# Investigating the X-ray polarization of lamp-post coronae in BHXRBs

Wenda Zhang1, Michal Dovčiak2, Michal Bursa2, Vladimír Karas2, Giorgio Matt3
and Francesco Ursini3
1National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun
Road, Beijing 100101, China
2Astronomical Institute, Czech Academy of Sciences, Boční II 1401, CZ-141 00
Prague, Czech Republic
3Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, via
della Vasca Navale 84, 00146 Roma, Italy E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

High-sensitivity X-ray polarimetric observations of black hole X-ray binaries,
which will soon become available with the launches of space-borne X-ray
observatories with sensitive X-ray polarimeters, will be able to put
independent constraints on the black hole as well as the accretion flow, and
possibly break degeneracies that cannot be resolved by spectral/timing
observations alone. In this work we perform a series of general relativistic
Monte–Carlo radiative transfer simulations to study the expected polarization
properties of X-ray radiation emerging from lamp-post coronae in black hole
X-ray binaries. We find that the polarization degree of the coronal emission
of black hole X-ray binaries is sensitive to the spin of the black hole, the
height of the corona, and the dynamics of the corona.

###### keywords:

polarization – stars: black holes – X-rays: binaries

††pagerange: Investigating the X-ray polarization of lamp-post coronae in
BHXRBs–Investigating the X-ray polarization of lamp-post coronae in BHXRBs

##  1 Introduction

Measuring the spin of black holes is an essential topic in contemporary
astrophysics. For accreting stellar-mass black holes, the black hole spin can
be measured by several methods. One is the continuum-fitting method (Zhang et
al., 1997), in which the spin of stellar-mass black holes are constrained by
fitting their continuum X-ray spectra. This approach turns out to be
particularly useful to study stellar-mass black holes, because their accretion
discs produce sufficiently clear signal of the thermal (multicolor) continuum
with signatures of general relativity in soft X-rays (Zhang et al., 1997; Li
et al., 2005). Another popular method is the iron line fitting method, where
the spin is measured by fitting the relativistically broadened iron K $\alpha$
line (e.g. Reynolds & Nowak, 2003; Miller, 2007). The latter approach has been
applied with stellar-mass as well as supermassive black holes. Both methods
have been extensively used in numerous studies (e.g. Gierliński et al., 2001;
Davis et al., 2006; Shafee et al., 2006; McClintock et al., 2006; Liu et al.,
2008; Gou et al., 2009; Gou et al., 2010; Gou et al., 2011; Blum et al., 2009;
Miller et al., 2009; Reis et al., 2009; Miller et al., 2013; Parker et al.,
2015; El-Batal et al., 2016; Miller et al., 2018; Xu et al., 2018a; Xu et al.,
2018b).

For the black hole X-ray binary (BHXRB) GRO J1655$-$40, inconsistent
measurements were obtained with these two methods (Shafee et al., 2006; Reis
et al., 2009). Interestingly, for this particular source where low- and high-
frequency quasi-periodic oscillations (QPOs) are simultaneously detected, one
can also measure its black hole spin by associating the frequencies of the two
QPOs with the Lense-Thirring precission and the Keplerian frequencies at the
innermost stable circular orbit, respectively (Motta et al., 2014). However,
the black hole spin measured from QPOs are consistent neither with continuum
fitting nor line fitting results.

X-ray polarimetric observations of accreting stellar-mass black holes will be
able to put independent constraints on the black hole spin. The strong
gravitational field of the black hole rotates the polarization vector of the
emerging X-rays, leading to stronger de-polarization effects at larger value
of spin (Connors et al., 1980). Dovčiak et al. (2008) and Li et al. (2009)
modelled the polarization signatures of accreting stellar-mass black holes in
the thermal-dominated states, and found the polarization degree to be
sensitive to the black hole spin. Schnittman & Krolik (2009) investigated how
the self-irradiation changes the polarization signatures. Abarr & Krawczynski
(2020) studied the polarization properties of the X-ray emission from warped
accretion discs. Taverna et al. (2020); Taverna et al. (2021) studied these
effects by treating the absorption of the disc atmosphere more realistically.
Dedicated X-ray polarimetric observations will soon become possible with the
launch of the Imaging X-ray Polarimetry Explorer (IXPE; Weisskopf et al.,
2016) and the enhanced X-ray Timing and Polarimetry mission (eXTP; Zhang et
al., 2019a).

In addition to the spin of the black holes, polarimetric observations of
BHXRBs in the low-hard state have also the potential to constrain the physical
properties of the hot coronae. Schnittman & Krolik (2010) studied the
polarization properties of wedge and spherical coronae (inside truncated
discs), and found the polarization degree to be dependent on the geometry of
the corona and parameters of the black holes.

It’s also possible that the x-ray emission originates from aborted jets or the
base of relativistic jets (e.g. Ghisellini et al., 2004; Markoff et al.,
2005), in which cases the coronae are located above the discs. In this paper
we investigate the polarization properties of coronae by modelling the
observed signal from different geometries using Monte–Carlo methods. The case
of the coronal emission in Active Galactic Nuclei is explored in an
accompanying paper (Ursini et al., 2022). The results of the X-ray
polarization of relativistic jets in BHXRBs will be presented in a follow-up
paper.

##  2 Method

###  2.1 The Numerical Code

The Monte–Carlo simulations are carried out with Monk (Zhang et al., 2019b), a
Monte–Carlo radiative transfer code that includes all general relativistic
effects. Monk samples seed photons and ray-traces the emitted photons along
null geodesics in curved spacetime of the Kerr black hole. If the photon
travels through a plasma medium, Monk also takes into account various
interactions between the medium and the photons, including the Compton
scattering, the free-free absorption, and the synchrotron self-absorption. In
this paper we consider Compton scattering only. Monk utilises the
“superphoton” method where each photon is assigned a statistical weight $w$.
The weight $w$ has the physical meaning of the number of photons generated per
unit time as measured in a distant observer’s frame (see Zhang et al., 2019b).

In particular, Monk supports polarized radiative transfer in curved
spacetimes, which enables us to study the polarization properties as well. In
this paper we restrict ourselves to the case of linear polarization, as the
Compton scattering induces the linear polarization only (Berestetskii et al.,
1971; Connors et al., 1980). When only linear polarization is considered, the
polarization degree is relativistically invariable, while the polarization
angle is connected with a complex constant of motion: the Walker-Penrose
constant $\kappa_{\rm wp}$ (Walker & Penrose, 1970; Chandrasekhar, 1983).
While propagating the photon we conserve its Walker-Penrose constant. If the
photon gets scattered off an electron, we sample the energy of the photon, re-
evaluate the polarization degree and angle, and update the value of the
Walker-Penrose constant. We assume Klein-Nishina Compton scattering cross
section. A detailed description of how Monk handles the scattering process can
be found in Zhang et al. (2019b).

In order to simulate the signal expected at a detector we collect photons
arriving at infinity. For each photon we have the following information: its
statistical weight $w$, energy $E_{\infty}$, polar angle $\theta_{\rm obs}$
(measured from the accretion disc symmetry axis, see Sec. 2.2), polarization
degree $\delta$, and its polarization angle $\psi_{\infty}$ derived from
$\kappa_{\rm wp}$. The three Stokes parameters $I(E)$, $Q(E)$, and $U(E)$ (in
units of energy per unit time per energy interval) can be constructed with the
following equations:

$\displaystyle I_{E}$ $\displaystyle=$
$\displaystyle\frac{4\pi\sum_{k}w_{k}}{\Delta E\Delta\Omega},$ (1)
$\displaystyle Q_{E}$ $\displaystyle=$
$\displaystyle\frac{4\pi\sum_{k}w_{k}\delta_{k}\ {\rm cos}2\psi_{k}}{\Delta
E\Delta\Omega},$ (2) $\displaystyle U_{E}$ $\displaystyle=$
$\displaystyle\frac{4\pi\sum_{k}w_{k}\delta_{k}\ {\rm sin}2\psi_{k}}{\Delta
E\Delta\Omega},$ (3)

where the sum is performed over all photons with $\theta_{\infty}\in(i-\Delta
i/2,i+\Delta i/2]$ and $E_{\infty}\in(E-\Delta E/2,E+\Delta E/2]$, $\Delta E$
is the width of the energy bin, $\Delta\Omega=2\pi[{\rm cos}(i-\Delta
i/2)-{\rm cos}(i+\Delta i/2)]$ is the solid angle subtended by the inclination
bin, and $E_{\infty}$, $\theta_{\infty}$ are the energy and polar angle of the
photons at infinity, respectively. In this work we take $\Delta i=10^{\circ}$.
As Compton scattering only induces linear polarization, we always maintain the
Stokes parameter $V_{E}=0$. The corresponding polarization angle $\delta$ and
the polarization degree $\psi$:

$\displaystyle\delta$ $\displaystyle=$
$\displaystyle\frac{\sqrt{Q_{E}^{2}+U_{E}^{2}}}{L_{E}},$ (4)
$\displaystyle\psi$ $\displaystyle=$ $\displaystyle\frac{1}{2}{\rm
atan}\frac{U_{E}}{Q_{E}}.$ (5)

We define the polarization angle in such a way that the polarization angle is
0 or $\pi/2$ if the polarization vector is parallel with or perpendicular to
the plane defined by the line of sight and the accretion disc symmetry axis,
respectively.

###  2.2 Model Assumptions

We assume a razor-thin Keplerian accretion disc located on the equatorial
plane around a Schwarzschild or Kerr black hole. The disc extends down to the
innermost stable circular orbit (ISCO). In the rest frame of the disc fluid,
the emission of the disc follows a blackbody spectrum with an effective
temperature that follows the Novikov-Thorne temperature profile (Novikov &
Thorne, 1973; Page & Thorne, 1974). We also adopt a color correction factor of
1.7. Throughout the paper we assume a black hole mass of $10~{}\rm M_{\odot}$.

