 70 (2009) 1034–1040
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for instance L3, and the acoustic field in the given plane will be analysed as a function of the proportions c = L1/L3, and b = L2/L3. For each pair (c, b), the mean value of the sound pressure level in the plane, Lpm, and its mean squared deviation, r, will be calculated. Maps of Lpm = function(c, b) and r = function(c, b) are generated as a result of this procedure. The optimal geometry with the most uniform acoustic field will present the higher values of Lpm and the lower values of r. To improve room geometry, a figure of merit, fom, which combines Lpm and r is introduced as follows:
fomðc; bÞ ¼
Fig. 3. Sound pressure levels in the plane (L1/2 ± 10 cm, L2/2 ± 10 cm, 2 cm) of a room with dimensions (L1, L2, L3) = (59 cm, 53 cm, 40 cm), produced by five tweeters of equal volume velocity in the ceiling, with dx = 10 cm, for fc = 3000 Hz and n = 0.01; (a) coherent sum; (b) incoherent sum.
separation dx = 10 cm, for the cases of coherent, Fig. 3a, and incoherent, Fig. 3b, sum. Due to the symmetrical disposition of the tweeters and the animal cage, see Fig. 2, a symmetrical acoustic field is obtained with a maximum at the centre of the cage. The average of Lp in the analysed square is 103 and 101 dB SPL, for coherent and incoherent cases, respectively. Mean squared deviations are 1.1 and 0.7 dB SPL, for coherent and incoherent cases, respectively. This model allows obtaining the acoustic field produced by the five sources in any plane of the chamber. The optimization procedure is as follows. First, the minimum dimension is fixed,
1 Lpm ðc; bÞ r1 ðc; bÞ þ : 1 2 maxfLpm g maxfr g
ð14Þ
Notice that fom is 1 in the most favourable condition: Lpm maximum and r minimum. Fig. 4 shows the fom maps for the conditions of coherent sums and dx = 5, 10 and 15 cm. Fig. 5 shows the corresponding fom maps for the conditions of incoherent sums. It is worth noting that when the separation between sources, dx, increases the zones of high values of fom are broader for the condition of coherent sum. For the incoherent sum condition, the configuration corresponding to dx = 10 cm provides the (c, b) map with more zones of high fom. Table 2 summarises the maximum values of (c, b) for each analysed configuration. Notice that a chamber with dimension ratios (c, b) = (1.54, 1.46) provides a chamber with spatially homogeneous sound field for dx = 5 and dx = 15, with both coherent and incoherent sum. The only configuration which is inside the Bolt map, Fig. 1, is (c, b) = (1.485, 1.95), corresponding to dx = 10 cm and incoherent sum. Table 3 shows alternative values of (c, b) that, although are not maximal, provide a high value of fom being within the Bolt zone. Therefore, a rectangular chamber with the dimension ratios in Table 3 guarantees a high, spatially and spectrally smooth, sound field in the zone where the cage with the animals is placed. The smaller the chamber, the higher the sound pressure level possible in its interior for a given number of sources. It is easier
Fig. 4. Fom maps for a room with L3 = 0.4 m, fc = 3000 Hz, n = 0.001, dy = 10 cm, dz = 2 cm, and coherent sum. (a) dx = 5 cm, (b) dx = 10 cm, (c) dx = 15 cm.
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P. Cobo et al. / Applied Acoustics 70 (2009) 1034–1040
Fig. 5. Fom maps for a room with L3 = 0.4 m, fc = 3000 Hz, n = 0.001, dy = 10 cm, dz = 2 cm, and incoherent sum. (a) dx = 5 cm, (b) dx = 10 cm, (c) dx = 15 cm.
Table 2 Maximum values of (c, b) for each analysed configuration, for a room with L3 = 40 cm, fc = 3000 Hz, n = 0.001, dy = 10 cm, and dz = 2 cm.
Coherent sum Incoherent sum
dx = 5 cm
dx = 10 cm
dx = 15 cm
(1.547, 1.46) (1.545, 1.46)
(1.547, 1.515) (1.485, 1.95)
(1.547, 1.46) (1.545, 1.46)
to drive all the sources with the same amplifier (coherent sum condition). Therefore, the configuration with five tweeters connected in phase, separated by dx = 5 cm, was chosen. For L3 = 40 cm, this configuration provides a chamber with interior dimensions of 52 60 40 cm. 4. Design of sound stimuli for noise exposure
Table 3 Alternative values of (c, b), within the Bolt zone, for each analysed configuration, for a room with L3 = 40 cm, fc = 3000 Hz, n = 0.001, dy = 10 cm, and dz = 2 cm.
