# Directed Autonomous Motion and Chiral Separation of Self-Propelled Janus
Particles in Convection Roll Arrays

Poulami Baga, Shubhadip Nayaka, Tanwi Debnathb, and Pulak K. Ghosha111Email:
<EMAIL_ADDRESS>a Department of Chemistry, Presidency University,
Kolkata 700073, India b Department of Chemistry, University of Calcutta,
Kolkata 700009, India

###### Abstract

Self-propelled Janus particles exhibit autonomous motion thanks to engines of
their own. However, due to randomly changing direction of such motion they are
of little use for emerging nano-technological and bio-medical applications.
Here, we numerically show that the motion of chiral active Janus can be
directed subjecting them to a linear array of convection rolls. Rectification
power of self-propulsion motion here can be made more than 60% which is much
larger than earlier reports. We show that rectification of chiral Janus
particle’s motion leads to conspicuous segregation of dextrogyre and levogyre
active particles from a racemic binary mixture. Further, we demonstrate how
efficiently the rectification effect can be exploited to separate dextrogyre
and levogyre particles when their intrinsic torques are distributed with
Gaussian statistics.

Artificial microswimmers are cleverly designed bio-inspired nanometer-to-
micrometer sized self-propelled particles Schweitzer-1 ; Schimansky-Geier-1 ;
Ramaswamy ; Medin ; JPCL-1 ; Schauer ; Magdanz ; JPCL-2 ; Bunea ; Srivastava ;
Granick ; JPCL-3 ; Muller ; Jiang . They acquire self-propulsion taking
advantage of local gradients resulting from some self-phoretic processes
(e.g., diffusiophoresis, thermophoresis or electrophoresis) occurring at the
particle-solvent interfaces Bunea ; Srivastava ; Granick ; Muller ; Jiang . As
the self-propulsion acts as an external energy source, there is no balance
between fluctuations and dissipations; thus, active particles (APs) are
typical non-equilibrium systems and exhibit correlated Brownian motion with
unusual transport features Golestanian-1 ; Golestanian-2 ; Teeffelen ; Stark ;
Volpe ; Marchetti1 ; Marchetti2 ; Redner ; Buttinoni . According to Pierre
Curie’s conjecture, the motion of such particles can be rectified in spatial
periodic structures with broken inversion symmetry. This effect is of
concerted interest, both conceptual and technological.

Much effort is presently directed in establishing net transport of self-
propelled particles in the absence of external bias ourPRL ; Reichhardt ; Bao
; Misko-1 ; Jaideep ; Pietzonka ; soft-sepa . It has been proved that APs of
the Janus kind exhibit directed autonomous motion in appropriate corrugated
channels ourPRL ; our-chiral ; cos . Such an effect is very robust and
rectification power is almost orders of magnitude larger than the conventional
thermal ratchets ourPRL . Rectification of APs motion has further been
examined in asymmetric periodic substrate potentials Reichhardt ; der . These
studies provide suggestive options in achieving reliable transport control of
active Janus particles (AJPs) in periodic structures. However, unwanted
particle-wall/substrate interactions pose challenges to observe autonomous
motion in the desired way. In this letter, we propose a more affordable option
to establish ratchet transport of AJPs and sort them according to
chiralitytechnical .

We numerically demonstrate that chiral AJPs exhibit directed motion in a
linear periodic counter-rotating array of steady planer convection rolls. The
rectification effect here does not require any additional ratchet potential.
Diffusing heavy AJPs in convection roll arrays feel a periodic structure with
broken upside-down symmetry due to their weight. This leads to rectification
of chiral AP motion. It may appear that chirality torq  (i.e., intrinsic
torques) is an additional criterion for rectification. However, in practice,
zero intrinsic torque of an AJP is very unlikely. Inevitable fabrication
defects, even to a little extent [see Fig.1(c)], produce apparent asymmetry
over the coated surface. Thus, an uneven rate of self-phoretic processes
taking place over the active surface produces intrinsic torque in the self-
propulsion motion.

Our simulation results prove that the average drift velocity of autonomous
motion can be made close to the self-propulsion speed by suitably adjusting
advection speed. We show how ratcheting can efficiently be utilized to
separate dextrogyre ($d$) and levogyre ($l$) AJPs from mixtures (binary or
multi-components).

Figure 1:  (Color online) (a) A sketch for practical realization of a linear
convection roll array of Rayleigh-Bénard type. The active particle of Janus
kind depicting self-propulsion model encoded in Eq. (2) is illustrated (b).(c)
Schematic of Janus particles with fabrication defects, thus possessing
intrinsic torques. (d) Chiral separation set up; at $t=0$ the mixture is
injected in the middle cell and particles are collected at the left absorbing
($L_{a}$) and right absorbing ($R_{a}$) ends. Distribution of $l$ (blue
circle) and $d$ (wine circle) AJPs in a convection array with stream function
of Eq.(1) at $t=10^{4}$ starting with uniform distribution in the middle cells
(framed in yellow). Parameters:
$g=0.5,\;v_{0}=1,\;D_{0}=D_{\theta}=0.01,\;|\Omega_{0}|=0.57$.

Note that many biomedical and nano-technological applications Bunea ;
Srivastava ; soto ; Minfeng ; Zhiyong  require self-propelled particles with
desired transport features. Further, dynamical properties of active particles
largely depend on their intrinsic torque and hence chirality. As laboratory
synthesis always produces AJP with different torques, it is desirable to sort
them for practical purposes.

We restrict our attention here to the low packing fraction region ($\phi\leq
0.1$) where impact of laminar flows around finite-size particles on advective
drag of the suspension fluid can be ignored Zoettl ; Rusconi ; Qi . Further,
our study focuses on low Reynolds number regimes where impact of hydrodynamics
and inertia on the dynamics of nano- and micro-particles Kirby  can be
ignored.

Model – We consider a mixture of $N$ interacting AJPs with different chirality
diffusing in the convection array of stream function,

$\psi(x,y)=({U_{0}L}/{2\pi})\sin({2\pi x}/{L})\sin({2\pi y}/{L}),$ (1)

The parallel walls at, $y=0$ and $y=L/2$ act as reflecting boundaries [see
Fig.1]. The pair of counter-rotating rolls are characterized by the array unit
cell of length $L$ and the maximum advection velocity $U_{0}$. Combining these
two constants, one can conveniently define the advection diffusion time scale
as, $D_{L}=U_{0}L/2\pi$ and the roll vorticity, $\Omega_{L}=2\pi U_{0}/L$.

A sketch of an ideal experimental set-up for convection rolls is presented in
Fig. 1(a). Stationary Rayleigh-Bénard type counter-rotating cells can be
produced in a plane horizontal layer of fluid heated from the bottom
Bodenschatz ; Getling . Recent studies wan1 ; wan2 ; wan3 ; hul  witness a
significant advances in experimental methods controlling fluid dynamics.
Considering the Rayleigh-Bénard type rolls are counter-rotating cylinders
along the z-axis, the z coordinate of a suspended particle can be ignored;
hence the reduced two-dimensional (2D) flow pattern of eq. (1).