The photons emerging from the disc midplane experience scattering before
escaping the photosphere if the disc atmosphere is partially or fully ionized.
Due to the scattering process, the radiation becomes anisotropic and
polarized. We utilise analytical formulae of Chandrasekhar (1960), chapter X,
to evaluate the angular distribution and polarization degree of the disc
photons.

We assume isothermal, homogeneous coronae. We assume thermal electrons whose
velocity distribution follows the Maxwell-Jüttner distribution. We consider
three different geometries for the coronae:

  * •

Spherical coronae: illustrated in Fig. 1 (a). We assume that the spherical
coronae are located on the black hole rotation axis. Motivated by Beloborodov
(1999), we assume the coronae to be moving towards the $+z$ direction with
velocity of $\beta=0.3$ as measured by a stationary observer. The coronae can
be parameterized by the height above the disc $h$, the radius $R_{c}$, the
electron temperature in the rest frame of the corona $kT_{e}$, and the
Thompson optical depth $\tau_{\rm T}\equiv n_{e}\sigma_{\rm T}R_{c}$, where
$n_{e}$ is the electron density and $\sigma_{\rm T}$ is the Thompson
scattering cross section.

  * •

Off-axis spherical coronae: illustrated in Fig. 1 (b). Motivated by Wilkins &
Fabian (2012), we assume that the spherical coronae are above the disc, with
its center off the black hole rotation axis. The coronae can be parameterized
by the height above the disc $h$, the distance between the center of the
corona to the black hole rotation axis $s$, the radius $R_{c}$, the electron
temperature in the rest frame of the corona $kT_{e}$, and the Thompson optical
depth $\tau_{\rm T}\equiv n_{e}\sigma_{\rm T}R_{c}$. We assume the spherical
coronae to be rotating about the black hole rotation axis with an angular
velocity of $\omega=1/(s^{3/2}+a)$, i.e. co-rotating with the underlying disc,
where $a$ is the black hole spin.

  * •

Conical coronae: illustrated in Fig. 1 (c). The corona can be parameterized
by: the height of the corona base $h$, the thickness of the corona $\Delta h$,
the opening angle $\alpha$, the Thompson optical depth of the corona
$\tau_{\rm T}\equiv n_{e}\sigma_{\rm T}\Delta h$, and the electron temperature
in the rest frame of the corona $kT_{e}$. We let the Lorentzian factor of the
bulk motion of the corona $\gamma=1/\Theta$ where $\Theta$ is the opening
angle of the corona (e.g. Blandford & Königl, 1979; Daly & Marscher, 1988;
Komissarov et al., 2009). We assume that the corona moves upwards, towards the
$+z$ direction.

(a) Spherical coronae

(b) Off-axis coronae

(c) Conical coronae

Figure 1: Schematic plots of the various corona geometries. In each subplot,
the black circle represents the black hole horizon, the horizontal line is a
cross-section of a standard thin accretion disc, the vertical line represents
the black hole rotation axis, and the yellow region represents the corona.

##  3 Results

###  3.1 Spherical coronae

In Fig. 2 we present the results for a disc-corona system that contains a
spherical corona, for observers located at various inclinations. The
parameters are: the black hole spin $a=0.998$, the mass accretion rate
$\dot{M}=4.32\times 10^{15}~{}\rm g~{}s^{-1}$, $h=5~{}\rm\rm GM/c^{2}$,
$R_{c}=3.5~{}\rm\rm GM/c^{2}$, $\tau_{\rm T}=1$, and $kT_{e}=100~{}\rm keV$.
The energy spectrum (top panels) is dominated by thermal (red) and non-thermal
(blue) radiation in the low- and high-energy regimes, respectively. The
thermal radiation contains both seed photons that directly reach the observer
and that pass through the corona without getting scattered. The polarization
degree (PD) of the thermal radiation decreases with energy, as high-energy
thermal photons originate from the disc close to the black hole where, the de-
polarization effect of the strong gravitational field of the black hole is
most pronounced. The behavior of the thermal component is consistent with what
was found by Dovčiak et al. (2008); Li et al. (2009) where the polarization
properties of the thermal radiation were thoroughly investigated.

The non-thermal radiation (blue) has a power-law shape with a photon index of
$\sim 1.75$. The PD of the non-thermal Comptonized radiation increases with
energy, reaching a maximum value at $\sim 1~{}\rm keV$, and then decreases
with energy. The Comptonized emission is more polarized than the thermal
emission, and its PD increases with the observer’s inclination, from
unpolarized at $\theta_{\rm obs}=10^{\circ}$ to $\sim 5\%$ at $\theta_{\rm
obs}=75^{\circ}$. At all inclinations the PA of the Comptonized radiation is
close to $0$.

Figure 2: From top to bottom: the energy spectra, polarization degree, and
polarization angles of the radiation emerging from a disc-corona system around
a stellar-mass black hole, as seen by distant observers at various
inclinations. The contributions of the disc and the coronae are plotted in red
and blue colors, respectively, while the sum of the two are plotted in black.

To understand the behavior of the Comptonized emission, we extract the energy
spectra and PD of different scattering orders. The result for $\theta_{\rm
obs}=75^{\circ}$ are presented in Fig. 3. We find that the photons scattered
once ($N_{\rm sca}=1$) are most polarized, with a peak PD of $\sim 8\%$ at
$\sim 2~{}\rm keV$. The PD decreases with the scattering order, to $\sim 3\%$
for $N_{\rm sca}=2$ and $\sim 1\%$ for $N_{\rm sca}\geq 3$, while the PAs are
close to $0$ for all components. This explains why the PD of the Comptonized
emission decreases beyond $\sim 1~{}\rm keV$ where the emission of higher
scattering orders dominates. For the Comptonization process, the PD depends
sensitively on the scattering angle, and the photons are most polarized if the
scattering angle is $\pi/2$, i.e. the direction of the in-coming photon is
perpendicular to the direction of the scattered photon (e.g. Berestetskii et
al., 1971; Connors et al., 1980). Compared with the first-scattering photons
where the in-coming photons originate from the disc, the directions of the in-
coming photons of high scattering orders are more isotropic, thus leading to
lower polarization degree.

Figure 3: The PD (upper panel) and PA (lower panel) of the coronal emission,
for various scattering orders in different colors. The observer is located at
an inclination of 75∘.

####  3.1.1 Dependence on corona height and black hole spin

We also study how the polarization properties change with the height of the
corona. In Fig. 4 we compare the polarization properties of coronae with
heights of $h=5$ (blue), $8$ (orange), $10$ (green), $15$ (purple), and
$20~{}\rm GM/c^{2}$ (brown) while keeping other parameters fixed as follows:
$a=0.998$, $\dot{M}=4.32\times 10^{15}~{}\rm g~{}s^{-1}$, $R_{\rm c}=3.5~{}\rm
GM/c^{2}$, $kT_{e}=100~{}\rm keV$, and $\tau_{\rm T}=1$. The observers are
located at an inclination of $75^{\circ}$. The energy spectra (the upper
panel) have similar shape. In contrast, the PD is quite sensitive to the
height of the corona, with the maximum PD first decreasing from $\sim 5\%$ at
$h=5~{}\rm GM/c^{2}$ to $\sim 3\%$ at $h=10~{}\rm GM/c^{2}$, then increasing
to $\sim 11\%$ at $h=20~{}\rm GM/c^{2}$. The polarization angle also changes
with the coronal height: when $h=5~{}\rm GM/c^{2}$, the PA is around 0. At
intermediate heights ($h=10~{}\rm GM/c^{2}$), the PA increases from 0 to
$\pi/2$ as the photon energy increase; while when $h=15$ and $20~{}\rm
GM/c^{2}$, the PA is close to $\pi/2$.

Figure 4: The energy spectra (top panel), PD (middle panel), and PA (bottom
panel) of the coronal emission originating from spherical coronae. Results of
different heights are plotted in different colors, as indicated in the plot.
The observer is located at an inclination of $75^{\circ}$.

Now we investigate the dependence of the polarization properties on the black
hole spin. We perform simulations for Schwarzschild ($a=0$) black holes,
assuming the same coronal heights with Kerr black holes (namely 5, 8, 10, 15,
and 20$~{}\rm GM/c^{2}$). We set $\dot{M}=2.45\times 10^{16}~{}\rm g~{}s^{-1}$
Schwarzschild black holes, such that the power of the thermal emission is the
same with Kerr black holes. For Schwarzschild black holes we set $R_{\rm
c}=2.5~{}\rm GM/c^{2}$, such that the corona at $h=5~{}\rm GM/c^{2}$ does not
enter the black hole event horizon. Other properties are the same:
$kT_{e}=100~{}\rm keV$ and $\tau_{\rm T}=1$.

In Fig. 5 we present the energy spectra, PD, and PA of the Componized emission
for Schwarzschild black holes, for observers located an inclination of
$75^{\circ}$. While the energy spectra (the upper panel) have similar shape,
the polarization properties are quite distinct. The PD is quite large at
smaller heights ($\leq 10~{}\rm GM/c^{2}$), and decreases towards larger
heights. The switch of the PA from 0 to $\pi/2$ is also seen, but at
$h=20~{}\rm GM/c^{2}$, a larger height than Kerr black holes.

The reason for the dependence of the polarization properties on the coronal
height and black hole spin is that, both parameters changes the incident angle
of the seed photons that enters the corona. While for the height this is
straightfoward, for black hole spin the change of the incident angle is due to
the change in the ISCO. As we discussed earlier, the PD of the Comptonized
radiation, in particular the first scattering component, is sensitive to the
scattering angle.

Figure 5: The same with Fig. 4, but for Schwarzschild black holes.