Coherent sum Incoherent sum
dx = 5 cm
dx = 10 cm
dx = 15 cm
(1.3, 1.5) (1.545, 1.95)
(1.485, 1.69) (1.545, 1.95)
(1.52, 1.92) (1.45, 1.75)
The audio chain required to generate the exposing noise inside the chamber includes: A workstation (PC) that generates the signal through its sound card with sampling frequency 44,100 Hz. Wave Lab Lite software was used to generate the signal.
Fig. 6. Frequency response of the 1-inch KEF tweeter.
P. Cobo et al. / Applied Acoustics 70 (2009) 1034–1040
A power amplifier with an input channel (the signal generated by the PC) and five output channels. Five 1-inch KEF tweeters distributed in a symmetrical cross in the ceiling of the chamber. Fig. 6 shows the frequency response of such a tweeter measured in the anechoic room of the Instituto de Acustica (Madrid).The signal driving each tweeter is the output from the corresponding channel of the power amplifier. The signals generated by the PC should always include a highpass filter to avoid driving the tweeters below their cut off frequency (in this case, 2 kHz). A linear-with-frequency gain has been also included to compensate for the high frequency losses of the sound inside the chamber. This gain provides signals with a spectrum biased towards the high frequency scale, a kind of violet colouring. Therefore, two signals have been synthesised for driving the tweeters:
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Violet noise. It is synthesised from a white noise in the frequency range (0, fs/2), fs being the sampling frequency. This noise is high-pass filtered beyond the cut off frequency fc, and multiplied by a linear with frequency gain, mf f. This signal is identified as violet noise(fs, fc, mf). Violet swept-sine. It consists of a swept-sine in the frequency range (f1, f2), in the time T, also with a linear with frequency gain of slope mf. The initial frequency of the swept, f1, is in this case the cut off frequency for high-pass filtering. This signal is identified as violet swept-sine(fs, f1, f2, T, mf).
Figs. 7 and 8 show the time history, panels (a) and magnitude spectrum, panels (b), of the stimuli violet noise(44100, 2000, 40) and violet swept-sine(44100, 2000, 20000, 10, 40), respectively. Both stimuli are sampled at 44,100 Hz, and have been high-pass filtered at 2000 Hz. The violet noise contains frequencies up to the
Fig. 7. (a) Time history, and (b) magnitude spectrum of the stimulus violet noise (44100, 2000, 20).
Fig. 8. (a) Time history, and (b) magnitude spectrum of the stimulus violet swept-sine (44100, 2000, 20000, 10, 40).
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P. Cobo et al. / Applied Acoustics 70 (2009) 1034–1040
with two kinds of stimuli, violet noise and violet swept-sine, which includes a high-pass filter, to avoid driving the tweeters below their cut off frequency, and a linear-with-frequency gain, to compensate for the high frequency losses of the sound inside the chamber. We claim that a precise control of the acoustic conditions of animal exposure to noise is essential to modulate the qualities of the noise and to produce reproducible and accurate in vivo data. Acknowledgements This work has been supported by the Spanish Ministry of Education and Science, through Grant TRA2007-68080-C03-02/MODAL to PC and by funds from the Comunidad de Madrid (IV PRICYT IC0530), DIGNA Biotech (Ref. 065510), the CIBERER (U761), MICIN (SAF2008-00470) and the Fundación Investigación Médica Mutua Madrileña (Ref. 20070504) to IVN. The authors are grateful to Carlos de la Colina, Enrique de Costa, José Luis López, Ramón Navares Zaera, Lourdes Rodríguez de la Rosa and Javier Pérez García for their suggestions and technical assistance. References Fig. 9. Sound map in a plane of size (20 cm, 20 cm) around the point (L1/2, L2/2, 2 cm) inside the chamber.