We consider AJPs as interacting disks of radius $r_{0}$. They interact with
each other through a truncated Lennard-Jones (LJ) potential,
$V_{ij}=4\epsilon[\left({\sigma}/{r_{ij}}\right)^{12}-\left({\sigma}/{r_{ij}}\right)^{6}],\;\;{\rm
if}\;\;r_{ij}\leq r_{m}$; otherwise, $V_{ij}=0$ . Here, $r_{m}$ locates the
potential minimum, and $\sigma=2r_{0}$. We choose,
$\epsilon=v_{e}\sigma^{2}/24$, with Ran , $v_{e}=v_{0}$ (self-propulsion
velocity).

The following equation encodes the dynamics of $i^{th}$ AJP in the mixture,

$\displaystyle\dot{\mathbf{r}_{i}}={\mathbf{u}}_{i}+\mathbf{g}+\sum_{j}\mathbf{F}_{ij}+{\mathbf{v}}_{0,i}+\sqrt{D_{0}}{\bm{\xi}}_{i}(t),$
(2)

where, $i,j=1,\dots N$ and $\mathbf{r_{i}}\equiv(x_{i},y_{i})$ defines
position of the center of mass. Here,
${\mathbf{u}}_{i}\equiv(\partial_{y},-\partial_{x})\psi$ is the advection
velocity and $\mathbf{g}\equiv(0,-g)$ represents the drag due to particles’
apparent weight weight  (i.e., weight minus buoyant force). Further,
$\mathbf{F}_{ij}$ represents short-ranged repulsive force derived from the LJ
pair potential. The orientation of the self-propulsion velocity,
${\mathbf{v}}_{0,i}=v_{0}(\cos\theta_{i},\sin\theta_{i})$ evolves as,
$\dot{\theta}_{i}=\Omega_{0,i}+(\alpha/2)\nabla\times{\mathbf{u}}_{i}+\sqrt{D_{\theta}}~{}\xi^{\theta}_{i}(t)$.
Here, $\Omega_{0,i}$ represents intrinsic torque. The shear torque on the AJPs
is proportional to the local fluid vorticity, $\nabla\times{\mathbf{u}}_{i}$
RR2 ; Neufeld . We adopt Faxén’s second law, which, for an ideal no-stick
spherical particle, yields $\alpha=1$. The thermal translational noises,
${\bm{\xi}}_{i}(t)=(\xi_{x,i}(t),\xi_{y,i}(t))$ and the rotational noise
$\xi_{\theta,i}(t)$ are assumed to be stationary, independent, delta-
correlated Gaussian noises,
$\langle\xi_{\mu,i}(t)\xi_{\nu,j}(0)\rangle=2\delta_{ij}\delta_{\mu,\nu}\delta(t)$,
with $\mu,\nu=x,y,\theta$. The persistence time and length of self-propulsion
velocity are given by, $\tau_{\theta}=1/D_{\theta}$ and
$l_{\theta}=\tau_{\theta}v_{0}$, respectively. For an AJP the rotational
diffusion largely depends on the self-propulsion mechanisms. Thus, $D_{0}$,
$v_{0}$, and $D_{\theta}$ can safely be treated as independent parameters
cataly2 ; Golestanian-1 ; Teeffelen .

By conveniently rescaling position
$(x,y)\to(\tilde{x},\tilde{y})=(2\pi/L)(x,y)$ and time
$t\to\tilde{t}=\Omega_{L}t$, the tunable model parameters read
$\sigma\to(2\pi/L)\sigma$, $v_{e}\to v_{e}/U_{0}$, $v_{0}\to v_{0}/U_{0}$,
$D_{0}\to D_{0}/D_{L}$ and $D_{\theta}\to D_{\theta}/\Omega_{L}$. Upon setting
$L=2\pi$ and $U_{0}=1$, our simulation results can be assumed in dimensionless
units. However, one can easily scale back to desired dimensional units.

The Langevin Eq. (2) has been numerically integrated by means of a standard
Milstein scheme Kloeden . A very short integration time step,
$10^{-4}-10^{-5}$, has been used to ensure numerical stability. We numerically
calculate average drift velocity, fluxes at the left absorbing ($L_{a}$) and
right absorbing ($R_{a}$) ends [see Fig.1(d)] and spatial distribution of the
particles. Simulation details are given in the SI (item A2). Results reported
in Fig. 2-4 are obtained by averaging over $10^{3}-10^{4}$ trajectories. We
define the average drift velocity as,
$\overline{v}=\lim_{t\rightarrow\infty}(1/N)\langle\sum_{i}[x_{i}(t)-x_{i}(0)]/t\rangle$.
We express $\overline{v}$ in the unit of self-propulsion velocity,
$\kappa=\overline{v}/v_{0}$. Our study focuses on the high Péclet number
regime where advection wins over diffusion, $D_{L}/D_{0}\gg 1$. Further, we
vary the parameters: $g/U_{0}$, $v_{0}/U_{0}$, $\Omega_{0}/\Omega_{L}$ , and
$D_{\theta}/\Omega_{L}$ over the range $0$ to $\gg 1$.

Autonomous AJPs ratchet — We first consider the limit of vanishingly small
packing fraction, $\phi=2\pi r_{0}^{2}N/L^{2}\rightarrow 0$, when AJPs can be
assumed as non-interacting disks. Simulation results presented in the Fig. 2
reveal that non-interacting chiral AJPs ($|\Omega_{0}|>0$) exhibit directed
autonomous motion in the convection roll arrays. The rectification power,
defined as, $\eta=|\kappa|$, can easily be raised to more than 60$\%$ by
suitably adjusting advection. Further, for vanishingly small rotational
diffusion [ $D_{\theta}=0$ and $10^{-4}$ in Fig. 2(f) ] the rectification
power approaches to 90%. The average velocity, $\overline{v}$ , is a non-
monotonic function of self-propulsion parameters, $\Omega_{0}$ and $g$.

Figure 2:  (Color online) (a-c) The spatial distributions, $p(x,y)$ of a non-
interacting AJP in the laminar flow of Eq. (1) for different $\Omega_{0}$ and
$g$ (see legends) and $v_{0}=0.2,\;D_{0}=0.01,\;D_{\theta}=0.005$. The chart
levels are color coded on natural logarithmic scales as indicated. (d)
$\kappa\;vs.\;v_{0}/U_{0}$ for different $D_{\theta}$ (see legends) and
$D_{0}=0.01,\;g=0.1,\;\Omega_{0}=0.57$. Inset:
$\kappa\;vs.\;\Omega_{0}/\Omega_{L}$ with varying $g$ (see legends) and
$v_{0}=1,\;D_{0}=D_{\theta}=0.01$. (e) $\kappa\;vs.\;v_{0}/U_{0}$ for
different $g$ (see legends) and
$D_{0}=0.01,\;\Omega_{0}=0.03,\;D_{\theta}=0.001$. (f) Similar plots as (d),
but $D_{0}=0.001,\;g=1,\Omega_{0}=0.09$.

The symmetry breaking mechanism leading to directed autonomous motion can be
understood by examining spatial distribution, $p(x,y)$ of AJPs in the
convection roll arrays. Numerical results presented in Fig. 2(a-c) [also
Figure S3 of supporting information (SI)] show that when the self-propulsion
length is larger than the array width, $l_{\theta}>L/2$, particles tend to
slide along array edges until they accumulate in the stable stagnation
regions, namely at the center of the ascending (against the upper wall) and
descending flows (against the lower wall). As long as,
$g\ll\\{U_{0},v_{0}\\}$, $p(x,y)$ of an achiral particle develops a periodic
structure with apparent inversion symmetry [see Fig. 2(a)]. With growing $g$,
the effective spatial structure or potential, a heavy achiral AJP experiences,
loses its upside-down symmetry, however, the left-right symmetry retains there
[see Fig. 2(b)]. On the other hand, a chiral AJP exhibiting orbiting motion
(with radius of curvature, $R_{\Omega}=v_{0}/\Omega_{0}$) gets dissimilar
forces in upper and lower halves of the rolls. Thus, they encounter an
effective periodic structure which lacks both the left-right, as well as, the
upside-down symmetry.