####  3.1.2 Dependence on mass accretion rate

In this section we investigate the effect of changing $\dot{M}$, the black
hole mass accretion rate. We pick three values of $\dot{M}$: $4.32\times
10^{13}$, $4.32\times 10^{14}$ and $4.32\times 10^{15}~{}\rm g~{}s^{-1}$, such
that the bolometric luminosity of the thin disc is $10^{-5}$, $10^{-4}$, and
$10^{-3}$ Eddington luminosity, respectively. Other parameters are fixed:
$a=0.998$, $h=10~{}\rm GM/c^{2}$, $R_{\rm c}=3.5~{}\rm GM/c^{2}$,
$kT_{e}=100~{}\rm keV$, and $\tau_{\rm T}=1$. The observer is located at an
inclination of $75^{\circ}$. In Fig. 6 we present the energy spectra (the
upper panel) and PD (the lower panel) of the coronal emission for different
$\dot{M}$. The peak PD remains more or less constant at $\sim 2\%$ as
$\dot{M}$ changes, but the photon energy corresponding to the peak PD
increases with $\dot{M}$, from $\sim 0.4~{}\rm keV$ to $\sim 1.1~{}\rm keV$.
As shown in Fig. 3, the photons that scattered once are most polarized. As
$\dot{M}$ increases, the temperature of the seed photons also increases,
leading to an increase of the peak energy of the photons that scatter once,
and subsequently an increase of the energy corresponding to the peak PD.

Figure 6: The energy spectra (upper panel) and PD (lower panel) of the coronal
emission originating from spherical coronae. Results of different mass
accretion rates are plotted in different line styles. The observer is located
at an inclination of $75^{\circ}$.

###  3.2 Off-axis coronae

In Fig. 7 we present the energy spectra, PD, and PA of the Comptonized
emission for an off-axis corona with an offset of 10 $\rm GM/c^{2}$ from the
symmetry axis, and compare the results with an on-axis coronae at the same
heights. Other parameters are fixed: $a=0.998$, $\dot{M}=4.32\times
10^{15}~{}\rm g~{}s^{-1}$, $h=10~{}\rm GM/c^{2}$, $R_{\rm c}=8~{}\rm
GM/c^{2}$, $kT_{e}=100~{}\rm keV$, and $\tau_{\rm T}=1$. The observer is
located at an inclination of $75^{\circ}$. For the off-axis corona the
emission is averaged over all orbital phases of the rotation, since the
orbital period is short compared with any reasonable exposure time for X-ray
polemetric observations. In both cases the energy spectra have photon indices
of $\sim 1.8$ and luminosities $\sim 2\times 10^{34}~{}\rm erg~{}s^{-1}$. The
polarization properties are also similar, both with maximum PD of $\sim 10\%$
and PA of $\sim\pi/2$. This shows that the polarimetric properties do not
change much between on- and off-axis coronae.

Figure 7: The energy spectra (upper panel), PD (middle panel), and PA (bottom
panel) of the coronal emission originating from an on-axis (solid) corona and
an off-axis corona (dotted). The observer is located at an inclination of
$75^{\circ}$.

###  3.3 Relativistic coronae

To assess the effect of the relativistic motion of the coronae on the
polarization properties, we simulate the emission from conical coronae moving
along the $+z$ direction with relativistic velocities (Fig. 1 (c)). In Fig. 8
we present the energy spectrum, PD, and PA of the radiation from a disc-corona
system containing a conical corona with $kT_{e}=100~{}\rm keV$, $\tau_{\rm
T}=2$, and $\gamma=4$ (corresponding to an opening angle of $\sim
14^{\circ}$), for observers at various inclinations. The emission is highly
inclination-dependent: the $2-10~{}\rm keV$ luminosity of the coronae emission
decreases from $4.32\times 10^{35}~{}\rm erg~{}s^{-1}$ at $10^{\circ}$ to
$\sim 9.58\times 10^{32}~{}\rm erg~{}s^{-1}$ at $75^{\circ}$, due to stronger
relativistic beaming effects at lower inclinations. The spectral shape also
varies with the observer’s inclination. We fit the $2-10~{}\rm keV$ spectra
with a power-law model, and find the photon index to be 0.63, 1.32, 1.71 and
1.99 for $\theta_{\rm obs}=10^{\circ}$, $30^{\circ}$, $60^{\circ}$, and
$75^{\circ}$, respectively.

The most striking feature of relativistic coronae is the high PD: when
$\theta_{\rm obs}\geq 30^{\circ}$, the PD can reach as high as $\sim 20-30\%$
above $\sim 3~{}\rm keV$, much more polarized than stationary spherical/oblate
coronae. The PD are also varying with $\theta_{\rm obs}$: the peak PD is only
$8\%$ when $\theta_{\rm obs}=10^{\circ}$. The PA of the coronal emission are
always close to $90^{\circ}$.

Figure 8: The energy spectra (top panel), PD (middle panel), and PA (bottom
panel) of the coronal emission originating from a relativistic conical corona
with $\gamma=4$. The results for different inclinations are plotted in
different colors, as indicated in the plot.

In Fig. 9 we compare the mean PD in the $2-8~{}\rm keV$ band (the energy band
of IXPE) of the coronal emission emitted by conical coronae with various
Lorentz factors. For comparison we also present the results for a stationary
conical corona ($\gamma=1$). The PD increases rapidly with $\gamma$: the
maximum PD changes from $\sim 7\%$ to $\sim 30\%$ as $\gamma$ varies from $1$
to $4$. While at low Lorentz factor ($\gamma=1,2$), the PD decreases
monotonically from an edge-on observer to a face-on observer, at high Lorentz
factor ($\gamma=4$), the peak PD is reached at an inclination of $35^{\circ}$
and then decreases with the inclination.

Figure 9: 2–8 keV PD as a function of the observer’s inclination, for conical
coronae with various Lorentz factors.

For coronae that move at relativistic velocity, the distribution of the
direction of seed photons measured by fluids co-moving with the corona gets
much narrower as compared with stationary coronae. This can be seen in Fig. 10
where we plot $\mu_{\rm in}\equiv{\rm cos}\theta_{\rm in}$ as a function of
the Lorentz factor $\gamma$ (here $\theta_{\rm in}$ is the angle between the
seed photon and the black hole symmetry axis measured in the rest frame of the
corona). For the corona with $\gamma=4$, the values of $\mu_{\rm in}$ fall in
a narrow range around 0.25, while for the stationary corona the distribution
is much broader. Since for the Compton scattering process the PD depends
sensitively on the scattering angle, we expect more polarized emission for
narrower distribution of $\mu_{\rm in}$. The distribution of $\mu_{\rm in}$
also explains the shift of the inclination corresponding to the peak PD with
increasing $\gamma$, as it is evident that the value of $\mu_{\rm in}$
corresponding to the peak of $\mu_{\rm in}$ distribution changes with
$\gamma$.

Figure 10: The probability distribution of ${\rm cos}\theta_{\rm in}$, where
$\theta_{\rm in}$ is the incident angle of the seed photons as measured in the
rest frame of the corona. Results of coronae with different velocities are
plotted in different line styles, as indicated in the plot.

##  4 Discussion

###  4.1 Spectral states

BHXRBs exhibit different accretion states in which the spectral and timing
properties of their X-ray emission are quite distinct. While several
definitions of the accretion states have been proposed, in this work we follow
the definition of Remillard & McClintock (2006): the source is classified as
high-soft (low-hard) state if the $2-20~{}\rm keV$ band powerlaw fraction
$f_{\rm PL}<25\%$ ($>80\%$), and as intermediate state if otherwise. Note that
the definition of Remillard & McClintock (2006) makes use of timing
information as well (such as the fractional rms), which is not available in
our work. The accretion states corresponding to different cases in our work
are presented in Fig. 11. It seems that the cases in our work cover all three
spectral states, including the high-soft state. Among the cases classified as
in the high-soft state, four of them are spherical coronae at large heights
($h\geq 10~{}\rm GM/c^{2}$; cases G-K) viewed at large inclinations. For
$h\geq 8~{}\rm GM/c^{2}$, to compare with the case of smaller heights, we fix
the coronal radius at a small value of $R_{\rm c}=3.5~{}\rm GM/c^{2}$, leading
to a low powerlaw flux and subsequently a small value of $f_{\rm PL}$. Since
the PD is not expected to change much with $R_{\rm c}$, our conclusions can be
applied to coronae with larger radii that have larger $f_{\rm PL}$ and
corresponds to BHXRBs in the hard and intermediate states. Relativistic
coronae (cases H & I) viewed at high inclinations are also classified as in
the high-soft state, since in this cases the coronal emission is beamed.
However, it is known that relativistic jets are quenched in the high-soft
state (Fender et al., 2004). This indicates that the results of relativistic
coronae viewed at high inclinations hardly correspond to any observation. Most
other cases are classified as in the hard or intermediate states. Therefore
our results are applicable to BHXRBs in the hard and intermediate states.

Figure 11: $2-20~{}\rm keV$ powerlaw fraction of various cases. A-E: spherical
coronae above Schwarzschild black holes, with heights of 5, 8, 10, 15, and 20
$\rm GM/c^{2}$, respectively. F-J: spherical coronae above extreme Kerr black
holes, with heights of 5, 8, 10, 15, and 20 $\rm GM/c^{2}$, respectively. K:
off-axis coronae. L: the conical corona with $\gamma=2$. M: the conical corona
with $\gamma=4$. The results for different observer’s inclinations are plotted
in different colors, as indicated in the plot.