Nyquist frequency. The violet swept-sine includes a linear sweep in frequency, from 2 kHz up to 20 kHz, in 10 s. 5. Experimental results Measurements of the acoustic field inside the reverberant chamber have been carried out with five B&K microphones connected to a B&K PULSE system. The sound pressure level, Lp, was measured at 100 points of a squared grid of size (20 20 cm) centred at the point (L1/2, L2/2, 2 cm). Fig. 9 shows the sound map in this zone. The mean sound pressure level was 96.6 dB SPL. The maximum and minimum Lp were 99 and 95 dB SPL, respectively. 6. Conclusions An optimization procedure to calculate the dimensions of a reverberant chamber for laboratory animal experiments has been presented that achieves the maximal sound level, with the minimal deviation, at the selected area inside the chamber where the animals are located. The exposure noise in the chamber is generated through tweeters, more suited to the upper frequency band of rodents hearing. The animals inside the chamber can be exposed
[1] Ngan EM, May BJ. Relationship between the auditory brainstem response and auditory nerve thresholds in cats with hearing loss. Hearing Res 2001;156:44–52. [2] Brand-Larsen R, Lund SP, Jepsen GB. Rats exposed to toluene and noise may develop loss of auditory sensitivity due to synergistic interaction. Noise Health 2000;3:33–44. [3] Fechter LD, Chen G-D, Rao D, Larabee J. Predicting exposure conditions that facilitate the potentiation of noise-induced hearing loss by carbon monoxide. Toxicol Sci 2000;58:315–23. [4] Noreña AJ, Eggermont JJ. Enriched acoustic environment after noise trauma reduces hearing loss and prevents cortical map reorganization. J Neurosci 2005;19:699–705. [5] Murillo-Cuesta S, Contreras J, Zurita E, Cediel R, Cantero M, Varela-Nieto I, et al. Melanin-related metabolites prevent premature age-related and noiseinduced hearing loss in albino mice. Eur J Neurosci 2008. [6] Davis RR, Franks JR. Design and construction of a noise exposure chamber for small animals. J Acoust Soc Am 1989;85:963–6. [7] Zheng QY, Johnson KR, Erway LC. Assessment of hearing in 80 inbred strains of mice by ABR threshold analyses. Hearing Res 1999;130:94–107. [8] Bolt RH. Note on normal frequency statistics for rectangular rooms. J Acoust Soc Am 1946;18:130–3. [9] Moreno A, Ruiz J, de la Colina C. Re-visiting Bolt’s criterium for homogeneous distribution of normal frequencies in rectangular enclosures. ACUSTICA, Madrid; 2000. [10] Cox TJ, D’Antonio P, Avis MR. Room sizing and optimization at low frequencies. J Acoust Eng Soc 2001;52:640–51. [11] Blaszak MA. Acoustic design of small rectangular rooms: normal frequency statistics. Appl Acoust 2008;69:1356–60. [12] Nelson PM, Elliotm SJ. Active control of sound. London: Academic Press; 1992. [13] Fahy F. Foundations of engineering acoustics. San Diego: Academic Press; 2001. [14] Kinsler LE, Frey AR, Coppens AB, Sanders JV. Fundamentals of acoustics. New York: John Wiley & Sons; 1982.
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Design of a reverberant chamber for noise exposure experiments with small animals Pedro Cobo a,*, Silvia Murillo-Cuesta b, Rafael Cediel b,c, Antonio Moreno a, Patricia Lorenzo-García b, Isabel Varela-Nieto b a
Instituto de Acústica, CSIC, Acustica Ambiental, Serrano 144, 28006 Madrid, Spain Instituto de Investigaciones Biomédicas Alberto Sols, CSIC-UAM, CIBER-ER Unit 761, Arturo Duperier 4, 28029 Madrid, Spain c Departamento de Anatomía, Facultad de Veterinaria, Universidad Complutense de Madrid, Avda. Puerta de Hierro s/n, 28040 Madrid, Spain b
a r t i c l e
i n f o
Article history: Received 29 October 2008 Received in revised form 9 March 2009 Accepted 12 March 2009 Available online 14 April 2009 Keywords: Noise exposure experiments Reverberant chamber
a b s t r a c t Previous work on the acoustic design of small reverberant chambers for studies on laboratory animals has paid, in general, more attention to the frequency response at certain points in their interior. These designs aimed to provide a frequency response as flat as possible at the receivers, thus avoiding unpleasant spectral coloration effects. However, an equally important, and frequently neglected, aspect is to set an acoustic field as spatially uniform as possible inside the zone where the animals are to be placed during the exposure to noise. Here, an optimization procedure is described to calculate the proportions of the chamber dimensions that confers the highest sound level with the minimum mean squared deviation averaged in a given area inside the chamber. In addition, new stimuli have been designed with a high-pass filtering and linear with frequency gain. These stimuli were intended to adapt the characteristics of the exposing noise to the rodent hearing spectrum, displaced toward higher frequencies than the hearing frequency band of humans. