# Repeating gas ejection events from comet 45P/Honda-Mrkos-Pajdušáková

Alessondra Springmann Lunar & Planetary Laboratory, University of Arizona 1629
E University Blvd., Tucson, AZ 85721-0092, USA  Walter M. Harris  Lunar &
Planetary Laboratory, University of Arizona 1629 E University Blvd., Tucson,
AZ 85721-0092, USA  Erin L. Ryan  SETI Institute, 189 Bernardo Ave., Mountain
View, CA 94043-5138, USA  Cassandra Lejoly  Lunar & Planetary Laboratory,
University of Arizona 1629 E University Blvd., Tucson, AZ 85721-0092, USA
Ellen S. Howell  Lunar & Planetary Laboratory, University of Arizona 1629 E
University Blvd., Tucson, AZ 85721-0092, USA  Beatrice E.A. Mueller  Planetary
Science Institute, 1700 East Fort Lowell Rd., Tucson, AZ 85719-2395 USA  Nalin
H. Samarasinha  Planetary Science Institute, 1700 East Fort Lowell Rd.,
Tucson, AZ 85719-2395 USA  Laura M. Woodney  California State University, San
Bernardino, 5500 University Pkwy., San Bernardino, CA 92407-2397, USA  Jordan
K. Steckloff  Planetary Science Institute, 1700 East Fort Lowell Rd., Tucson,
AZ 85719-2395 USA

###### Abstract

Studying materials released from Jupiter-family comets (JFCs) — as seen in
their inner comæ, the envelope of gas and dust that forms as the comet
approaches the Sun — improves the understanding of their origin and
evolutionary history. As part of a coordinated, multi-wavelength observing
campaign, we observed comet 45P/Honda-Mrkos-Pajdušáková during its close
approach to Earth in February 2017. Narrowband observations were taken using
the Bok 90” telescope at Kitt Peak National Observatory on February 16 and 17
UT, revealing gas and dust structures. We observed different jet directions
for different volatile species, implying source region heterogeneity,
consistent with other ground-based and in situ observations of other comet
nuclei. A repeating feature visible in CN and C2 images on February 16 was
also observed on February 17 with an interval of $7.6\pm 0.1$ hours,
consistent with the rotation period of the comet derived from Arecibo
Observatory radar observations. The repeating feature’s projected gas velocity
away from the nucleus is 0.8 km s-1, with an expansion velocity of 0.5 km s-1.
A bright compact spot adjacent to the nucleus provides a lower limit of the
amount of material released in one cycle of $\sim$9.2 kg, depending on
composition — a quantity small enough to be produced by repeated exposure of
nucleus ices to sunlight. This repeating CN jet, forming within 400 km of the
nucleus, may be typical of inner coma behavior in JFCs; however, similar
features could be obscured by other processes and daughter product species
when viewed from distances further than the scale length of CN molecules.

comets — observations — jets

††facilities: Bok 90” (90Prime), Arecibo Observatory (Planetary Radar
System)††software: astropy (Astropy Collaboration et al., 2013, 2018); sbpy
(Mommert et al., 2019)

##  1 Introduction

As comets approach the Sun, gases sublimate from ices and form a gas-rich
coma. Processes occurring in the inner coma provide information about volatile
production from the nucleus, as well as information about photochemical
evolution of short-lived species in the coma. We define the inner coma as the
region where collisions between gas molecules occur, affecting the velocities
of other particles. Outside of the inner coma, particle velocities are not
affected by collisions. Inner-coma processes occur quickly and/or on small
spatial scales and generally can neither be temporally nor spatially resolved
with ground-based telescopes. These processes are often blocked from view by
other photodissociation product species in the outer coma. Short of in situ
exploration, our best opportunity to study inner coma processes is for a comet
to experience a close approach to Earth, as outer coma daughter species
obscure short-lived inner coma species.