###  4.2 Comparison with AGNs

We find that the PD of spherical coronal in BHXRBs in the X-ray band can be as
high as $\sim 12\%$. This is much larger than the PD of spherical coronae in
AGNs, where a PD of only $1-3\%$ is expected (Ursini et al., 2022). This is
not surpurising though, since for BHXRBs the seed photons have much larger
temperature, and the first scattering photons, which is most polarized, can
already reach the X-ray band. On the other hand, the X-ray emission of AGNs
are contributed by photons that already scattered a few times, for which lower
PD is expected.

##  5 Summary

In this work we investigate the polarization properties of lamp-post coronae
around stellar-mass black holes. We find that the polarization property is
sensitive to the properties of the black hole and the coronae. In particular:

  * •

The polarization degree of spherical, lamp-post coronae increases with the
observer’s inclination and decreases with the photon energy.

  * •

The polarization properties of spherical, lamp-post coronae are sensitive to
the black hole spin and the coronal heights. As the coronal height increases,
the PD decreases and increases below and above a critical height,
respectively. The PA switches from $0$ to $\pi/2$ at this critical height. The
critical height increases with the black hole spin.

  * •

The polarization properties of spherical, lamp-post coronae do not change much
if the coronae are on or off the black hole rotation axis.

  * •

The PD of coronal emission with different mass accretion rates have similar
profiles, while the photon energy corresponding to the maximum PD increases
with the mass accretion rate.

  * •

The energy spectra and PD are very sensitive to the Lorentz factor of the
coronae. The PD of the corona emission is boosted when the corona moves at
relativistic velocity: at a Lorentz factor of 4, the PD of the coronal
emission increase with the photon energy in the X-ray band, and can reach as
high as $\sim 30\%$.

These results indicate that X-ray polarimetric observations of accreting
stellar-mass black holes can offer us independent information of the systems
that can be used to put constraints on the black hole spin, the coronal
geometry, and the dynamics of the coronae. High-sensitivity X-ray polarimetric
observations have become possible with the launch of the IXPE in 2021 and eXTP
is planned to be launched in 2027. Our results are applicable to BHXRBs in the
hard and intermediate states, where the Comptonized emission makes a
significant contribution to the 2–8 keV band.

## Acknowledgements

We thank the anonymous referee for his/her useful comments. WZ acknowledges
the support by the Strategic Pioneer Program on Space Science, Chinese Academy
of Sciences through grant XDA15052100. MD and MB thank for the support from
the GACR project 21-06825X and the institutional support from RVO:67985815. VK
acknowledges the Czech-Chinese Inter-Excellence mobility program (8JCH1080).
GM and FU acknowledge financial support from the Italian Space Agency (grant
2017-12-H.0). This work is also supported by The Ministry of Education, Youth
and Sports, Czech Republic, from the Large Infrastructures for Research,
Experimental Development and Innovations project “e-Infrastructure CZ -
LM2018140”. This research makes use of matplotlib (Hunter, 2007), a Python 2D
plotting library which produces publication quality figures.

## Data availability

The authors agree to make simulation data supporting the results in this paper
available upon reasonable request.

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# Monitoring and Control System Development and Experimental Validation for a
Novel Extrapulmonary Respiratory Support Setup
††thanks: The authors are with the Departments of Mechanical Engineering and
Biomedical Engineering at the University of Maryland, College Park, and the
University of Maryland School of Medicine in Baltimore, MD, USA. Emails:
(mdoostho, karoom<EMAIL_ADDRESS>(MCulligan<EMAIL_ADDRESS>(cthamire<EMAIL_ADDRESS>(stephen.a.roller<EMAIL_ADDRESS>
<EMAIL_ADDRESS>(jhahn12<EMAIL_ADDRESS>(Phone:+1
301-405-6617)††thanks: ∗Corresponding author.

Mahsa Doosthosseini, Kevin R. Aroom, Majid Aroom, Melissa Culligan, Warren
Naselsky,
Chandrasekhar Thamire, Henry W. Haslach, Jr., Stephen A. Roller,
James Richard Hughen, Joseph S. Friedberg, Jin-Oh Hahn, Hosam K. Fathy∗

###### Abstract

This paper presents a novel mechatronic setup intended for providing
respiratory support to patients suffering from pulmonary failure. The setup
relies upon the circulation of an oxygenated perfluorocarbon (PFC) through the
abdominal cavity. Such circulation provides a potential pathway for the
transport of oxygen to the bloodstream. However, the viability of this
technology for $CO_{2}$ clearance has not been established. Moreover, there is
a lack of experimental data enabling the modeling and identification of the
underlying dynamics of this technology. To address these gaps, we develop a
flexible experimental perfusion setup capable of monitoring and controlling
key variables such as perfusate flowrate, temperature, pressure, and
oxygenation. The paper (i) briefly summarizes the design of this setup; (ii)
highlights the degree to which its data acquisition system enables the
collection and cross-correlation of both perfusion-related and physiological
variables; and (iii) discusses the development of flow, pressure, and
temperature control algorithms for the setup. Experiments with large animals
(swine) show that the setup is capable of successfully controlling the
perfusion process, as well as gathering extensive data to support subsequent
modeling and identification studies.

##  I Introduction

This paper addresses the need for the integrated monitoring and control of a
novel setup that can augment respiration without interfacing with the blood
stream or utilizing the lungs. The setup is intended to address the societal
need for providing pulmonary-independent life support to patients with
respiratory failure. Respiratory failure is a life-threatening condition whose
causes include acute respiratory distress syndrome (ARDS), pulmonary embolism,
pneumonia, toxic inhalation, COVID-19 infection, etc. The fact that the U.S.
alone has historically seen more than 100,000 ARDS-related hospitalizations
annually, even during pre-pandemic years, highlights the public health
magnitude of acute pulmonary failure [1].

The main functions of the respiratory system are to bring oxygen into the body
and expel $CO_{2}$ out of the body. If either of these two functions,
oxygenation or $CO_{2}$ removal, falls below critical levels, then the patient
will not survive without additional support. If the condition is severe, then
the patient will require mechanical ventilation. This is a technique where the
airway is intubated with a tube and a balloon that can achieve an airtight
seal, allowing positive pressure assistance of the lungs. Normally,
spontaneous respiration is a negative pressure phenomenon. A potential
complication of mechanical ventilation, therefore, is barotrauma to the lungs,
which can result in ventilator induced lung injury (VILI). VILI can compound
the underlying lung dysfunction and exacerbate the pulmonary failure –
potentially to a fatal degree [2, 3, 4, 5, 6]. In such situations, unless gas
exchange is augmented by extra-pulmonary means, the patient will not survive.

Extra-corporeal membrane oxygenation (ECMO) is currently the only pulmonary-
independent modality available to supplement gas exchange. It involves drawing
blood out of the patient through a vascular cannula, oxygenating it, then
pumping it back into the patient through another cannula [7]. Unfortunately,
ECMO is an expensive resource, with one study indicating a mean total hospital
cost above $200,000 per patient[8]. The availability of ECMO is limited by
cost and personnel requirements: its initiation is typically performed by
specially trained cardiac surgeons, and its maintenance requires constant
monitoring by highly trained personnel. Even when available, ECMO is
accompanied by contraindications or exclusion criteria that may make it a
nonviable option for patients with potentially reversible lung failure. [9].
Therefore, there is a need for additional ways to support respiration that do
not require the lungs or ECMO.

Figure 1: Schematic of the third lung concept

The main idea motivating this paper is to supplement gas exchange by perfusing
(i.e., circulating) an oxygenated perfluorocarbon (PFC) through a patient’s
peritoneal (i.e., abdominal) cavity. Perfluorocarbons (PFCs) are organic
compounds consisting either predominantly or entirely of carbon and fluorine.
They are inert and recognized for their very high oxygen and carbon dioxide
solubilities [10, 11]. Thanks to these properties, PFCs are well-suited for
medical applications [12, 13, 14, 15]. For example, they have been
investigated as blood substitutes [16, 17] and are also used for
ophthalmologic surgeries [18]. One particularly relevant application is the
use of PFCs for liquid ventilation, or “liquid breathing”. This refers to
filling the lungs partially or completely with an oxygenated PFC in an effort
to augment gas exchange[19, 20, 21, 22]. Both laboratory studies and clinical
trials have been performed on liquid ventilation. These studies show that
while liquid ventilation does indeed supplement gas exchange [23, 24, 25, 26],
its benefits do not justify its adoption as an alternative to mechanical
ventilation [27].

The research in this paper is similar to liquid ventilation in its use of PFC
to augment gas exchange, but fundamentally distinct in its use of the
abdominal cavity, as opposed to the lungs, for gas exchange. Figure (1)
summarizes this respiratory support approach. A perfusion circuit is used for
oxygenating PFC, removing $CO_{2}$ from it, and warming it to body
temperature. The oxygenated PFC is then perfused through the abdomen, where
processes such as diffusion allow it to exchange oxygen and $CO_{2}$ with the
bloodstream. Finally, the PFC is drained out of the abdomen, potentially using
negative pressure from a suction/vacuum pump. The end result is an innovative
approach that allows the peritoneal cavity to be used “like a lung,” analogous
to the way it is used “like a kidney” for peritoneal dialysis [28]. One
potential benefit of this “third lung” concept is the fact that it offers a
pulmonary-independent means of gas exchange that can supplement mechanical
ventilation, thereby resting the lungs and helping them heal. Another
potential benefit is the fact that the third lung innovation does not require
a direct blood-device interface, thereby avoiding many of the risks and
contra-indications of ECMO.