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction An important part of the investigation in audiology is made using small animals, typically rodents, as models to understand the cellular and molecular bases of hearing and deafness. Noise is an important damaging factor for the inner ear hair cells. According to the World Health Organization, exposure to excessive noise from different sources (social, environmental and occupational noise) is the major avoidable cause of permanent hearing impairment and therefore an important public health priority. Research needs to be carried out on noise pathogenic mechanisms including risk factors, individual susceptibility and interaction with other toxic agents. Diverse approaches have been taken to understand otic damage after noise exposure in animal models by using different experimental settings. In general, laboratory animals are exposed to an intense acoustic field with the aim to produce a severe hearing loss. Ngan and May [1] exposed cats to a severe sound of 108–111 dB SPL, during 2–4 h, within an anechoic chamber. Brand-Larsen et al. [2] subjected rats to a gaussian noise of 90–105 dB in the frequency band 4–20 kHz within an anechoic chamber. Fechter et al. [3] exposed rats to a noise stimulus consisting of one-octave band noise around 13.6 kHz, at a sound level of 95 dB, during two hours. Noreña and Eggermont [4] caused and acoustic trauma in cats, exposing them * Corresponding author. Tel.: +34 91 5618806; fax: +34 91 4117856. E-mail address: [email protected] (P. Cobo). 0003-682X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.03.005
to tones of 5 kHz at 120 dB during two hours in an anechoic room. Murillo-Cuesta et al. [5] used genetically modified mice to study the relationship between the pigment melanin and hearing recovery after exposure to a swept-sine noise at 90–100 dB during 12 h. Although these and other authors use in-house acoustic chambers for noise exposure, there is not standardization of their acoustic properties. A far bigger problem is the variability of effect associated with noise exposure studies. Identically exposed animals have varying hearing losses. In general, the acoustic design of the noise exposure chamber is ill-defined, with exceptions such as the work by Davis and Franks [6] that describe the design of a noise exposure chamber for chinchillas. They proposed an anechoic chamber to produce a homogeneous field as high as 130 dB, using a horn loudspeaker in the ceiling. The type of chamber, whether anechoic or reverberant, is related to the objective. An anechoic chamber provides a unique and direct sound from the source. On the contrary, each point inside a reverberant chamber will be reached by the addition of direct plus reverberant sound. Therefore, the sound level produced by a source in a receiver will be louder in a reverberant than in an anechoic chamber. Since the hearing loss induced will be directly proportional to the product of the exposure time by the sound level, the higher the level the lower the exposure time required. This is an important aspect of the design of an experimental paradigm of noise damage by using noise exposure chambers. As mentioned above, Davis and Franks [6] designed an anechoic chamber with a horn loudspeaker in the ceiling able to produce a
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maximum sound field of 130 dB. However, these horns radiate in a frequency band (100 Hz, 10 kHz) which is rather below the hearing spectrum of rodents. Zheng et al. [7] established a reference for hearing ability of commonly used mice based upon the auditory brainstem response (ABR) thresholds of 80 inbred strains of mice. Although these mice can hear over a range of frequencies between 0.5 and 120 kHz, normal mice are most sensitive to frequencies of 8–24 kHz [7]. Tweeters are loudspeakers with a higher frequency band response, and therefore more appropriated for rodent noise exposure experiments. Here we show the acoustic basis for the design of a reverberant chamber, which should allow more controlled noise exposure, using tweeters as noise sources. Some improvements concerning linearity of reverberation time and sound diffusion inside