Due to left-right symmetry in $p(x,y)$ of achiral APs, the direction of
rectification gets reverted on reverting intrinsic torque,
$\overline{v}(-\Omega_{0})=-\overline{v}(\Omega_{0})$. However, the interplay
between the advection, self-propulsion and apparent weight governs dynamical
details of the rectification mechanism; hence the amplitude and direction
$\overline{v}$.

In Fig. 2(d), we report $\overline{v}$ versus $v_{0}$ when particle’s weight
is one-tenth of the maximum advection velocity and $\Omega_{0}$ is comparable
to the average advection torque $2\Omega_{L}/\pi$. For $v_{0}\ll g$, AJP
motion does not get rectified as self-propulsion fails to depin particles from
the stagnation areas. Again, in the opposite limit, $v_{0}\gg\\{U_{0},\;g\\}$,
the particles feel very weak ratchet potential where they exhibit free
diffusion pkg1 ; pkg2 , $D_{eff}=v_{0}^{2}/2D_{\theta}$ with
$\overline{v}_{0}=0$. Multiple current reversals are witnessed with the
variation of $v_{0}$ over the range: $v_{0}\ll\\{g,U_{0}\\}$ to
$v_{0}\gg\\{g,U_{0}\\}$.

A heavy active particle preferably falling down around descending flow center,
gets advected along bottom array edges until self-propulsion is opposed by
advection or the vertical component of self-propulsion surpasses the apparent
weight, $v_{0}\sin{\theta}>g$. Simulation results (see Fig. 2(a-c), also
Figure S3-S5 in SI) well corroborate this assertion. In the complete noiseless
situation, particles are pinned at a distance, $\delta
x\sim\sin^{-1}(U_{0}/v_{0})$, from centres of the ascending flow. Here, it is
assumed that no appreciable $\mathbf{v}_{0}$ direction change occurs before
reaching the stagnation point. When, $v_{0}\ll U_{0}$, chiral APs are pinned
close to array separatrices, thus, self-propulsion helps lifting the particle
along the ascending flow.

Figure 3:  (Color online) (a) $\kappa\;vs.\;v_{0}/U_{0}$ for $l$ (empty
symbols) and $d$ (solid symbols) AJPs in equimolar binary mixtures with
varying $\phi$ (see legends). Other parameters:
$g=1,\;D_{\theta}=0.001,\;D_{0}=0.01,\Omega_{0}=0.03,\;r_{0}=0.025$. (b-c)
Flux ratio of $d$ and $l$ type particles at the left-absorbing point,
$J_{-}^{L}/J_{+}^{L}$ vs. $N$ for different $v_{0}/U_{0}$ (see legends); Other
parameters: in (b)
$g=0.25,\;D_{\theta}=D_{0}=0.01,\;r_{0}=0.025,\;\Omega_{0}=0.57$; in (c)
parameter are the same as (b), however, $g=1,\;\Omega_{0}=0.03$. (d-e) Spatial
distribution of equimolar binary mixture of $l$ (blue) and $d$ (wine) AJPs
($N=4560$) in the laminar flow of Eq. (1) at $t=10^{4}$ starting with uniform
distribution in the middle cell spanning over the range: $-\pi\;{\rm
to}\;+\pi$. Parameters having the same values as (b) but $v_{0}$ values are in
the legends. (f) Similar plots as (d-e) but $g=1.0,\;|\Omega_{0}|=0.03$ and
$v_{0}=0.9$. For better visibility, the piles at the terminals and middle
cells have been zoomed in.

In the upper-half of the roll, the intrinsic torque pushes the $l$ ($d$)
particles to the left (right) leading to negative (positive) current. The
amplitude of current keeps growing with $v_{0}$ as it facilitates lifting
particles against their weight. A negative current peak appears around
$v_{0}\sim 2g$. Around this value of $v_{0}$, rectification does not require
movement of AJPs through the rolls interior, thus, $\kappa$ becomes
insensitive to the advection torque (see Figure S6 of SI).

On increasing $v_{0}$ beyond the first peak [see Fig. 2(d)], the stagnation
point shifts appreciably far from the ascending flow centres. Getting
displaced there vertically, particles encounter advection torque which tends
to oppose counter-clockwise rotation due to the intrinsic torque leading to
decrease of negative current amplitude. With growing $\delta x$, current
direction is reverted and thereafter gets maximized around the point
$v_{0}\sim U_{0}$. For $v_{0}>U_{0}$, peaks and reversal points appear around
$v_{0}=m\pi\Omega_{0}/4$, with $m=4,5,6,7...$.

The structure of $\kappa$ versus $v_{0}$ remains insensitive to the variation
of both the rotational and translational diffusion constants [see Fig. 2(d)
and Figure S6(b) in SI]. However, rectification power considerably enhances
with lowering noise level in the system. On the other hand, as expected,
ratcheting does not occur for the very high noise level [$D_{0}\gg D_{L}$ and
$D_{\theta}\gg\Omega_{L}$].

Inset of 2(d) depicts $\kappa$ vs. $\Omega_{0}$ for different apparent weight
$g$. Here, we set $v_{0}/U_{0}=1$, where current is maximum [see Fig. 2(d)].
As long as $g$ is small enough in comparison to the $v_{0}$ and $U_{0}$
prominent current peaks are observed at $\Omega_{0}\sim 2\Omega_{L}/\pi$.
However, with increasing $g$ rectification gets suppressed and peaks are
shifted to the lower value of $\Omega_{0}$. To identify parameter regimes for
better rectification power, we explore $\kappa\;vs.\;v_{0}$ [see Fig. 2(e,f)
with varying $g$ and $D_{\theta}$ for $\Omega_{0}\ll\Omega_{L}$] and also
$\kappa\;vs.\;\Omega_{0}$ [shown in SI: Figure S7]. Figure 2(e,f) show
that:(i) rectification becomes noticeable for $v_{0}\geq g$, (ii) direction of
current can be reverted by varying $v_{0}$ for very slow rotational diffusion,
(iii) the negative current peak gets broader with lowering rotational noise
strength. The rectification power around the negative current peak is in
excess of $60\%$ which is much larger than the previously reported directed
autonomous motion of APs. Also, self-propulsion parameters chosen here in
rescaled units, are consistent with the corresponding values reported in ref.
Volpe . To this end, we conclude that to rectify motion of AJPs with low
torque, $\Omega_{0}\ll\Omega_{L}$, advection should be adjusted so that,
$\\{g/U_{0},\;v_{0}/U_{0}\\}\gtrsim 1$. On the other hand, for
$\Omega_{0}\sim\Omega_{L}$, ratcheting occurs even for $g\sim U_{0}/10$, over
a long range of $v_{0}$.