Previous medical research by one of this paper’s co-authors (Friedberg) shows
that the third lung concept is indeed effective at providing oxygenation to
large hypoxic animal models (namely, laboratory swine) [29]. While this prior
research is encouraging, it leaves at least four important open questions and
research challenges. First, it is not clear what operating conditions (e.g.,
perfusion flowrates, pressures, temperatures, PFC oxygenation levels, etc.)
are ideal for the third lung concept. Second, the impact of the third lung
intervention on hemodynamic variables such as heart rate has yet to be fully
characterized. Third, the impact of the intervention on $CO_{2}$ clearance has
not yet been examined in the literature. Fourth, there is a need to implement
the third lung concept using a mechatronic setup with extensive data
acquisition and control capabilities supporting both ongoing animal
experiments and potential future human interventions. To address these
challenges, the authors have developed a novel mechatronic setup capable of
(i) performing controlled peritoneal PFC perfusion experiments and (ii)
gathering extensive datasets characterizing these experiments, from both
setup-side and physiological sensors.

The goal of this paper is to present the above mechatronic setup, focusing on
its monitoring and control capabilities. The remainder of the paper is
organized as follows. Section II summarizes the setup’s mechanical design.
Section III describes the setup’s monitoring and data acquisition system.
Section IV summarizes the setup’s key closed-loop control functionalities.
Section V presents preliminary data from laboratory animal experiments
highlighting some of the setup’s successes in controlling perfusion parameters
such as perfusate flowrate, temperature, pressure, and oxygenation level.
Finally, Section VI summarizes the paper’s conclusions.

Figure 2: The third lung ventilator setup diagram

##  II Design of the third lung ventilator

Experiments on the third lung intervention have, to date, focused on large
laboratory animals (swine) because they are close in size, core body
temperature, and ventilation needs to human patients. The perfusion setup
described in this paper is designed to facilitate these experiments, with the
ultimate goal of enabling emergency interventions in human patients. The setup
is designed to meet five key requirements, namely:

  1. 1.

Oxygenating the PFC and removing $CO_{2}$ from it prior to perfusion.

  2. 2.

Providing a PFC perfusion flowrate sufficient for supplementing gas exchange.
For large animal experiments, prior research suggests that flowrates of up to
6 liters per minute may potentially be required.

  3. 3.

Delivering up to 11 liters of PFC to the abdomen at any given time. This is
important, considering the degree to which the abdominal cavity distends
during perfusion. Filling the distended abdomen of a 40-50kg adult pig, for
example, typically requires 6-7 liters of PFC.

  4. 4.

Achieving perfusion temperatures that are consistent with core body
temperature - namely, $37^{\circ}C$ for human patients and $39^{\circ}C$ for
laboratory pigs.

  5. 5.

Ensuring safety by avoiding intra-cavity pressures conducive to compartment
syndrome.

Figure (2) presents the design of the third lung setup, tailored to meet the
above requirements. When filled, the setup can accommodate 26 liters of PFC,
of which 11 liters can be supplied to the animal’s or patient’s body at any
time. The remaining PFC must stay in the setup to ensure that the setup is
properly primed and able to sufficiently oxygenate the PFC. PFC enters and
leaves the abdomen through tubes typically used as central venuous catheters.
Different catheter sizes can be accommodated, a typical size being 36 on the
French scale (i.e., $12$mm). An oxygenated PFC (specifically, a mix of cis-
and trans-Perfluorodecalin) is perfused through the abdomen of the patient or
animal. The PFC then drains into an accumulator using a combination of
gravitational drainage and active suction via a vacuum pump. Two different
versions of this accumulator have been built and can be rapidly interchanged,
namely: a single-canister system and the dual-canister system in Fig. (3). The
former system uses one canister to receive fluid drained from the test animal
and supply it to the rest of the setup. In contrast, the dual-canister system
switches periodically between a canister that recovers fluid from the animal
versus a canister from which fluid is pumped into the rest of the setup.

Figure 3: The two-canister accumulator system

Once the fluid is recovered by the accumulator system, it is filtered then
exposed to an ultraviolet flood light. The fluid then passes through a chamber
where $CO_{2}$ is purged. The specific setup sketched in Fig. (2) uses PFC
heating plus exposure to an oxygen stream as means of $CO_{2}$ removal, the
idea being to rapidly achieve equilibrium between dissolved and incoming gas
concentrations. Alternative $CO_{2}$ removal mechanisms include the use of
vacuum to bubble $CO_{2}$ out of the PFC as well as the use of chemical
removal means (e.g., soda lime canisters). If the temperatures used for
$CO_{2}$ removal exceed the ideal perfusion temperature, the setup provides
the option to pass the warm PFC through a heat exchanger connected to cold
water flow from a cardioplegic heater/chiller. The PFC is then oxygenated
using a gas bubble chamber connected to an oxygen tank through an actively-
controlled valve, with the possibility that future designs may employ membrane
gas exchangers instead. Next, the temperature of the PFC is regulated to meet
the desired perfusion target using a mix of electric heating and heat exchange
with hot water from the cardioplegic heater/chiller unit. Finally, the
oxygenated PFC is pumped into the abdomen.

As shown in Fig. (2), the setup needs to transfer PFC from the suction
canisters to the $CO_{2}$ removal chamber, then to the oxygenation chamber,
then finally to the abdomen. Two peristaltic pumps are used for achieving
these three functionalities. A dual-head “retrieval pump” transfers fluid from
the suction canister(s) to the $CO_{2}$ removal chamber, then to the
oxygenation chamber. Next, a “perfusion pump” supplies PFC to the animal.
Balancing the PFC fluid levels in the various chambers can be achieved through
bypass valves, as shown in Fig. (2), with the recognition that modifying the
setup to incorporate three independent pumps may potentially provide greater
control authority. The setup incorporates a mix of spring-loaded passive and
actively-controlled mechanical bypass valves on the final perfusion line.
These valves provide the ability to bypass the abdomen if intra-cavity
pressure increases beyond critical limits dictated by setup design (in case of
the passive valves) or operator input, if the operator dictates a software-
based pressure limit (in case of the active valves). This is important for
avoiding cavity pressures conducive to compartment syndrome.

Temperature control is potentially critical for the success of the third lung
intervention, and requires significant fluid heating capabilities. Heating is
needed for ensuring compatibility between perfusion temperature and core body
temperature. Heating beyond core body temperature is also potentially
important for $CO_{2}$ removal. For illustrative purposes, consider the
problem of heating the PFC from a room temperature of $22^{\circ}C$, to a
desired $CO_{2}$ removal temperature of $42^{\circ}C$, assuming a PFC flowrate
of $5$ liters per minute. Knowing that the density, $\rho$, of
Perfluorodecalin is $1.93\leavevmode\nobreak\ [kg/L]$ and its specific heat
capacity, $C_{p}$, is $1000\leavevmode\nobreak\ [J\leavevmode\nobreak\
kg^{-1}\leavevmode\nobreak\ K^{-1}]$, Eq. (1) solves for the heat, $Q_{th}$,
required for this functionality:

$\begin{split}Q_{th}&=\dot{m}c_{p}\Delta T\\\\[5.0pt] &=(5\leavevmode\nobreak\
[\frac{L}{min}])*(1.93\leavevmode\nobreak\
[\frac{kg}{L}])*(1000\leavevmode\nobreak\
[\frac{J}{KgK}])*(20\leavevmode\nobreak\ [K])\\\\[5.0pt]
&=193000\leavevmode\nobreak\
[\frac{J}{min}]=\frac{193000}{60\leavevmode\nobreak\ [sec]}\cong
3216\leavevmode\nobreak\ [W],\end{split}$ (1)

where $\Delta T$ is the desired rise in PFC temperature and $\dot{m}$ is the
mass flowrate of PFC.

The setup is equipped with two $250[W]$ electric heaters in its $CO_{2}$
removal chamber plus a $100[W]$ electric heater attached to the final
perfusion line. Moreover, the setup is connected through heat exchangers to
the hot and (optionally) cold water outputs of a cardioplegic chiller/heater
unit. The chiller/heater unit can provide up to $3000[W]$ of heat to its
output hot water, which can be raised to temperatures as high as
$41^{\circ}C$. Given the proximity of this hot water temperature to the final
perfusion temperature, three of the setup’s four heat exchangers are used for
heating the PFC, compared to a single optional heat exchanger for cooling.
These details highlight the importance of the coordinated control of the
setup’s heating (and potential cooling) assets in order to ensure effective
perfusion temperature control. Other critical variables that the setup must
monitor and control include perfusion flowrate, total perfused volume,
perfusate gas concentrations, and intra-cavity pressure. The remainder of this
paper presents a detailed description of the monitoring, data acquisition, and
control functionalities implemented to meet these goals.

Figure 4: Setup monitoring and data acquisition system

##  III Setup monitoring and data acquisition

Figure (4) provides a high-level overview of the components of the setup’s
monitoring and data acquisition system. This system: (i) monitors the setup’s
performance, (ii) monitors the effect of perfusion on the test animal, and
(iii) enables important closed-loop control functionalities. Up to 43 signals
are collected by this system, from 28 different sensors and patient monitors,
in order to collectively satisfy the data acquisition requirements below. Note
that the physical locations of these sensors, where possible, are indicated in
Fig.s (2-3).

  * •

Fluid height/volume monitoring (6 sensors, 6 signals): The setup has the
ability to monitor the height of the PFC in all of its canisters - namely, the
oxygenation canister, the $CO_{2}$ removal canister, and its 1-2 canister
accumulator. This is important for controlling the setup, as well as
estimating the total volume of fluid delivered to the animal. To achieve this
functionality, pressure sensors are mounted at the bottoms of all four
canisters. Moreover, two pressure sensors are mounted at the tops of the two
suction canisters in the dual-canister accumulator in order to measure air
pressure during suction. The difference between air pressure in each canister
and the pressure at the bottom of the canister enables the estimation of fluid
height in the canister.

  * •

Secondary fluid height/volume monitoring (4 sensors, 4 signals): The setup is
equipped with an optional redundant method for estimating the height of the
fluid in its canisters using 4 fluid level sensors.