the room can be obtained in non rectangular chambers. However, this does not improve the distribution of natural frequencies. On other hand, the chamber normally contains a rectangular cage. Furthermore, it will be placed in a laboratory which is, in general, also rectangular. Therefore, for practical reasons, we decide to focus our attention on the design of a rectangular reverberant chamber. As pointed out by Bolt [8], the spectral response in each point inside a rectangular reverberant chamber is largely determined by its dimensions. He proposed a chart to choose the proportions between the room dimensions that provides a homogeneous distribution of normal frequencies inside the chamber. More specifically, the Bolt’s chart, Fig. 1, provides the relative dimensions of a small rectangular room giving the smoothest frequency response. In this chart, the dimension ratios c:b:1 are normalized to the smaller one (see Section 3). Thus, rectangular chambers with spectrally homogeneous sound field have dimension proportions which should lie within the white area of Fig. 1. The original design chart of Bolt has been further updated by other authors [9–11] emphasizing its universal character in the whole frequency range, by using a new
assessing equation with strictly statistical meaning and not far from Bolt’s equation. The new chart restricts some zones inside, and adds some other outside, the Bolt’s area. The Bolt’s criterion seeks to provide even frequency response at a point inside the room or chamber. This avoids unwanted coloration effects on the sound, mainly at low frequencies, which influence the quality of sound perception. In noise exposure experiments with small animals, in order to ensure a proper dose-effect correlation, it is even more important to avoid the spatial variation of sound levels along the zone where the animals are to be located than the spectral coloration at each point. Hence, a new criterion is formulated to calculate the dimensions of the room or chamber considering the spatial uniformity of the sound field inside it. This criterion has also been harmonised with the spectral uniformity proposed by Bolt. In summary, in this work: (i) the normal mode approach to model the acoustic field in a reverberant chamber is re-examined; (ii) the dimensions of the chamber are optimised so that the acoustic field is as homogeneous as possible both in the frequency and space domains; and (iii) two sound stimuli are proposed as an standardized paradigm for noise exposure studies. Experimental results, regarding the measurement of the sound field inside the chamber, are presented. 2. Sound in a reverberant chamber The acoustic pressure, at the frequency x, in a point r = {x, y, z} inside a lightly damped rectangular chamber with dimensions (L1, L2, L3), damping factor n, wall surfaces S1, S2, and S3, and volume V, is [12]
pðr; xÞ ¼
1 X
an ðr; xÞwn ðrÞ;
ð1Þ
n¼0
where
wn ðrÞ ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
en1 en2 en3 cos
n 1 px n2 py n3 pz cos cos ; L1 L2 L3
ð2Þ
is the nth normal mode, which satisfies the orthogonality condition
Z V
wn ðrÞwm ðrÞdV ¼ Vdnm ;
ð3Þ
dnm being the Kronecker function,
eni ¼
1 if ni ¼ 0 ; 2 if ni > 0
ð4Þ
{n1, n2, n3} are integer numbers,
an ðr; xÞ ¼
q0 c20 An ðxÞ V
Z V
wn ðrÞqv ol ðrÞdVm;
ð5Þ
is the nth modal coefficient,
An ðxÞ ¼
x
; 2nn xn x þ jðx2 x2n Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 n1 n2 n3 xn ¼ c0 p þ þ L1 L2 L3
ð6Þ ð7Þ
is the frequency of the nth mode,
en S1 þ en2 S2 þ en3 S3 nn ¼ n 1 2ðS1 þ S2 þ S3 Þ
Fig. 1. Bolt’s chart for choosing dimension ratios of rectangular enclosures with homogeneous spacing of normal frequencies.
ð8Þ
is the modal damping coefficient in the chamber walls, qvol is the complex strength of the sources inside the room volume, and q0 and c0 are the mass density and sound speed of the air, respectively. Eqs. (1)–(8) allow the calculation of the acoustic field in any point inside the chamber provided that its dimensions, wall
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damping, and distribution of sound sources are known. Thus, m sources located in rm with strengths, qm, produce a sound field given by
pðr; xÞ ¼
q
2 0 c0
V
xX n
X wn ðrÞ q w ðrm Þ: 2nn xn x þ jðx2 x2n Þ m m n
ð9Þ