To check ratcheting of interacting AJPs, in Fig. 3(a) we present $\kappa$
versus $v_{0}/U_{0}$ for a binary racemic mixture torq . With increasing the
packing fraction, the amplitude of current as well as the shape of $k$ versus
$v_{0}$ change noticeably [detail analysis have been provided in the SI (item
A3)]. However, rectification power is high enough for experimental
demonstration of this striking effect in interacting AJPs. In the mixture, $l$
particles drift opposite to the $d$ ones. It is apparent from Fig. 3(a) that
within the limit of statistical error, the relation
$\overline{v}(\Omega_{0})=-\overline{v}(-\Omega_{0})$ holds for the entire
range of self-propulsion. Thus, $l$ and $d$ particles can easily be separated,
by injecting their mixture in a convection roll array.

Figure 4:  (Color online) (a) Torque distributions of absorbed particles in
the $L_{a}$ (empty symbols) and $R_{a}$ (solid symbols) ends, when injected
particle torques have Gaussian distribution (solid line) with zero mean and
variance $\overline{\Omega}=0.05$. Other parameters:
$D_{0}=D_{\theta}=0.003,\;r_{0}=0.025\;g=U_{0}=1,\;v_{0}=1.4$. (b,c) Ratio of
$d$ and $l$ particles absorbed at the $L_{a}$ end for for the same parameters
as (a), unless mentioned in the legends.

Chiral separation — To better illustrate the chiral separation taking
advantage of ratcheting in convection roll arrays, we consider a set up [as
shown in the Fig. 1(d)], where, particles are injected in the middle cell
(spanning over $-L/2$ to $+L/2$) and they are absorbed/collected at $n$ cells
apart $[x=\pm(k+1/2)L]$ from the injecting cell. We choose $k=3$ for all the
simulation results reported in this paper. However, the conclusions of our
study are insensitive to this choice. To keep particle number $N$ fixed
between two absorbing points ($L_{a}\;{\rm and}\;R_{a}$), absorbed particles
are re-injected in the middle cell. We examine the distribution of particles
and flux at the absorbing points $L_{a}\;{\rm and}\;R_{a}$. First, we consider
chiral separation in a racemic binary mixture torq  where $l$ and $d$ AJPs
have sharply defined torques, $+\Omega_{0}$ and $-\Omega_{0}$, respectively.
Then, a more realistic situation has been considered where particle torques
have Gaussian distribution with zero mean and variance $\overline{\Omega}$,
$P(\Omega_{0,i})=1/\sqrt{2\pi\overline{\Omega}}\exp[-\Omega_{0,i}^{2}/2\overline{\Omega}]$.

Racemic binary mixture — Figure 3(d-f) [also, in SI: Figure S8-S10] depict
distribution of AJPs [1:1 dl mixture] at $t=10^{4}$, starting with an uniform
distribution in the middle cell. It is apparent that $l$ and $d$ particles
preferably diffuse in the opposite direction to each other leading to
separation of two sorts of species. Our simulation results show that the
segregation mechanism for the particles with large torque
($\Omega_{0}\sim\Omega_{L}$) works better for low g ($\sim U_{0}/10$) [see
Fig. 3(b, d-e)]. On the other hand, better separation of chiral particles in
low torque regimes requires $g\geq U_{0}$ [Fig. 3(c,f)]. For the both limits
of $\Omega_{0}$, the separating device operates over a long range of self-
propulsion. For $v_{0}\ll\\{U_{0},\;g\\}$, similar as noted for
$\phi\rightarrow 0$, pinning action suppresses autonomous motion of the APs.
Thus, neither separation nor flux becomes noticeable. As soon as $v_{0}$
approaches to $g$, separation of two sorts of species into distinct phases
gets appreciable. Further, for $U_{0}\sim g$ and $v_{0}\geqslant U_{0}$ phase
separation occurs with the formation of preferably one-species clusters of
different size. Cluster formation is initiated by the confining action exerted
by the active particles and largely depends on the self-propulsion properties,
intrinsic torques and other aspects of the microscopic mixture dynamics MP1 ;
MP2 ; MP3 ; MP4 ; MP55

We numerically estimate particle fluxes at the both absorbing ends, $L_{a}$
and $R_{a}$ [see Fig.1(d)]. Fluxes of $l$ and $d$ AJPs at $L_{a}$ end are
denoted as, $J_{+}^{L}$ and $J_{-}^{L}$, respectively. They are defined as,
$J_{\pm}^{L}=\langle n_{\pm}^{L}\rangle/t$. Where, $n_{+}^{L}$ is the number
of $l$ JP absorbed at the $L_{a}$ end over the time $t$. Similar notations,
$J_{\pm}^{R}$, are used for fluxes at $R_{a}$ end.

As current gets reverted on reverting direction of the intrinsic torques,
$J_{+}^{L}=J_{-}^{R}$ and $J_{-}^{L}=J_{+}^{R}$. The separation efficiency
efficiency  can best be quantified by analysing the ratio of $l$ and $d$
particles absorbed at the $L_{a}$ or $R_{a}$ ends. Figure 3(b) and 3(c) depict
variation of flux ratio, $J_{-}^{L}/J_{+}^{L}$ as a function of particle
number $N$ for the high and low torque regimes, respectively. These results
prove that for the both torque regimes and over a long range of $v_{0}/U_{0}$,
almost 98% - 99.99% of either $l$ or $d$ AJPs are selectively absorbed at the
one end. As anticipated, the segregation efficiency is much better for low
density. Simulation results show that impacts of inter-particle interactions
are noticeable even for low packing fractions (for details, see item A3 of
SI). Further, this chiral separation device can be operated over a large
parameter regimes (see SI, item A5).

Mixture with distributed particle torque —  Finally, our analysis focuses on
separation of $d$ and $l$ AJPs from a mixture where particle torques are
normally distributed with variance $\overline{\Omega}$. Particle torques due
to fabrication defects cannot be considered sharply defined two values
$\pm\Omega_{0}$ . Rather, they should be distributed over a range. Figure 4(a)
shows the torque distribution of the particles absorbed in the $L_{a}$ and
$R_{a}$ ends, when AJPs with Gaussian torque distribution are injected at the
middle cell. It is apparent that $d$ type AJPs are preferably absorbed in the
$L_{a}$ end and vice-versa. The flux ratio, $J_{-}^{L}/J_{+}^{L}$ (see
Fig.4(b-c), also, Figure S11 in SI), further confirms that one can separate
$d$ and $l$ AJPs from a mixture with high efficiency. Almost, 90% to 98.5%
separation efficiency can easily be achieved over a large range of
$\overline{\Omega},\;g\;$ and $v_{0}$. Strikingly, confining action initiates
motility induced phase separation, thereby the $l$ and $d$ AJPs tend to pile
up in the well-separated stagnation areas (shown in Figure S12-S13 of SI).

In conclusions, our study offers an experimentally adoptable demonstration of
ratcheting, as well as, an efficient way of sorting $d$ and $l$ AJPs from
their mixture. Our simulation results prove that the chiral separation device
can be operated on any scale, however, it requires the ratios, $v_{0}/U_{0}$
and $\Omega_{0}/\Omega_{L}$, to be within the range 0.1 to 2 and 0.001 to 1.0,
respectively. Further, these effects can be reproduced in artificial swimmers
regardless of their propulsion mechanism, especially, not only for fabricated
active Janus particles. We expect, our proposed rectification and chiral
separation protocols carry huge application potentials in the micro-swimmer
technology and biomedical sciences.

## Supporting Information

The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.jpclett.2c03193.