Jupiter-family comet 45P/Honda-Mrkos-Pajdušáková (45P hereafter) passed within
0.14 au of Earth between 2016 and 2017, providing excellent circumstances for
observing its inner coma with ground-based telescopes. Jupiter-family comets
(JFCs) have orbital periods less than 20 years; they originate as trans-
Neptunian objects that evolve into Centaurs and eventually migrate into the
inner Solar System (Duncan & Levison, 1997; Duncan et al., 2004; Dones et al.,
2015; Tiscareno & Malhotra, 2003; Di Sisto & Brunini, 2007; Sarid et al.,
2019; Steckloff et al., 2020). Because of their trans-Neptunian origin,
studying JFCs can provide insight into Solar System evolutionary processes.

Visible-wavelength observations of 45P during its close approach were
conducted as part of a multi-wavelength, global, coordinated observing
campaign (Harris et al., 2017). Observing 45P in 2016–2017 was one of the last
opportunities for close study of inner coma processes in JFCs for the next
several decades. The goals of the campaign were to use ground-based
observations in visible, infrared, radar, and radio wavelengths to obtain
holistic, multi-wavelength understandings of the behavior of inner coma gas
and dust species and their interactions with the comet nucleus.

###  1.1 Comet 45P Overview

Comet 45P is approximately 0.6–0.65 km in diameter, with a 7.6 $\pm$ 0.5 h
rotation period (Lejoly et al., 2017). It has low H2O production rates
compared to similar JFCs and is depleted with respect to H2O in some volatile
species, including CN and H2O (Fink, 2009).

Other observations taken during the 2017 apparition of 45P on January 6–8,
shortly after perihelion on 2017 December 31 show volatile species
preferentially released from one section of the nucleus and processing of
nucleus ices before being incorporated into the broader coma (DiSanti et al.,
2017). Moulane et al. (2018), observing from 2017 February 10–March 30,
confirmed low gas and dust activity and did not detect any outbursts; and that
45P, like 41P, has a carbon-bearing species composition typical of comets.
Observations by Dello Russo et al. (2020), taken 2017 February 13 and 19,
indicated “a relatively symmetric and uniform coma […] with small spatial
differences noted between some volatile species.” Observations from previous
as well as the 2017 apparitions measuring C2 and CN production rates, as well
as C2H2 and HCN abundances, appear consistent with HCN being the primary
parent of CN. Dello Russo et al. (2020) noted the dust-to-gas ratio increased
from February 13 to 19.

In this paper we present observations in filters targeting volatile species
and dust of comet 45P. In Section 2 we provide an overview of CN, C2, OH, and
dust observations taken at Kitt Peak National Observatory. Specifics of the
standard reduction and image analysis techniques used are reported in Section
3. Section 4 describes a repeating, discontinuous CN feature, as well as
features seen in other wavelengths. We discuss in Section 5 possible causes of
the repeating feature, radar observations of 45P, and comparison of these 45P
observations to those taken of other comets. We summarize the results from
this campaign and for observations of future close approaches of JFCs to Earth
in Section 6.

##  2 Observations

Observations were conducted using the Bok 90”/2.3-meter telescope at Kitt Peak
National Observatory outside of Sells, Arizona, USA, on 2017 February 16 and
17 UT (Table 1). Observations were also obtained at the Kuiper Telescope,
Large Binocular Telescope, MMT Observatory, Arecibo Observatory, and Arizona
Radio Observatory as part of a coordinated, multiwavelength campaign to
characterize three Jupiter-family comets (Harris et al., 2017). Comet 45P was
observed 1.5 months after perihelion and 5–6 days after perigee to identify
any changes in the rotation of the nucleus and coma evolution (e.g. Howell et
al., 2018; Schleicher et al., 2019).

Narrowband filters (CN, C2, OH, and blue continuum (BC)) originally designed
for the comet Hale–Bopp (C/1995 O1) observational campaign (Farnham et al.,
2000) were used to ensure consistency of data across observing sites and
telescopes. Both BC as well as broadband SDSS-r′ were used as a proxy for
dust. The BC images show the same features as the r′ images, however, the r′
exposures have more temporal coverage and better signal-to-noise ratios with
shorter exposure times (and thus shorter star trails) with r′ than BC images.
We limit the analysis presented here to r′-filter images, as the images are
otherwise indistinguishable. Although r′ is a broadband filter and has some
gas contamination, unless the comet is very dust-poor, the flux in r′ images
is dominated by scattered dust, not by gas. Using r′ as a proxy for dust is a
reliable method for comets with a moderate to high dust-to-gas ratio (Farnham
et al., 2000), such as 45P (Fink, 2009), and has been successfully used for
other comets (e.g. Mueller et al., 2013; Knight et al., 2021).