Eq. (9) yields the sound field as the sum of an infinite number of modes. Therefore, to calculate the sound field at each point in the room or chamber, this sum must be truncated to include just a finite number of modes. The number of modes to attain an acceptable approach to the exact solution depends on the frequency. The lower the frequency, the smaller the number of modes required. 3. Optimization of the reverberant chamber dimensions Since Bolt [8] many criteria have been suggested to optimise the proportions of the room dimensions so that the spectral response at each point inside it is as even as possible. The Bolt’s criterion is based on the uniformity of the natural frequencies along the low frequency range of the spectral response. Cox et al. [10] proposed an optimization method based on finding the room dimensions with the flattest possible modal frequency response. This optimization procedure uses a cost parameter which is the sum of the squared deviation of the modal response from a least squares fitted straight line drawn through the spectra. In this paper, the aim is to design a chamber with the flattest possible spatial room response in a small area where the animals are to be placed. Thus, following the proposal of Cox, we will define a cost function that will contain the squared deviation of the sound field in the cage from a flat sound field. The characteristics of the reverberant chamber to be optimised are the following (Fig. 2):
Table 1 Coordinates of the sources and receivers inside the room. Source
Coordinates rm
Coordinates r
1 2 3 4 5
(L1/2, L2/2, L3) (L1/2 dx, L2/2, L3) (L1/2 + dx, L2/2, L3) (L1/2, L2/2 dx, L3) (L1/2, L2/2 + dx, L3)
x 2 ½L21 dy cm; L21 þ dy cm y 2 ½L22 dy cm; L22 þ dy cm z = dz cm
a symmetrical cross centred at the ceiling of the chamber (plane (x, y, zmax)).The separation between sources, dx, will be a variable of the model. The acoustic field at the square (L1/2 ± dy, L2/2 ± dy, dz) (Fig. 2) will be considered. The square is at a height dz from the floor (height of the animal heads) centred in the point (L1/2, L2/2). Both the half-width of the cage, dy, and the height of the plane, dz, will be variables of the model. Table 1 summarises the coordinates of the sources and receivers inside the room. If all the sources radiate with the same volume velocity, q, the acoustic pressure normalized by such volume velocity, at frequency x, is 5 X pðr; xÞ q0 c20 x X wn ðrÞwn ðrm Þ ¼ : q V m¼1 n 2nn xn x þ jðx2 x2n Þ
ð10Þ
Sound pressure levels, instead of spectra, will be used. Eq. (10) can be used for calculating the sound pressure in each frequency band (one-third-octave bands, for instance) L1/3 octave,i. The sound pressure level will be
Lp ¼ 10 log
" X
#
0:1L1=3octav e;i
10
:
ð11Þ
i
A number of tweeters are located in the ceiling, in a centred symmetrical cross. Several sound sources inside the chamber are used in order to overcome the rather limited sound power of a unique source and therefore to have a better control of sound level, a key parameter in noise exposure experiments. In free field, two incoherent sources radiating the same sound pressure level, Lp, produce a level 6 dB superior, i.e. Lp + 6. In a reverberant field, the reinforcement will depend on the relative location of the sources. Therefore, for a target level of about 120 dB, and assuming that each source radiates about 90 dB, we will consider 5 point omnidirectional sources, with equal volume velocity q, located in
Low frequency restriction. The frequency band of the calculation determines the number of modes to be used. Thus, this design procedure guarantees the homogeneity at low and medium frequencies. High frequency uniformity can be expected due to the room diffusivity [13]. Therefore, the cut off frequency, fc, is another variable of the model. In the following, a cut off frequency slightly higher than the Schroeder frequency of the room will be used. For instance, fc = 3000 Hz for a chamber with dimensions (L1, L2, L3) = (0.59 m, 0.53 m, 0.4 m). The number of modes of a room of volume V, below the cut off frequency fc is [14]
N
3 4pV fc : 3 c0
ð12Þ
For the above referred chamber, N = 350. Coherent or incoherent sum. This parameter relates to how the five tweeters are driven. If the five tweeters are driven with the same signal, then the sound pressures at the receiver add to each other coherently, and the total pressure can be calculated with Eq. (10). On the other hand, if the signal driving each tweeter comes from a different generator, the sum will be incoherent, and the total sound pressure at each point should be
8 2 91=2 = 5 X pðr; xÞ q0 c20 x
Fig. 2. Reverberant chamber to be optimised. Five tweeters are located in the ceiling with inter-separation dx. During exposition the animals are placed in a cage on the floor with dimensions (dy, dy, dz).