A1: Meaning of some technical terms; A2: Simulation methods; A3: Impact of
inter-particle interactions on the rectification and separation; A4:
Simulation results supporting the rectification mechanism; A5: Additional
figures for current and flux, and spatial distribution.

## Acknowledgments

P.B. thanks UGC, New Delhi, India, for the award of a Junior Research
Fellowship. P.K.G. is supported by SERB Core Research Grant No.
CRG/2021/007394.

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11institutetext: University of Brighton, East Sussex BN2 4GJ, United Kingdom
11email<EMAIL_ADDRESS>22institutetext: Royal Holloway
University of London, Surrey TW20 0EX, United Kingdom
22email<EMAIL_ADDRESS>
# Audio feature ranking for sound-based COVID-19 patient detection

Julia A. Meister 11 0000-0003-2951-7217 Khuong An Nguyen 11 Zhiyuan Luo 22

###### Abstract

Audio classification using breath and cough samples has recently emerged as a
low-cost, non-invasive, and accessible COVID-19 screening method. However, a
comprehensive survey shows that no application has been approved for official
use at the time of writing, due to the stringent reliability and accuracy
requirements of the critical healthcare setting. To support the development of
Machine Learning classification models, we performed an extensive comparative
investigation and ranking of 15 audio features, including less well-known
ones. The results were verified on two independent COVID-19 sound datasets. By
using the identified top-performing features, we have increased COVID-19
classification accuracy by up to 17% on the Cambridge dataset and up to 10% on
the Coswara dataset compared to the original baseline accuracies without our
feature ranking.

###### Keywords:

COVID-19 classification Audio event engineering Sound feature ranking.

##  1 Introduction

A widely accessible, non-invasive, low-cost testing mechanism is the number
one priority to support test-and-trace in most pandemics. The advent of
COVID-19 has abruptly brought respiratory audio classification into the
spotlight as a viable alternative for mass pre-screening, needing only a
smartphone to record a breath or cough sample [3].

It has long been common knowledge that respiratory diseases physically alter
the respiratory environment in a way that often induces audible changes [17].
Consequently, manually listening to lung sounds (auscultation) is a common
method to identify and diagnose respiratory disorders. However, many
abnormalities only subtly affect auditory cues, making the inherently
subjective auscultation process error-prone even when performed by a trained
medical professional [2]. To counteract subjectivity, automated audio
classification approaches with promising results have become more and more
common in recent years [1, 2, 9].

One of the main limiting factors is the lack of ground truth data which may be
difficult to obtain, prone to limited population diversity, and requires
medical training to label correctly. Because COVID-19 detection is a
widespread and critical problem, multiple universities and research
institutions have published COVID-19 audio datasets [3, 19]. This offers a
unique opportunity to verify classification solutions on independently
collected samples from a diverse population. The datasets have supported the
development of a variety of applications with Machine Learning (ML) audio
classification. However, at the time of writing, none have yet been officially
endorsed for medical usage, largely because of the high accuracy and
reliability expectations for such a critical healthcare task.

The paper gives a comprehensive overview of relevant audio features (Section
2) and identifies the most indicative ones for COVID-19 (Section 3). Finally,
the findings are put into the context of existing literature (Section 4).

###  1.1 The paper’s contributions

The rigorous feature analysis presented in this paper improves COVID-19
respiratory classification by optimising and holistically evaluating audio
signal representations for Machine Learning (ML). The following contributions
are made:

  * •

_Audio feature analysis and ranking_. We performed an extensive comparative
analysis and ranking of 15 sound features prevalent and less-common in audio
classification. The evaluation was carried out on two independent datasets,
allowing the findings to be generalised.

  * •

_Highlighted effective features._ We identified sound-based ML features with
strong discriminative performance that go against common rules of thumb.

  * •

_Increased COVID-19 detection accuracy._ We improved accuracy up to 17% by
incorporating new training features based on our feature ranking.

##  2 Audio features overview

As in any Machine Learning (ML) application, feature engineering is a vital
step for COVID-19 cough classification. We provide a detailed overview of 15
audio features from a variety of signal domains (Table 1) before rigorously
evaluating their performance.

Table 1: _Audio feature selection._ The 15 audio features evaluated in the paper. Domain |  Feature category |  Name |  Intuition
---|---|---|---
Time |  Signal energy |  RMSE |  Loudness of the signal.
Waveform |  ZCR |  Percussive vs tonal.
Frequency |  Spectral |  S-BW |  Perceived timbre.
Spectral |  S-CENT |  ‘Brightness’ of a sound.
Spectral |  S-CONT |  Prevalence of formants.
Spectral |  S-FLAT |  Similarity to white noise.
Spectral |  S-FLUX |  Rate of frequency changes.
Spectral |  S-ROLL |  ‘Skewness’ of the energy.
Time-frequency |  Cepstral |  MFCC |  Timbre, tone colour/quality.
Cepstral |  MFCC-$\Delta{}$ |  Velocity of temporal change.
Cepstral |  MFCC-$\Delta{}^{2}$ |  Acceleration of temporal change.
Tonal |  C-ENS |  Pitch.
Tonal |  C-CQT |  Pitch.
Tonal |  C-STFT |  Pitch.
Tonal |  TN |  Pitch & pitch height.

###  2.1 Time domain

Low-level features extracted directly from the signal are in the time domain.
They may identify crackling sounds caused by secretions in the throat and
lungs [17], and have been previously used for COVID-19 classification [3, 19].

##### Root mean square energy (RMSE).

A measure of the signal’s amplitude over $N$ frames, see Eq. (1). $x_{n}$ is
the average energy per frame [15].

$\textstyle\textnormal{RMSE}=\sqrt{\frac{1}{N}\sum^{N}_{n=1}x^{2}_{n}}$ (1)

##### Zero-crossing rate (ZCR).

The signal’s sign change rate (Eq. (2)). $x_{n}$ is amplitude at frame $n$ of
$N$. $sign(a)$ returns $1$ if $a>0$, $0$ if $a=0$, and $-1$ else [15].

$\textstyle\textnormal{ZCR}=\frac{1}{2}\times\sum^{N}_{n=2}|sign(x_{n})-sign(x_{n-1})|$
(2)

###  2.2 Frequency domain

To reveal frequency information of digital audio, it is decomposed into its
constituent frequencies. This domain may identify abnormal lung sounds caused
by an infection by examining the signal’s intensity [17]. A subset has
previously been used for COVID-19 detection [3, 19].

_Spectral bandwidth._ Eq. (3) shows energy concentration, i.e. variance of
expected frequency $E$ given energy $P_{k}$ and frequency $f_{k}$ in $1\leq
k\leq K$ bands [16].

$\textstyle\textnormal{S-BW}=\sqrt{\sum^{K}_{k=1}(f_{k}-E^{2}\times P_{k})}$
(3)

_Spectral centroid._ Eq. (4) shows the weighted and unweighted sums of
spectral magnitudes $P_{k}$ in the $k$-th of $K$ subbands. $f_{k}$ is the
corresponding frequency [20].

$\textstyle\textnormal{S-CENT}=\frac{\sum^{K}_{k=1}P_{k}\times
f_{k}}{\sum^{K}_{k=1}P_{k}}$ (4)

_Spectral contrast._ Compare spectral peaks $P_{k}$ and valleys $V_{k}$ in
frequency band $k$, see Eq. (5). $N$ is the number of frames and
$x^{\prime}_{k,n}$ the FFT vector [7].