Over the course of two nights, 19 science images were taken: 16 on February
16, and only three on February 17 due to weather. The close approach of comet
45P to Earth allowed for plate scales of $\sim$40 km/pixel, or resolutions of
$\sim$80 km/arcsecond.

Table 1: Observing circumstances for comet 45P on UT 16 and 17 February 2017 from the 90” Bok telescope on Kitt Peak, Arizona, USA. Date | UT | Days from | Days from | $R$ | $\Delta$ | Elong. | Phase
---|---|---|---|---|---|---|---
| Start–End | perihelion | perigee | (au) | (au) |  (∘) |  (∘)
16 Feb | 07:04–12:35 | 47 | 5 | 1.05 | 0.11 | 124–126 | 50
17 Feb | 07:55–08:20 | 48 | 6 | 1.07 | 0.11 | 130–131 | 44

##  3 Image Reduction & Analysis

Standard techniques were followed for bias subtraction and flat fielding using
dome flats. Measured efficiencies of the filters and the color gradient from
r′ to BC were used to determine appropriate subtraction scaling. Dust
contamination is an issue with C2 images. To remove dust contamination, scaled
r′ images taken as close as possible in time to the C2 images were
photometrically scaled using methods outlined in Farnham et al. (2000) and
subtracted from C2 images. Both CN and OH filters have a minimal, low-contrast
contribution from dust: this does not affect the analysis of the images
presented here. CN integration times were 900–1200 s; BC, 1200 s; C2, 1200;
and r′, 180. The CN image exposure times are different as a resulting of
optimizing the signal-to-noise ratio of the images.

Images obtained on the first night were taken under photometric conditions.
Observations of standard star HD 30246 was used for calibrating all comet
images. Sky background values were separated from the coma background by
extending a radial profile until it becomes indistinguishable from flat sky at
the signal-to-noise ratio of the background levels. This may result in slight
excess of background signal subtraction, though this amount is less than the
variation in sky flat signal (1–2%). Due to the large area of the detector, we
were able to measure background signal levels sufficiently far away from the
comet to eliminate coma contamination.

Inner coma structures are only a few percent above background coma signal
levels, so image enhancement techniques are required for monitoring evolution
of these structures, determining the periodicity of features, and measuring
outflow velocities of species. Because the original, reduced science images
are dominated by background comet flux for the species concerned, we used
radial profile-based enhancement methods described in Samarasinha & Larson
(2014). Sky background values were separated from the coma background by
creating a median pixel value radial profile centered on the nucleus until it
became indistinguishable from flat sky at the signal-to-noise ratio of the
background levels. Science images were then divided by the median image radial
profile to enhance coma features (Figure 1). This may result in slightly too
much background signal subtraction, but by less than the variation in sky flat
signal (1–2%). Owing to the large area of the detector, we were able to
measure background signal levels sufficiently far away from the comet to
eliminate coma contamination.

Figure 1: Four enhanced images of 45P taken in the CN filter on 2017 February
16 UT. Integration times are 900 s for (a) and 1200 s for (b) to (d). North is
up; east is to the left; 104 km scalebars are in the lower left; midpoints of
exposure times in UT hours are at bottom right. These images are color
enhanced to show contrast. Different CN exposure integration times were used
to optimize the signal-to-noise ratios of the images. The Sun position angle
of 262∘ is shown in the upper left of (a). Star trails are visible as bright,
straight, parallel lines. The images are color-enhanced to show contrast, with
purple corresponding to lower fluxes and light blue corresponding to higher
fluxes.

##  4 Results

Preliminary inspection of the raw, un-enhanced images revealed a bright
compact spot adjacent to the nucleus (Section 4.1). Enhanced images show a
repeating feature in CN associated with the bright compact spot not seen in
other filters (Section 4.2). C2 and dust images show jets in the same
direction as the repeating CN feature, but there is no detection of repeating
features (Sections 4.3; 4.4).