  * •

PFC flowrate monitoring (1 sensor, 1 signal): The setup monitors perfusion
using a PFC flowrate sensor.

  * •

Oxygen flowrate monitoring (2 sensors, 2 signals): The setup monitors the rate
at which oxygen flows into the $CO_{2}$ removal tank using a gas mass flowrate
sensor. This rate is adjusted using a manual valve. The setup also controls
oxygen flowrate into its oxygenation chamber using an active gas flowrate
controller. This controller provides a measurement of the achieved oxygen
flowrate back to the setup’s data acquisition system.

  * •

Oxygen concentration monitoring (1 sensor, 1 signal): An optical sensor is
mounted on the final perfusion line in order to monitor the concentration of
dissolved oxygen in the PFC.

  * •

Fluid temperature monitoring (6 sensors, 6 signals): Thermocouples are used
for monitoring PFC temperatures at multiple critical points in the setup.
Specifically, six thermocouples are used for monitoring PFC temperature at:
(i) the $CO_{2}$ removal tank; (ii) the inlet of the oxygenation tank; (iii)
the inlet of the perfusion pump; (iv) the outlet of the perfusion pump; (v)
the last point in the setup prior to perfusion; and (vi) either the return
flow line or the surface of the final polishing heater, depending on usage of
the setup.

  * •

Perfusion pressure monitoring (4 sensors, 4 signals): The setup has the
ability to measure the test animal’s abdominal intra-cavity pressure and
bladder pressure through two catheter-mounted pressure sensors. This is
important for ensuring safe perfusion. Moreover, the setup uses two additional
pressure sensors for monitoring internal fluid pressures prior to perfusion in
order to avoid excessive pumping rates.

  * •

Physiological signal monitoring (4 monitors, 19 signals): The setup has the
ability to interface with four different medical monitoring systems in order
to collect data regarding the test animal’s physiological state (e.g.,
hemodynamics) and response to perfusion. Specifically, the setup can interface
with: (i) a Nellcor pulse oximeter; (ii) a Capnomac capnograph; (iii) a Penlon
anesthesia machine; and (iv) a TRAM-RAC patient monitor. Collectively, these
devices provide 19 different measurements of physiological and/or anesthesia-
related variables, with some of these measurements providing an important
degree of redundnacy. For example, pulse oximetry is monitored using both the
Nellcor oximeter and the TRAM-RAC patient monitor.

The setup’s monitoring and control system is built around a central data
acquisition board - in this case, a dSpace MicroLabBox II board. Similar data
acquisition boards are often used for instrumentation and control research
[30, 31]. All analog sensor/monitor signals are read directly by the dSpace
board’s analog-to-digital converter. For sensor signals that use a current-
based (i.e., $4-20mA$) analog communication protocol, standard integrated
circuits are used for converting the signals to a voltage-based protocol
first, prior to dSpace-based data acquisition. The remaining signals are
communicated using either the RS-232 serial protocol or the serial peripheral
interface (SPI) protocol. Two Arduino Mega 2560 boards, together with a Teensy
board (an Arduino clone) are used for reading these non-analog signals. As
shown in Fig. (4), one of the Arduino boards is used for aggregating data from
the pulse oximeter and anesthesia machine. The second Arduino board adds
capnograph and SPI-based temperature data to this aggregate datastream, and
forwards it to the dSpace board. Finally, the Teensy board selects specific
signals from the fairly large dataset communicated serially by the TRAM-RAC
patient monitor, repackages these signals, and communicates them directly to
the dSpace board. Minimizing the amount of physical wiring necessary for
communicating between these various devices is important, given the space
limitation of a typical operating room. To address this issue, the setup
collects the signals from all the medical devices using a custom printed
circuit board (PCB), as shown on the left hand side of Fig. (5). A second
custom PCB board, shown on the right hand side of Fig. (5) is then used to
input these signals into the Arduino and dSpace boards.

Figure 5: Medical equipment communication boards

Different components of the above data acquisition system monitor different
underlying dynamics, with significantly different associated time constants.
For example, if any of the setup’s tubes are accidentally pinched during an
experiment, the dynamics of the associated rise in fluid pressure are likely
to be much faster than the dynamics of animal blood gas concentrations. With
this in mind, the setup’s dSpace board has a relatively fast master sampling
time of $10ms$, corresponding to a sampling rate of 100 samples/second. Other
components of the setup have progressively slower sampling rates and/or data
processing times. For example: (i) The SPI protocol is used for reading
temperatures every $100ms$. (ii) The Arduino boards communicate data to the
dSpace board every $150ms$. (iii) The Teensy board communicates data to the
dSpace board every $500ms$. (iv) The pulse oximeter, anesthesia machine, and
patient monitor communicate data to the Arduino and Teensy boards every
$2000ms$. (v) The capgnograph communicates data to the corresponding Arduino
board every $10,000ms$. (vi) Finally, the oxygen sensor updates its readings
every $60$ seconds, with the caveat that this is the only sensor that is read
by a (proprietary) standalone program not communicating with the dSpace board.

Ensuring proper calibration of the above sensors and monitors is essential for
the successful use of the setup. Four particular calibration efforts are
needed on a regular basis, potentially as frequently as once per use of the
setup for animal experiments. First, it is important to calibrate the PFC
flowrate sensor, especially if it is used for closed-loop perfusion flowrate
control. This is achieved by using the setup to pump a known volume of fluid
into an external tank, then calibrating the sensor’s data processing software
to ensure that the time integral of the flowrate measured by the sensor
matches the volume of fluid delivered. Second, it is important to calibrate
the canister pressure sensors to ensure correct fluid height estimates. This
is done by filling the canisters to known fluid heights, then adjusting the
reference voltage outputs of these sensors to furnish height estimates
matching these known heights. Third, it is particularly critical to calibrate
the cavity and bladder pressure sensors. This is done at the beginning of each
animal experiment by exposing these sensors to atmospheric pressures, then
adjusting the reference voltage outputs of these sensors to furnish a correct
reading of atmospheric pressure. Finally, it is important to calibrate the
optical dissolved oxygen concentration sensor. This sensor produces a raw
output signal that does not equal dissolved oxygen concentration, but can be
correlated to it. To calibrate this sensor, two samples of PFC were prepared
with dissolved oxygen concentrations corresponding to partial oxygen pressures
of 159mmHg and 760mmHg, respectively, at room temperature. These samples were
then mixed in different proportions in order to prepare PFC samples with
intermediate oxygen partial pressures. A small but noticeable increase in
fluid turbidity occurred at dissolved oxygen partial pressures approaching
760mmHg. The sensor’s reading was then correlated to dissolved oxygen
fraction, defined as the partial pressure of dissolved oxygen divided by
760mmHg. Figure (6) shows the resulting sensor calibration plot.

Figure 6: Calibration plot for optical oxygen sensor

##  IV Setup control

Four closed-loop control functionalities are implemented in the setup.
Specifically, the setup contains discrete-event algorithms to control: (i) the
filling of the two-canister system when in use; and (ii) the filling of the
$CO_{2}$ removal chamber and oxygenation chambers. The setup also contains
proportional-integral (PI) algorithms for controlling (iii) the temperatures
of the PFC in the $CO_{2}$ removal chamber and final perfusion line; and (iv)
the final perfusion flowrate/pressure. These controllers are discussed below.

Multi-Canister Switching Control

The intent of the dual-canister accumulator is twofold. First, it enables
smooth, continuous PFC drainage from the test animal into the setup,
potentially in the presence of active suction via a vacuum pump applied to the
canisters. Second, it achieves this while minimizing the loading that this
suction may apply on the retrieval pump. Discrete-event logic is needed for
switching between two configurations. In one configuration, the “left”
canister is receiving drained PFC and the “right” canister is supplying PFC to
the rest of the setup. In the second configuration, these roles are reversed.

Figure (7) summarizes the discrete-event logic used for operating the dual-
canister system when it is used. The figure generalizes this algorithm to an
$N$-canister system. Most of the time, the setup is in a “k-filling” state,
where canister $k$ is being filled and all other canisters are being emptied.
When canister $k$ is full or any other canister is empty, an immediate switch
takes place to a “transitioning” state. This state persists for a fixed
duration of time, during which the retrieval pump is shut down, suction is
applied to the next canister in the sequence of canisters to fill, fluid is
routed to that new canister, the outlet valves from the canisters to the rest
of the setup are opened and closed appropriately, and the retrieval pump is
restarted. Once this transition is complete, the discrete-event control
algorithm automatically moves to a state where it is filling the next canister
in the filling sequence, namely, canister number $(k+1)modN$.

Figure 7: Multi-canister switching control algorithm

Control of Oxygenation and $CO_{2}$ Chamber Filling

Three different control algorithms/loops are used for controlling the
retrieval pump and its associated bypass valves. Collectively, these loops
ensure that the oxygenation and $CO_{2}$ removal chambers are replenished with
fluid whenever possible, but prevented from overfilling.

  * •

The first loop controls the retrieval pump flowrate. During normal operation,
this flowrate is set to a constant value. However, when both the oxygenation
and $CO_{2}$ removal tanks are full or when all the canisters in the
accumulator are empty, the pump enters a temporary shutdown state, where
flowrate is set to zero. The pump dwells in this state for a fixed time
duration, then returns to normal operation. This translates to a 2-state
finite state machine governing the pump’s operation, where it transitions
automatically from normal operation to shutdown whenever needed. The setup’s
graphical user interface (GUI) allows the user to define the “empty” and
“full” fluid levels for all canisters. The GUI also allows the user to dictate
the constant flowrate used by the retrieval pump during normal operation. This
flowrate should ideally be 0.5lpm-1.0lpm larger than the desired perfusion
flowrate to ensure that the oxygenation and $CO_{2}$ removal tanks are always
replenished.