$\textstyle\textnormal{S-CONT}_{k}=P_{k}-V_{k}=(\log\frac{1}{N}\sum^{N}_{n=1}x^{\prime}_{k,n})-(\log\frac{1}{N}\sum^{N}_{n=1}x^{\prime}_{k,N-n+1})$
(5)

_Spectral flatness._ Eq. (6) measures similarity to white noise. $P_{k}$ is
the signal’s energy at the $k$-th frequency band s.t. $1\leq{}k\leq{}K$ [10].

$\textstyle\textnormal{S-FLAT}=\frac{(\prod^{K}_{k=1}P_{k})^{\frac{1}{K}}}{\frac{1}{K}\sum^{K}_{k=1}P_{k}}$
(6)

_Spectral flux._ Eq. (7) measures a signal’s energy change between frames.
$E_{n,k}$ is the $k$-th of $K$ Discrete Fourier Transform coefficients in
frame $n$ [20].

$\textstyle\textnormal{S-FLUX}_{n}=\sum^{K}_{k=1}E_{n,k}-E_{n-1,k}^{2}$ (7)

_Spectral rolloff._ Eq. (8) finds frequency $f_{R}$ s.t. the energy
accumulated below is no less than proportion $S$ of total energy. $P_{k}$ is
energy in one of $K$ bands [20].

$\textstyle\textnormal{S-ROLL}=\operatorname*{arg\,min}f_{R}\in\\{1,\ldots,K\\}\sum^{f_{R}}_{k=1}P_{k}\geq
S\sum^{K}_{k=1}P_{k}$ (8)

###  2.3 Time-frequency domain

This domain shows a signal’s frequency as it varies over time. We consider two
types of features: cepstral (timbre or tone colour) and tonal (pitch).

Cepstral features. Non-linear Mel-frequency Cepstrum (MFC) is ubiquitous in
respiratory classification because it explores a signal’s temporal frequency
content. It has been previously used for COVID-19 [3, 12].

_Mel-frequency cepstral coefficients._ Eq. (9) shows the signal’s
transformation. $s(k)$ is the log energy of the $k$-th of $K$ coefficients at
frame $n$ [3].

$\textstyle\textnormal{MFCC}_{n}=\sum^{K}_{k=1}s(k)\cos{\frac{\pi
n(k-0.5)}{K}}$ (9)

_MFCC- $\Delta{}$._ The first-order derivative of MFCC, velocity, represents
temporal change and is often included due to its low extraction cost [4].

_MFCC- $\Delta{}^{2}$._ The second-order derivative, acceleration, is commonly
included because it may improve audio classification [4].

Tonal features. Based on the human perception of periodic pitch [13]. Two
types are considered: chromagram and lattice graph. Secretions are a common
consequence of COVID-19 which may alter the pitch of in- and expiration [17].

_Chroma energy normalised._ Chroma abstraction considering short-time
statistics within chroma bands. Normalisation makes C-ENS resistant to timbre
[13].

_Constant-Q chromagram._ Extracted from a time-frequency representation. The
constant-Q transform (C-CQT) has a good resolution of low frequencies [8].

_Short-time Fourier Transform chromagram._ The difference to C-CQT is the
initial transformation, in this case the Short-time Fourier Transform (STFT)
[8].

_Tonnetz._ A lattice graph of harmonic information. Distances between points
become meaningful by encoding pitch as geometric areas [5].

##  3 Experimental method and results

The 15 investigated features range from prevalent to traditionally excluded
from audio classification. They were ranked based on the empirical results
analysis of two independent datasets. We assume that patterns repeated across
both datasets are likely inherent to the COVID-19 respiratory recordings.

###  3.1 Research questions

Three research questions were formulated to inform the experimental design and
results analysis. Each is focused on improving COVID-19 audio classification.

  * •

What are the most predictive audio features for Machine Learning?

  * •

Are the feature rankings comparable across independent datasets?

  * •

How much does the performance accuracy of Machine Learning models improve by
using the most dominant features?

###  3.2 The datasets

Two parallel independent datasets were considered throughout the paper to
indicate whether feature rankings were likely generally applicable: the
_Cambridge_ and _Coswara_ COVID-19 audio datasets. The sample counts are shown
in Table 2.

Introduced in [3], the _Cambridge dataset_ is a collection of healthy and
COVID-positive cough and breath recordings. The data we used is a curated set
of 48kHz WAV file samples, collected April-May 2020. Additionally, the Indian
Institute of Science has collected shallow and deep breath and cough
recordings in the _Coswara dataset_ [19]. Compatible samples from April-
December 2020 were considered. For consistency, we filtered for COVID-positive
and healthy participants.

Table 2: _Sample counts of the datasets._ Each Coswara participant has ‘shallow’ and ‘deep’ breath (B), cough (C), and breathcough (BC) recordings. Label | Cambridge | Coswara-deep | Cos.-shallow
---|---|---|---
| B | C | BC | B | C | BC | B | C | BC
COVID-19 | 111 | 111 | 111 | 81 | 81 | 81 | 81 | 81 | 81
Healthy | 194 | 194 | 194 | 1074 | 1074 | 1074 | 1074 | 1074 | 1074
$\sum{}$ | 305 | 305 | 305 | 1155 | 1155 | 1155 | 1155 | 1155 | 1155

###  3.3 Feature engineering

Cleaning the audio data was especially important because the recording devices
and environments were not controlled. The pre-processing steps were carried
out with the Python-toolkit `librosa`, and included trimming the
leading/trailing silences and normalising the amplitude to $(-1,1)$.

We evaluated 15 audio features from three signal domains (Section 2). To
standardise feature dimensions for Machine Learning (ML) models regardless of
sample length (1–30 seconds, Figure 1), seven summary statistics were
calculated to describe the feature distribution across frames:  (i) minimum,
(ii) maximum,  (iii) mean,  (iv) median,  (v) variance,  (vi) 1st quartile,
and  (vii) 3rd quartile . Only a small subset of features was considered for
evaluation and ranking at a time to avoid overfitting (812 features total,
Table 3).

Figure 1: _Sample lengths pre- and post-processing._ We trim leading and trailing silences (60dB, empirically identified). Lengths were reduced by 1–3 seconds. Table 3: _Feature dimensions._ 812 features were considered. 7 Summary statistics were taken across frames to ensure consistent dimensions (sample length 1–30s). To reduce overfitting risk, feature subsets were considered at a time for ranking. Dimension | Features (min, max, mean, median, var, Q1, and Q3)
---|---
(1x7) | RMSE, ZCR, S-BW, S-CENT, S-FLAT, S-FLUX, S-ROLL
(6x7) | TN
(7x7) | S-CONT
(12x7) | C-ENS, C-CQT, C-STFT
(20x7) | MFCC, MFCC-$\Delta{}$, MFCC-$\Delta{}^{2}$

###  3.4 Results description and analysis

We identified the most informative features by evaluating two datasets in
parallel. We propose that recurring predictive patterns are likely independent
of the dataset, and should be strongly considered for future ML COVID-19
classification applications. Features were analysed in the following
configurations:

  * •

The Cambridge, Coswara-deep, and Coswara-shallow datasets.

  * •

Breath (B), Cough (C), and BreathCough (BC) feature vectors. The latter is a
concatenation of the previous two feature vectors, i.e. double the size.