###  4.1 A bright compact release of material

A bright compact spot is visible in an un-enhanced image (Figure 2).
Preliminary inspection of the raw, un-enhanced images revealed a bright
compact spot with a projected area visible above the background coma of
$7.8\times 10^{4}$ km2 immediately to the west of the nucleus in the final CN
image of the night before dawn taken on February 16 12:42 UTC (Figure 2). The
area of the bright compact spot was measured by counting pixels with signal
above the background in the reduced, un-enhanced image. Measuring signal
obscured by the coma would affect photometric accuracy; thus, this measurement
is a lower bound on the area of the bright compact spot.

Possible explanations of the bright compact spot include jitter, optical
ghosts, and stars or other background objects: all of these would have
resulted in trailing visible in the image. Careful alignment of the nucleus
during image enhancement reveals a halo of emission around the bright compact
spot separate from the nucleus position (Figure 2), implying cometary-like
behavior of the bright compact spot, which would be unlikely if it were a
background asteroid or other astronomical object. It is likely that this
bright compact spot would have been visible in a C2 image; however, our
observing strategy close to sunrise prioritized CN and r′ images.

We calculated the production rate of material in the bright compact spot
(Figure 2) as approximately $3.7\times 10^{24}$ molecules s-1, consistent with
the overall flux for the inner coma of $2.2\times 10^{24}$ molecules per
second measured by Moulane et al. (2018), using fluorescent efficiencies for
CN at $R=1.05$ au (Schleicher, 2010).111A calculator for comet fluorescence
efficiencies/g-factors for common comet volatile species based on Schleicher
(2010) is available at: https://asteroid.lowell.edu/comet/cover_gfactor.html
Our calculated production rate is likely an underestimate because we only
measured signal detectable above background levels.

Using the production rate of the bright compact feature we calculated 4.4 kg
as a lower limit of the total CN mass ejected from the nucleus.

Figure 2: The final 900-s CN exposure of February 16 with a exposure midpoint
of 12:42 UTC. The first two images (a, b) are reduced but un-enhanced. The
final image (c) has been enhanced by azimuthal subtraction. The bright nucleus
is visible (a), and closer inspection (b) reveals a second bright spot
detached and to the west of the nucleus. The enhanced image (c) shows the
detached bright spot signal as part of a larger bright, discontinuous feature
moving away from the nucleus toward the northwest.

###  4.2 Repeating, Discontinuous CN Feature

Image enhancement revealed that the bright compact spot is part of a larger CN
cloud, roughly elliptical in shape, retreating from the nucleus (Figure 1). We
see CN material brightening at the nucleus then retreating as a large cloud of
material originating from the nucleus. The cloud brightness ramps up rapidly,
and the material moving away from the nucleus has a discontinuity in its
morphology: the material does not move as one continuous jet emission from the
nucleus along the northwest direction. A plume of material is initially
visible in the first images taken on February 16 (Figure 1a), which eventually
detaches from the nucleus as a 24,000 km $\times$ 16,000 km bean-shaped cloud
with the short axis aligned toward the nucleus (Figure 1b). A second plume
forms (Figure 1c), visible as a bright mass of CN gas detaches from the
nucleus (Figures 1d, 2). Ultimately, three separate clouds of CN gas are
visible moving away from the nucleus.

The duration of the observations on the first night (5.8 h) is less than one
full nucleus rotation (7.6$\pm$0.5 h, E.S. Howell, personal communication). We
fortuitously have CN images from the first and second night taken 22.8 h or
approximately three rotation cycles apart (Figures 4, 5). The repeating
feature is visible in the same position in both images. This periodicity is
consistent with a repeating event releasing material from the nucleus into the
inner coma.