  * •

The second loop controls the bypass valve for the first retrieval pump head.
This valve is closed during normal operation, allowing the retrieval pump to
supply PFC from the accumulator to the $CO_{2}$ removal tank. However, when
the $CO2$ removal tank is full, this valve automatically switches to a state
where it is open, allowing flow to bypass the $CO_{2}$ removal tank. The valve
dwells in this state for a fixed time duration, then automatically returns to
the normal operation state. This makes it possible for the retrieval pump to
replenish the oxygenation tank through its second pump head, without
overfilling the $CO_{2}$ removal tank.

  * •

The third loop controls the bypass valve for the second retrieval pump head.
The logic governing this loop is identical to the logic governing the second
control loop, the only difference being the the transition from closed- to
open-valve operation is governed by fluid level in the oxygenation chamber.
This loop allows the $CO_{2}$ chamber to be replenished, without overfilling
the oxygenation chamber.

PFC Temperature Control

Two different loops are used for controlling PFC temperature (i) in the
$CO_{2}$ removal chamber and (ii) at the final perfusion point. Both loops
rely on proportional integral (PI) control with saturation and anti-windup
logic. In both cases, the dynamics of PFC temperature are assumed to be
governed by the following simple energy balance:

$\begin{split}\rho VC_{p}\frac{dT}{dt}&=\rho QC_{p}(T_{in}-T)\\\
&+hA(T_{\infty}-T)+uR_{o}I_{o}^{2}\end{split}$ (2)

In the above equation, $T$ is the PFC temperature in the given control volume,
assumed to be equal to the control volume’s outlet temperature. Depending on
the control loop, this control volume is either the $CO_{2}$ removal chamber
or the pipe section/manifold being heated by the final perfusion heater. The
volume of PFC being heated is denoted by $V$. Moreover, the density and
specific heat capacity of the PFC are denoted by $\rho$ and $C_{p}$,
respectively. Thus, the term $\rho VC_{p}dT/dt$ equals the rate of change of
thermal energy stored in the control volume, assuming that the amount of PFC
in this control volume, $V$, is approximately constant. The first term
contributing to this rate of change, $\rho QC_{p}(T_{in}-T)$, equals the rate
of energy transfer due to the flow of PFC, where $Q$ is the volumetric
flowrate of the PFC and $T_{in}$ is the PFC temperature at the inlet of the
control volume. The second term contributing to temperature change,
$hA(T_{\infty}-T)$, represents the rate of convection heat transfer, where $h$
is the heat transfer coefficient, $A$ is the area exposed to convection, and
$T_{\infty}$ is ambient temperature. Finally, the term $uR_{o}I_{o}^{2}$
represents electric heating of the PFC, where $R_{o}$ is the heater’s
effective resistance, $I_{o}$ is the nominal current flowing through the
heater when it is turned on, and $u$ is an adjustable pulse width modulation
(PWM) duty ratio for the heater. This PWM duty ratio is constrained to have a
value between 0 and 1. Note that the above model is used for controlling the
setup’s two sets of electric heaters, keeping in mind that additional
heating/cooling functionalities are provided in an open-loop manner by the
setup’s heat exchangers.

Figure (8) shows the PI loop used for temperature control in the $CO_{2}$
removal chamber. The plant dynamics block in the figure represents Eq. (2).
The difference, $E(s)$ between the desired reference temperature, $R(s)$, and
actual temperature, $T(s)$, is passed through a PI controller,
$k_{p}+k_{I}/s$, with a proportional gain $k_{p}$ and integral gain $k_{I}$,
in order to produce a PWM ratio $U^{\prime}(s)$. This PWM ratio is then passed
through a saturation function in order to ensure that the final commanded PWM
ratio, $U(s)$, lies between 0 and 1. If the saturation function is active,
meaning that there is a difference between the signals $U^{\prime}$ and $U$,
then the integral feedback functionality is disabled in order to prevent
integrator windup. When the saturation function is inactive, the resulting
closed-loop expression for the PFC temperature, $T(s)$, ensures ideal steady-
state target temperature tracking in the presence of constant ambient and
inflow temperature disturbances, as expected:

$T(s)=\frac{\rho
QC_{p}T_{in}+hAT_{\infty}+(k_{p}s+k_{I})R_{o}I_{o}^{2}R(s)}{s(\rho
C_{p}(Vs+Q)+hA)+(k_{p}s+k_{I})R_{o}I_{o}^{2}}$ (3)

Temperature control for the $CO_{2}$ removal chamber was tuned by fitting the
open-loop dynamics of Eq. (2) to an experimental step response test, then
using classical pole placement to set the gains $k_{p}$ and $k_{I}$. A similar
process was used for tuning the gains of the final perfusion temperature
controller, with one important caveat compared to the $CO_{2}$ chamber
temperature controller. Specifically, because the final perfusion heater is
mounted directly on a metal pipe carrying PFC, as opposed to being immersed in
a canister containing PFC, it is significantly more vulnerable to overheating.
This vulnerability is particularly noticeable for small or zero PFC flowrates.
To address this, the final perfusion heater’s controller contains an
additional term that brings the corresponding PWM ratio quickly to zero if the
temperature of the final perfusion heater exceeds $55^{\circ}C$. When this
function is activated, integral control is disabled in order to prevent
integrator windup.

Figure 8: Closed-loop temperature control

Perfusion Flowrate and Pressure Control

The final perfusion controller dictates the flowrate command to the perfusion
pump. The controller allows its user to select between two modes: a manual
mode and an automatic mode. In both modes, the controller determines a raw
flowrate command, $Q^{\prime}(t)$. In the manual mode, this flowrate command
is equal to $k_{ff}Q_{des}(t)$, where $Q_{des}(t)$ is the flowrate dictated by
the setup’s user through its GUI, and $k_{ff}$ is a feedforward calibration
constant determined through setup testing. In the automatic mode, the flowrate
command is related to the user-defined desired flowrate as follows:

$\begin{split}Q^{\prime}(t)&=k_{ff}Q_{des}(t)\\\
&+I(t)k_{q}\int_{0}^{t}(Q_{des}(\tau)-Q_{meas}(\tau))d\tau\\\
&+(1-I(t))k_{c}\int_{0}^{t}(P(\tau)-P_{set})d\tau\end{split}$ (4)

In the above control law, $P(t)$ denotes peritoneal cavity pressure, and
$P_{set}$ is a user-defined pertioneal cavity setpoint pressure that should
ideally not be exceeded for prolonged time durations. A dimensionless
indicator function, $I(t)$, is defined as being equal to 1 when
$P(t)>P_{set}$, and being equal to 0 otherwise. Therefore, when this indicator
function equals 1, the implication is that the peritoneal cavity pressure
setpoint has been exceeded. The volumetric flowrate, $Q^{\prime}(t)$, is
governed by three terms: a feedforward term identical to the one used for
manual flow control, plus two integral feedback terms. The controls gains for
these three terms are denoted by $k_{f}f$ (dimensionless) for the feedforward
gain, $k_{q}$ (units: $s^{-1}$) for the integral flowrate correction gain, and
$k_{c}$ (units: $m^{3}Pa^{-1}s^{-2}$) for the integral pressure correction
gain. Only one of the above integral feedback terms is active at any given
time. When peritoneal cavity pressure exceeds the setpoint pressure, an
integral controller with a gain $k_{c}$ is used for bringing cavity pressure
down to the setpoint. In contrast, when peritoneal cavity pressure is below
the setpoint, an integral controller with a gain $k_{q}$ is used for matching
the true perfusion flowrate measured by the flowrate sensor, $Q_{meas}(t)$, to
the desired flowrate dictated by the user. The actual flowrate command
communicated to the perfusion pump is equal to $Q^{\prime}(t)$ from the above
equation, with the exception of two extreme conditions:

  * •

First, when the fluid level in the oxygenation tank drops below a certain
minimum level, the perfusion pump controller enters a temporary discrete-event
state where perfusate flowrate is curtailed by 50% while the oxygention tank
is replenished. This prevents the excessive emptying of the oxygenation tank.

  * •

Second, when cavity pressure exceeds a user-defined safety limit
$P_{max}>P_{set}$, the perfusion pump controller enters a different temporary
discrete-event state where perfusion is completely disabled.

The intent of the above perfusion flowrate control algorithms is to ensure
steady-state tracking of a user-defined desired perfusion flowrate during
normal operation. For safety reasons, this is interrupted when perfusion
pressures increase beyond a user-defined setpoint and/or safety limit, or when
the oxygenation chamber becomes excessively empty.

Figure 9: The first and second animal experiment

##  V Results

Four animal experiments have been conducted to date, as illustrated in Fig.
(9). These experiments employed different functionalities in the above setup.
For example, the first animal experiment did not employ active suction for
drainage of PFC from the test animal, whereas the next 3 animal experiments
did. Moreover, the first two animal experiments employed a single-canister
accumulator, whereas the third and fourth experiments predominantly employed a
dual-canister accumulator. The purpose of this section is to discuss the
efficacy of the setup’s data acquisition and control functionalities, from a
mechatronics perspective. Future work will build on these results, with a
deeper focus on the viability of the setup’s use for supplementing test animal
gas exchange. Seven lessons are visible from experiments performed with the
setup to date:

First, the setup is capable of rapidly oxygenating its stored
Perfluorodecalin. Figure (10) illustrates this by plotting the open-loop
commanded flowrate of oxygen into the oxygenation chamber (blue) and the
resulting measured percentage of dissolved oxygen in the PFC as a function of
time (red), during one of the animal experiments. A rapid increase in
dissolved oxygen percentage is achieved while the PFC is recirculated through
the setup, in preparation for one of the perfusion events.