  * •

5 models, selected for the variety in which they partition the label space:
AdaBoost-Random Forest (ADA), K-Nearest Neighbours (KNN), Logistic Regression
(LR), Random Forest (RF), and Support Vector Machine (SVM).

5-fold Cross-Validation ensured reliable results. We selected 3 metrics to
compare the features’ efficiency: _Receiver Operating Characteristic_ (ROC),
_Precision_ (P), and _Recall_ (R). PR curves are well suited to imbalanced
data by omitting true negatives, counteracting ROC’s optimism [18]. The mean
over folds was a suitable indicator because the performance values passed the
normality test [6].

Feature categories. An overview of full feature vectors showed promising
results, as most models outperformed their no-skill equivalent in ROC and PR-
curves (Figure 2). SVM and RF outperformed their counterparts across BC, B and
C. Even though the two datasets had similarly shaped ROC curves, Cambridge had
the best Average Precision (AP), and illustrates ROC’s optimism on imbalanced
datasets. An influential factor in Coswara’s lower overall accuracies was the
greater imbalance of COVID samples (Coswara 13:1 vs Cambridge 2:1, Table 2).
Nonetheless, Coswara-trained models performed significantly better than their
unskilled classifier counterparts (13–38% vs 7% AP, Figure 2(b)).

(a) Mean ROC over 5-fold CV (positive: COVID). AUC is ‘Area Under Curve’.

(b) Mean PR over 5-fold CV (positive: COVID). AP is ‘Average Precision’.

Figure 2: _BreathCough results._ Even though the ROC-curves look similar
across datasets, the PR-curves reveal that Cambridge performed better overall.
We also identified SVM and RF as the top-performing models. In PR-curves, the
unskilled classifier corresponds to the dataset’s positive label ratio. Table
4: _BreathCough 5-fold CV ROC-AUC results as mean(std)._ SVM and RF achieved
the highest accuracies across most domains. The feature categories were be
ranked in the following increasing order: time, tonal, spectral, cepstral.

Dataset | Category | ADA | KNN | LR | RF | SVM
---|---|---|---|---|---|---
Cambridge | Time | 67.17(.04) | 77.96(.07) | 76.01(.07) | 78.21(.05) |  78.78(.07)
Spectral | 87.09(.04) | 85.34(.05) | 84.17(.06) |  87.15(.05) | 84.84(.07)
Cepstral | 83.84(.05) | 85.56(.07) | 83.27(.06) | 87.82(.07) |  87.15(.06)
Tonal |  84.74(.09) | 81.04(.05) | 81.44(.04) | 81.11(.07) | 82.59(.07)
Coswara-deep | Time | 55.65(.07) | 62.34(.02) | 54.21(.09) |  64.65(.05) | 63.94(.07)
Spectral | 65.77(.07) | 68.18(.04) | 72.03(.05) | 71.76(.06) |  74.46(.06)
Cepstral | 70.83(.06) | 71.03(.03) | 75.01(.05) |  77.55(.06) | 75.62(.08)
Tonal | 69.29(.06) | 66.27(.02) | 68.02(.03) | 72.32(.06) |  72.98(.03)
Coswara-shallow | Time |  61.63(.04) | 55.05(.06) | 56.16(.09) | 54.27(.07) | 55.90(.09)
Spectral | 66.69(.04) | 61.02(.05) | 69.85(.05) | 69.15(.05) |  72.32(.04)
Cepstral | 63.13(.09) | 68.35(.04) | 65.83(.03) |  71.79(.06) | 70.62(.04)
Tonal | 58.37(.08) | 63.98(.05) | 65.21(.08) | 67.17(.08) |  68.81(.08)

BC signal domain results confirmed SVM and RF as the best performing models
(Table 4). Considering SVM’s BC ROC-AUC across all datasets, we note that the
4 feature categories were broadly ranked in increasing predictive efficiency
(Cambridge, Coswara-deep, Coswara-shallow): _time domain_ (79%, 64%, 56%),
_tonal_ (83%, 73%, 69%), _spectral_ (85%, 74%, 72%), and _cepstral_ (87%, 76%,
71%). Spectral and cepstral categories achieved similarly high accuracies.
Interestingly, the same ranking was prevalent for all 5 ML models, leading to
the conclusion that the cepstral and spectral feature categories encode
particularly informative COVID-19 data from breath and cough signals. A
Repeated Measures ANOVA test [6] confirms that the feature domains lead to
statistically significant differences in ROC score for all three datasets
($p<0.02$).

Individual features. We start with the best-performing SVM classifier before
broadening to include all models to identify general predictive efficiency
patterns. The results forming the basis of our analysis are available in Table
5. A Repeated Measures ANOVA test [6] verifies that the sample type leads to
statistically significant differences in ROC score across all datasets
($p<0.05$).

Table 5: _5-fold CV ROC-AUC as mean(std)_. The majority of features showed the
most accurate results on the BreathCough (BC) vector. Feature categories were
ranked in increasing accuracy: time domain, tonal, spectral, and cepstral.

(a) SVM, Cambridge data.

|  | B | C | BC
---|---|---|---|---
All | All | 85.86(.07) | 85.80(.05) | 87.68(.06)
Time | All | 72.77(.04) | 74.90(.08) | 78.78(.07)
RMSE | 72.28(.05) | 76.45(.08) | 77.88(.08)
ZCR | 64.59(.08) | 69.73(.06) | 71.40(.06)
Spectral | All | 85.28(.06) | 84.03(.07) | 84.84(.07)
S-BW | 69.24(.08) | 71.57(.04) | 75.4(.08)
S-CENT | 73.45(.08) | 70.06(.08) | 78.07(.07)
S-CONT | 86.14(.06) | 84.03(.08) | 85.98(.08)
S-FLAT | 74.22(.07) | 75.44(.05) | 75.87(.06)
S-FLUX | 79.70(.08) | 77.14(.06) | 82.08(.06)
S-ROLL | 70.70(.07) | 67.22(.04) | 71.22(.06)
Cepstral | All | 86.25(.06) | 83.98(.06) | 87.15(.06)
MFCC | 86.56(.04) | 83.25(.05) | 87.68(.04)
MFCC-$\Delta{}$ | 84.21(.04) | 79.67(.08) | 85.54(.08)
MFCC-$\Delta{}^{2}$ | 84.25(.09) | 78.29(.07) | 85.24(.09)
Tonal | All | 79.69(.07) | 78.06(.07) | 82.59(.07)
C-CQT | 76.29(.06) | 71.12(.09) | 77.30(.06)
C-ENS | 77.56(.07) | 72.11(.07) | 83.50(.03)
C-STFT | 77.57(.05) | 72.65(.03) | 77.78(.07)
TN | 74.28(.04) | 70.85(.04) | 77.57(.05)

(b) SVM, Coswara-deep data.