Fig. 3 shows the acoustic field in a plane (L1/2 ± 10 cm, L2/ 2 ± 10 cm, 2 cm), produced by five tweeters in the ceiling of a room with dimensions (L1, L2, L3) = (59 cm, 53 cm, 40 cm), with a
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for instance L3, and the acoustic field in the given plane will be analysed as a function of the proportions c = L1/L3, and b = L2/L3. For each pair (c, b), the mean value of the sound pressure level in the plane, Lpm, and its mean squared deviation, r, will be calculated. Maps of Lpm = function(c, b) and r = function(c, b) are generated as a result of this procedure. The optimal geometry with the most uniform acoustic field will present the higher values of Lpm and the lower values of r. To improve room geometry, a figure of merit, fom, which combines Lpm and r is introduced as follows:
fomðc; bÞ ¼
Fig. 3. Sound pressure levels in the plane (L1/2 ± 10 cm, L2/2 ± 10 cm, 2 cm) of a room with dimensions (L1, L2, L3) = (59 cm, 53 cm, 40 cm), produced by five tweeters of equal volume velocity in the ceiling, with dx = 10 cm, for fc = 3000 Hz and n = 0.01; (a) coherent sum; (b) incoherent sum.
separation dx = 10 cm, for the cases of coherent, Fig. 3a, and incoherent, Fig. 3b, sum. Due to the symmetrical disposition of the tweeters and the animal cage, see Fig. 2, a symmetrical acoustic field is obtained with a maximum at the centre of the cage. The average of Lp in the analysed square is 103 and 101 dB SPL, for coherent and incoherent cases, respectively. Mean squared deviations are 1.1 and 0.7 dB SPL, for coherent and incoherent cases, respectively. This model allows obtaining the acoustic field produced by the five sources in any plane of the chamber. The optimization procedure is as follows. First, the minimum dimension is fixed,
1 Lpm ðc; bÞ r1 ðc; bÞ þ : 1 2 maxfLpm g maxfr g
ð14Þ
Notice that fom is 1 in the most favourable condition: Lpm maximum and r minimum. Fig. 4 shows the fom maps for the conditions of coherent sums and dx = 5, 10 and 15 cm. Fig. 5 shows the corresponding fom maps for the conditions of incoherent sums. It is worth noting that when the separation between sources, dx, increases the zones of high values of fom are broader for the condition of coherent sum. For the incoherent sum condition, the configuration corresponding to dx = 10 cm provides the (c, b) map with more zones of high fom. Table 2 summarises the maximum values of (c, b) for each analysed configuration. Notice that a chamber with dimension ratios (c, b) = (1.54, 1.46) provides a chamber with spatially homogeneous sound field for dx = 5 and dx = 15, with both coherent and incoherent sum. The only configuration which is inside the Bolt map, Fig. 1, is (c, b) = (1.485, 1.95), corresponding to dx = 10 cm and incoherent sum. Table 3 shows alternative values of (c, b) that, although are not maximal, provide a high value of fom being within the Bolt zone. Therefore, a rectangular chamber with the dimension ratios in Table 3 guarantees a high, spatially and spectrally smooth, sound field in the zone where the cage with the animals is placed. The smaller the chamber, the higher the sound pressure level possible in its interior for a given number of sources. It is easier
Fig. 4. Fom maps for a room with L3 = 0.4 m, fc = 3000 Hz, n = 0.001, dy = 10 cm, dz = 2 cm, and coherent sum. (a) dx = 5 cm, (b) dx = 10 cm, (c) dx = 15 cm.
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Fig. 5. Fom maps for a room with L3 = 0.4 m, fc = 3000 Hz, n = 0.001, dy = 10 cm, dz = 2 cm, and incoherent sum. (a) dx = 5 cm, (b) dx = 10 cm, (c) dx = 15 cm.
Table 2 Maximum values of (c, b) for each analysed configuration, for a room with L3 = 40 cm, fc = 3000 Hz, n = 0.001, dy = 10 cm, and dz = 2 cm.
Coherent sum Incoherent sum
dx = 5 cm
dx = 10 cm
dx = 15 cm
(1.547, 1.46) (1.545, 1.46)
(1.547, 1.515) (1.485, 1.95)
(1.547, 1.46) (1.545, 1.46)
to drive all the sources with the same amplifier (coherent sum condition). Therefore, the configuration with five tweeters connected in phase, separated by dx = 5 cm, was chosen. For L3 = 40 cm, this configuration provides a chamber with interior dimensions of 52 60 40 cm. 4. Design of sound stimuli for noise exposure
Table 3 Alternative values of (c, b), within the Bolt zone, for each analysed configuration, for a room with L3 = 40 cm, fc = 3000 Hz, n = 0.001, dy = 10 cm, and dz = 2 cm.
Coherent sum Incoherent sum
dx = 5 cm
dx = 10 cm
dx = 15 cm
(1.3, 1.5) (1.545, 1.95)
(1.485, 1.69) (1.545, 1.95)
(1.52, 1.92) (1.45, 1.75)
The audio chain required to generate the exposing noise inside the chamber includes: A workstation (PC) that generates the signal through its sound card with sampling frequency 44,100 Hz. Wave Lab Lite software was used to generate the signal.