Figure 10: Illustration of setup oxygenation performance

Figure 11: CO2 removal tank and perfusing PFC temperatures (second animal
experiment)

Second, the setup is capable of monitoring and controlling the temperature at
which $CO_{2}$ stripping takes place. Figure (11) (a) illustrates this, by
highlighting the setup’s $CO_{2}$ tank reference temperature tracking
performance during a portion of the second animal experiment. Good reference
tracking is achieved, with a very small steady-state error corresponding to
slight overheating of the PFC. As expected, once the PFC reaches this slightly
overheated state, the PWM command to the $CO_{2}$ tank heaters drops mostly to
zero.

Third, the setup is capable of monitoring and controlling the temperature of
the PFC at the final perfusion line. Figure (11) (b) illustrates this by
plotting perfusion temperature versus time for a portion of the second animal
experiment.

Fourth, the setup is capable of both monitoring and controlling the final
perfusion flowrate, in compliance with user input. Figure (12) illustrates
this by comparing the commanded (blue) versus measured (red) PFC flowrate
profiles during a portion of the third animal experiment. The setup was
operated in manual flowrate control mode during this particular experiment, as
opposed to automated control mode. Therefore, Fig. (12) illustrates successful
feedforward control tuning, as opposed to successful steady-state flowrate
command tracking through integral action.

Figure 12: Measured vs. commanded PFC flowrate (third animal experiment)

Fifth, the setup is capable of detecting and avoiding excessive peritoneal
intracavity pressures. Figure (13) illustrates this by plotting the setpoint
cavity pressure (red) versus measured cavity pressure (blue) for a portion of
the third animal experiment. Excursions beyond the setpoint pressure are
brief. Moreover, they are followed by rapid curtailment of fluid flowrate (not
shown), leading to rapid curtailment of cavity pressure. Negative cavity
pressures at the end of the plot are indicative of the use of active suction
for fluid retrieval.

Figure 13: The peritoneal cavity pressure measurement vs the pressure setpoint
(Data from the third animal experiment)

Sixth, the setup provides sufficient data for assessing the viability of
perfusion for oxygenating the test animal. Figure (14) illustrates this by
showing data from one of the animal oxygenation events. Specifically, the
figure plots the animal pulse oximetry (blue) and PFC flowrate (red) versus
time. The initial decline in pulse oximetry corresponds to a change in
ventilator settings inducing hypoxia. Subsequent improvements in pulse
oximetry may be due to a combination of physiological recovery by the animal
and/or PFC perfusion. Analyzing the viability of perfusion for improving pulse
oximetry is an open topic for ongoing research, exploiting this paper’s setup.
However, the figure clearly shows that the setup is capable of measuring key
variables that can be used for this type of analysis.

Figure 14: Perfusate flowrate and pulse oximetry (second animal experiment)

Finally, the setup provides sufficient data for assessing the viability of
$CO_{2}$ removal from test animals. Figure (15) illustrates this by plotting
perfusion flowrate, inspired $CO_{2}$ concentration, and end-tidal $CO_{2}$
concentration for a portion of the second animal experiment. Hypercarbia is
induced, in this case, through a reduction in minute ventilation. Improvements
in end-tidal $CO_{2}$ concentration (ETCO2) may be caused by physiological
recovery mechanisms or perfusion, or a combination of both effects. Analyzing
these different recovery mechanisms is left open for ongoing research,
building on the setup described in this paper. Please note that the setup’s
capnograph measures gas concentrations in a tracheal tube, and infers both
inspired and end-tidal $CO_{2}$ concentrations from tracheal measurements.
Therefore, changes in inspired gas concentration (FICO2) measurements are
likely to reflect gas mixing and re-breathing in the tracheal tube.

Figure 15: Inspired and end-tidal $CO_{2}$ concentrations and perfusate
flowrate (second animal experiment)

##  VI Conclusions and Future Work

This paper presents the development, design, and implementation of a
peritoneal perfusion setup for studies on animal oxygenation using
perfluorocarbons. The paper focuses predominantly on the setup’s monitoring,
data acquisition, and control capabilities as a mechatronics setup. Four
animal experiments have been conducted to date using this setup. These animal
experiments highlight the setup’s functionalities from an engineering
perspective. These functionalities include the ability to monitor and control
perfusate flowrate, pressure, and temperature. More importantly, the setup is
also capable of simultaneously tracking both physical perfusion variables and
physiological animal responses. The question of what factors affect the
efficacy of peritoneal PFC perfusion as a gas exchange mechanism remain open
for ongoing/future research. Moreover, the related question of the minimum
viable level of setup complexity and sophistication for gas exchange also
remains open for ongoing/future research. The design of the setup in this
paper focuses predominantly on achieving a level of sophistication in data
acquisition and control that is conducive to scientific exploration, with the
recognition that practical clinical implementation may benefit from potential
setup simplifications.

## ACKNOWLEDGEMENTS

This research was conducted under IACUC #0121006 at The University of Maryland
Medical School, Baltimore, MD (UMB). Support for this research was provided by
the Mechanical Engineering Department at The University of Maryland (UMD), UMD
startup funding for Dr. Hosam Fathy, an internal grant from The UMD Device
Development Fund, and a National Science Foundation (NSF) EAGER grant to Dr.
Hosam Fathy, Dr. Joseph Friedberg, and Dr. Jin-Oh Hahn (NSF CMMI Award
#2031251, #2031245). Any Opinions, findings and conclusions or recommendations
expressed in this material are those of the author(s) and do not necessarily
reflect those of NSF. The majority of the setup’s monitoring, data
acquisition, and control functionalities were developed through NSF funding,
with funding from other sources contributing to earlier hardware development.
The authors gratefully acknowledge all of these sources of support. The
authors also gratefully acknowledge the valuable support of other colleagues
at UMD/UMB, including Grace Anyetei-Anum, Dr. Hyun-Tae Kim, Dr. Joshua
Leibowitz, and Dr. Miao Yu.

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|  Mahsa Doosthosseini received her M.S. (2017) in Mechanical Engineering from
the Pennsylvania State University. She is currently a Ph.D. candidate in
Mechanical Engineering at the University of Maryland, College Park. Her
research focuses on optimal experiment design, control, and mechatronics.
---|---
|  Kevin R. Aroom earned his B.S. (2005) and M.S. (2007) in Biomedical
Engineering from the University of Maryland, and University of Texas at
Austin, respectively. His areas of expertise include rapid prototyping and
medical devices.
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|  Majid Reza Aroom recieved his B.Sc (1984) from the Northeastern University,
Boston Massachusetts, USA. He is a project engineer in Thermal Systems, and a
Mechanical Engineering Faculty Specialist currently at the University of
Maryland.
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|  Melissa Culligan received her M.S. in Clinical Research Management from
Drexel University. She is the Director of Clinical Research at the Division of
Thoracic Surgery at The University of Maryland Medical Center, and a Nursing
Science Ph.D. student at The University of Maryland School of Nursing.
---|---
|  Warren Naselsky earned his B.S. in Biochemistry (2012) and M.D. (2016) at
the University of North Carolina at Chapel Hill. He is currently an integrated
cardiothoracic surgical resident at the University of Maryland. He recently
completed an NIH T32 postdoctoral fellowship at the University of Maryland and
now is pursuing a career as an academic thoracic surgeon.
---|---
|  Chandrasekhar Thamire holds a B.S. (1987), M.S. (1997), and Ph.D. (1997)
degrees, all in mechanical engineering, and is a licensed engineer. His areas
of expertise are turbomachinery design and biological transport. He has worked
in industry and academia in various capacities. He is presently a principal
lecturer at the University of Maryland.
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|  Stephen A. Roller holds an MBA from the University of Minnesota Carlson
School of Management and has his M.Sc. from the University of Michigan in
Biomedical Engineering. He also holds his B.Sc. from the University of
Michigan in Mechanical Engineering. He serves as a venture advisor with a
focus on medical device technologies currently at the University of Maryland.
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|  Richard Hughen earned his BS and MBA degrees from The Pennsylvania State
University. He is currently CEO of a start-up company developing a predictive
continuous respiratory monitoring device for the patient bedside and home. His
main expertise is medical device commercialization and is an Entrepreneur in
Residence for University of Maryland Ventures.
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|  Henry W. Haslach, Jr earned a BS in mathematics from Trinity College, an MS
in mathematics from the University of Chicago, an MS in Engineering Mechanics
and a Ph.D in mathematics both from the University of Wisconsin-Madison. His
current research and expertise are on the experimental and analytical rupture
mechanics of the human aorta and on blast damage to the brain. He is currently
a Research Professor in Mechanical Engineering at the University of Maryland –
College Park.
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|  Joseph S. Friedberg is the Charles Reid Edwards Professor of Surgery and
head of the Division of Thoracic Surgery at the University of Maryland School
of Medicine. He received his bachelor’s degree from the University of
Pennsylvania, and received his M.D. from Harvard Medical School. His interests
include pleural mesothelioma, pleural malignancies and disorders, complex lung
cancer, chest wall tumors, pulmonary metastasis, malignant pleural effusions,
and diaphragm disorders.
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|  Jin-Oh Hahn received BS and MS degrees in mechanical engineering from Seoul
National University in 1997 and 1999, and PhD degree in mechanical engineering
from Massachusetts Institute of Technology (MIT) in 2008. He is currently with
the University of Maryland, where he is an Associate Professor in the
Department of Mechanical Engineering. His research interests include
applications of control, estimation, and machine learning theory to health
monitoring, fault diagnostics, maintenance and treatment of dynamical systems
with emphasis on health and medicine.
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|  Hosam K. Fathy earned his B.Sc. (1997), M.S. (1999), and Ph.D. degrees -
all in Mechanical Engineering - from The American University in Cairo, Kansas
State University, and The University of Michigan, respectively. His main area
of expertise is optimal estimation and control. He is currently a Mechanical
Engineering Professor at The University of Maryland.
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