B | C | BC
---|---|---
76.79(.04) | 70.85(.06) | 77.15(.05)
61.80(.04) | 58.58(.06) | 63.94(.07)
55.89(.10) | 61.14(.07) | 61.81(.07)
64.68(.03) | 59.45(.13) | 64.60(.04)
76.34(.05) | 66.74(.05) | 74.46(.06)
61.63(.07) | 63.51(.05) | 65.46(.04)
68.53(.06) | 59.91(.06) | 71.95(.05)
74.89(.05) | 63.42(.08) | 73.57(.09)
61.77(.08) | 59.86(.06) | 61.14(.03)
63.79(.06) | 62.76(.07) | 67.20(.04)
65.35(.05) | 63.16(.05) | 67.58(.08)
74.57(.03) | 70.15(.09) | 75.62(.08)
74.24(.03) | 70.74(.01) | 75.38(.05)
64.85(.07) | 68.90(.05) | 68.99(.04)
66.65(.08) | 67.72(.06) | 70.72(.07)
71.74(.05) | 64.06(.06) | 72.98(.03)
67.87(.04) | 62.78(.07) | 61.50(.05)
70.03(.07) | 65.14(.03) | 65.96(.05)
67.01(.05) | 61.80(.08) | 68.19(.10)
60.90(.04) | 62.84(.02) | 61.33(.03)

The majority of the 15 features significantly outperformed random guesses for
COVID-19 classification across all datasets and sample types. The lowest
accuracies were achieved by Coswara-shallow, matching previous findings.
Similarities between Cambridge and Coswara-deep were underlined by sample
types: BC achieved the highest mean ROC-AUC scores on average, whereas
Coswara-shallow was split evenly between B and C. However, given all
considered features, the Coswara-shallow dataset still showed its highest
accuracy on BC samples since cepstral and tonal features were the most
influential overall. MFCC (cepstral), S-CONT (spectral), and C-ENS/C-STFT
(tonal) were the highest-scoring features in their categories, whereas the
time domain was more variable.

Lastly, we note a surprising trend for MFCC. A prevalent rule of thumb
suggests 12–13 coefficients for audio classification [3, 7, 19]. However,
Figure 3 shows that higher-order features provided discriminative information
for COVID-19 on par with (Coswara-deep) or significantly outperforming
(Cambridge) lower orders. This phenomenon was most noticeable in BC/B vectors
and MFCC features. Since higher-order features contain information about
details such as pitch and tone quality [11], we extrapolate that timber is
highly relevant to COVID-19.

Figure 3: _Normalised ROC-AUC of MFCC and derivatives for BreathCough (BC),
Breath (B), and Cough (C) vectors._ Contrary to a common rule of thumb [3, 7,
19], 13+ features provided significant discriminatory data, and showed that
timbral information is especially relevant to COVID-19 classification.

Discussion. Our extensive analysis, comparison, and ranking of 15 features has
found recurring patterns of predictive efficiency for COVID-19 audio
classification across independent datasets. There was a distinct category
ranking consistent across models, sample types, and datasets (increasing):
time domain, tonal, spectral, and cepstral. Contrary to the intuitive
expectation, some ‘complex’ categories provided less discriminative
information than ‘simpler’ ones (e.g. tonal/spectral features). However, this
is justified when considering that tonal features describe pitch and so are
more suited to tasks with melodic content.

The ranking underlines the significance of frequency-based features by
elevating the spectral and cepstral categories describing timbral aspects and
tone quality/colour. We have also shown that the common guideline to use only
the first 13 MFCC features [3, 7, 19] was not applicable to COVID-19. Indeed,
the higher-order (timbre) features’ predictive efficiency provided
significantly more discriminatory information, especially for the BC and B
feature vectors.

Taking a step back from the individual features, we note that the most
prevailing pattern across all previous descriptions was that the concatenated
BC feature vector outperformed the individual B and C vectors in most cases.

Given our insights, we compare our results to the published baselines,
summarised in Table 6. The evaluated models were of similar type and
complexity; The major difference was our introduction of new training
features. We observe that our improved feature vectors significantly
outperformed both the Cambridge and Coswara baseline accuracies by 10–17%,
validating our feature selection.

Table 6: _Comparison to dataset papers’ 5-fold CV baseline results._ The most comparable configurations are shown (feature processing and classification model). Origin | Dataset | Sample | Model | ROC-AUC | Precision | Recall
---|---|---|---|---|---|---
This paper | Cambridge | BC | SVM |  87.68(.06) | 87.61(.07) | 81.39(.07)
[3] | Cambridge | BC | LR | 71.00(.08) | 69.00(.09) | 66.00(.14)
This paper | Cos-deep | BC | SVM |  77.15(.05) | 76.7(.05) | 53.09(.03)
[12] | Cos-Unknown | C | RF | 67.45(—) | — | —

##  4 Related work

During in- and exhalation, air travelling through the respiratory tract
undergoes turbulence and produces sounds. Consequently, any physical changes
to the airways or lungs (e.g. caused by diseases such as COVID-19) also alter
the produced respiratory sounds [17]. Even though listening and evaluating
lung sounds manually is inherently subjective, medical professionals have long
used this technique to non-invasively diagnose a wide variety of respiratory
diseases [2].

The popularisation of digital signal processing techniques and Machine
Learning (ML) have made the automatic classification of respiratory sounds
possible as a less subjective, low-cost, and patient-friendly (pre-)screening
method. A literature review of existing implementations shows that ML can
reliably pick up on subtle cues in audio signals for a variety of diseases.

Smartwatches and wearable devices have made audio monitoring for healthcare
purposes feasible. Nguyen et al. apply a dynamically activated respiratory
event detection mechanism to detect cough and sneeze events non-intrusively
[14]. [1] presents classifiers distinguishing between asthma and pneumonia in
pediatric patients. Lastly, an image classification solution with comparable
results is developed in [2], using spectrograms as the input.

One of the first COVID-19 audio datasets containing breath and cough samples
was presented in [3]. Using standard ML and audio processing techniques, the
authors report 71% ROC accuracy for COVID classification. [12] and [19]
consider further recording types such as vowel intonation and sequence
counting, achieving 67% and 66% accuracy with ML models respectively.

##  5 Conclusion and future work

Our extensive comparative analysis of 15 audio features has provided
significant insight into Machine Learning (ML) feature selection for COVID-19
respiratory audio classification and addressed the research questions laid out
in Section 3.1. Primarily, we identified the most informative feature
characteristics and verified their ranking across two independent datasets.
Since the two feature rankings showed considerable overlap, we conclude that
the features’ relative salience was likely inherent to the respiratory signals
rather than the evaluated datasets.

Throughout our analysis, a number of informative audio features were newly
incorporated in the context of COVID-19 classification. In combination with
our feature ranking, we achieved 88% and 77% accuracy on the Cambridge and
Coswara datasets. Since the complexity of the signal processing and ML models
is comparable to the baselines, the increase of up to 17% and 10% respectively
was a consequence of our feature selection. Our established feature ranking
could benefit future sound-based COVID-19 classification applications.

This paper provides a starting point for the holistic evaluation of
respiratory audio features for COVID-19 classification. Considerations that
could be addressed in future work are a comprehensive strategy to regularise
different sample lengths, and to identify the most informative audio features
for complex architectures such as Deep Learning neural networks.

Although sound-based COVID-19 detection was the primary purpose of this
research, many other respiratory diseases and disorders could benefit from the
development and improvement of automatic audio detection systems for
diagnosis, treatment, and management. Therefore, the approach described in
this paper could be generalised for the detection of other respiratory
diseases.

####  5.0.1 Acknowledgements

We would like to thank Chris Watkins for the stimulating discussions, and
University of Cambridge for access to the COVID-19 sound dataset. This
research is funded by University of Brighton’s Connected Futures, Radical
Futures’ initiatives, and Santander’s Global Challenges Research grant.

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