Fig. 6. Frequency response of the 1-inch KEF tweeter.
P. Cobo et al. / Applied Acoustics 70 (2009) 1034–1040
A power amplifier with an input channel (the signal generated by the PC) and five output channels. Five 1-inch KEF tweeters distributed in a symmetrical cross in the ceiling of the chamber. Fig. 6 shows the frequency response of such a tweeter measured in the anechoic room of the Instituto de Acustica (Madrid).The signal driving each tweeter is the output from the corresponding channel of the power amplifier. The signals generated by the PC should always include a highpass filter to avoid driving the tweeters below their cut off frequency (in this case, 2 kHz). A linear-with-frequency gain has been also included to compensate for the high frequency losses of the sound inside the chamber. This gain provides signals with a spectrum biased towards the high frequency scale, a kind of violet colouring. Therefore, two signals have been synthesised for driving the tweeters:
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Violet noise. It is synthesised from a white noise in the frequency range (0, fs/2), fs being the sampling frequency. This noise is high-pass filtered beyond the cut off frequency fc, and multiplied by a linear with frequency gain, mf f. This signal is identified as violet noise(fs, fc, mf). Violet swept-sine. It consists of a swept-sine in the frequency range (f1, f2), in the time T, also with a linear with frequency gain of slope mf. The initial frequency of the swept, f1, is in this case the cut off frequency for high-pass filtering. This signal is identified as violet swept-sine(fs, f1, f2, T, mf).
Figs. 7 and 8 show the time history, panels (a) and magnitude spectrum, panels (b), of the stimuli violet noise(44100, 2000, 40) and violet swept-sine(44100, 2000, 20000, 10, 40), respectively. Both stimuli are sampled at 44,100 Hz, and have been high-pass filtered at 2000 Hz. The violet noise contains frequencies up to the
Fig. 7. (a) Time history, and (b) magnitude spectrum of the stimulus violet noise (44100, 2000, 20).
Fig. 8. (a) Time history, and (b) magnitude spectrum of the stimulus violet swept-sine (44100, 2000, 20000, 10, 40).
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with two kinds of stimuli, violet noise and violet swept-sine, which includes a high-pass filter, to avoid driving the tweeters below their cut off frequency, and a linear-with-frequency gain, to compensate for the high frequency losses of the sound inside the chamber. We claim that a precise control of the acoustic conditions of animal exposure to noise is essential to modulate the qualities of the noise and to produce reproducible and accurate in vivo data. Acknowledgements This work has been supported by the Spanish Ministry of Education and Science, through Grant TRA2007-68080-C03-02/MODAL to PC and by funds from the Comunidad de Madrid (IV PRICYT IC0530), DIGNA Biotech (Ref. 065510), the CIBERER (U761), MICIN (SAF2008-00470) and the Fundación Investigación Médica Mutua Madrileña (Ref. 20070504) to IVN. The authors are grateful to Carlos de la Colina, Enrique de Costa, José Luis López, Ramón Navares Zaera, Lourdes Rodríguez de la Rosa and Javier Pérez García for their suggestions and technical assistance. References Fig. 9. Sound map in a plane of size (20 cm, 20 cm) around the point (L1/2, L2/2, 2 cm) inside the chamber.
Nyquist frequency. The violet swept-sine includes a linear sweep in frequency, from 2 kHz up to 20 kHz, in 10 s. 5. Experimental results Measurements of the acoustic field inside the reverberant chamber have been carried out with five B&K microphones connected to a B&K PULSE system. The sound pressure level, Lp, was measured at 100 points of a squared grid of size (20 20 cm) centred at the point (L1/2, L2/2, 2 cm). Fig. 9 shows the sound map in this zone. The mean sound pressure level was 96.6 dB SPL. The maximum and minimum Lp were 99 and 95 dB SPL, respectively. 6. Conclusions An optimization procedure to calculate the dimensions of a reverberant chamber for laboratory animal experiments has been presented that achieves the maximal sound level, with the minimal deviation, at the selected area inside the chamber where the animals are located. The exposure noise in the chamber is generated through tweeters, more suited to the upper frequency band of rodents hearing. The animals inside the chamber can be exposed
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