Figure 3: Enhanced image of 45P inner coma taken at 11:39 UT on 2017 February
16, with the angular region from 220–360∘ position angle highlighted (a) and a
portion of the image unwrapped and projected into position angle-radial
distance space from 220–360∘ (b). Three separate CN emission events are
labeled; event 1 is closest to the nucleus. Figure 4: Side-by-side comparison
of images from 2017 February 16 and 17 taken 22.8 h apart. The February 16
image is a 1200-s exposure; the February 17 image is a 900-s exposure. The
signal-to-noise ratio is lower in the February 17 image than the February 16
image owing to non-photometric conditions and the shorter exposure time.
Figure 5: Radial profiles of the repeating CN feature in the northwest
quadrant of the images taken on February 16 (a) and 17 (b). Profiles are
created by averaging signal over an azimuthal arc of 5∘ centered on the
nucleus to reduce signal from star trails and other noise. The sole profile
measured on February 17 (black; b) matches up with a profile taken the
previous night (yellow), approximately three rotation periods of $7.6\pm 0.1$
hours later. There is no shifting of the 09:19 February 16 profiles
superimposed over the February 17 profile (b). Vertical separation along the
y-axis between profiles is exaggerated to emphasize details in both plots.

We measured radial profiles (Figure 5) of the material moving to the northwest
of the nucleus, averaging over a wedge of 5∘ to reduce signal from star
trails. The radial profiles show a two-peaked mass of material moving away
from the nucleus into the coma. Subsequent observations show the peaks
broadening and dissipating as the cloud of material retreats from the nucleus.
Despite coverage gaps in the imaging sequence, a second emission of CN gas
becomes visible and leads to the bright signal visible in raw images (Figure
2).

Unwrapping the enhanced images into projected position angle-radial distance
space allows for improved tracking of material moving radially and thus
visibility of the three discrete clouds of material expanding away from the
nucleus (Figure 3). Three discrete clouds of material are visible moving away
from the nucleus. Because of the discontinuities in emission intensity visible
in the cloud radial profiles, it is possible to measure the expansion velocity
of retreating CN gas. We measured the center of the expanding cloud moving at
a projected velocity of $\sim$0.8 km s-1, approximately the velocity of gas
expansion at 1 au (Budzien et al., 1994). The sky plane-projected velocity
would be nearly the same as the actual outflow velocity for broad features
(e.g., Samarasinha, 2000). The cloud itself has an expansion velocity of
$\sim$0.5 km s-1.

###  4.3 C2 and OH features

The expanding cloud appears to be present in the C2 images, as well as the
southeast jet structure, though the greater continuum background in the C2
images makes detection by visual inspection more difficult (Figure 6a). C2 has
a broader spatial distribution than CN, which is consistent with CN being
primarily a daughter (second-generation) product, whereas C2 is primarily a
granddaughter (third-generation) product and thus has more opportunity to
retreat from the nucleus and increase its spread.

The bright compact feature that we observed in an un-enhanced CN image (Figure
2) does not appear in the un-enhanced C2 images, making it difficult to
constrain the mass of C2 released. Moulane et al. (2018) measured the C2/CN
production rate as $0.04\pm 0.003$; we therefore estimate that C2 adds 5–10%
of the mass of CN to the total amount of mass ejected ($\sim$4.6–4.8 kg).

Two jet structures are visible in the OH image (Figure 6c): a strong jet
pointing approximately 350∘, and a fainter jet pointing in the southeast
direction ($\sim 100^{\circ}$). The latter jet corresponds in position angle
to the southeast jet in the CN images. There there is no evidence for an OH
cloud in the northwest direction that would correspond to jets seen in either
the carbon or dust filters.

Although the jet features visible in the r′, BC, C2, and CN images are in
similar positions to the southeast and northwest of the nucleus, there is only
a faint structure at a similar position angle for the OH jet. Indeed, the
stronger OH jet pointing N and carbon species emission to the E are offset by
110∘ as projected into the image plane.

The curvature of the southeast jet seen in C2, CN, and particularly OH
suggests that the positive angular momentum vector is toward the viewer in the
northwest quadrant of these images, as OH is constantly produced while in
sunlight.

The northwest dust jet appears continuous, without evidence of the
discontinuous clouds seen in CN (Figure 6). The larger outflow velocity of CN
compared to dust could obscure potential discontinuous emission of dust.

Figure 6: Four enhanced images of 45P in C2 (a), CN (b), OH (c), and dust (d)
filters at the same distance scales, all taken on 2017 February 16 UT. North
is up; east is to the left; 104 km scalebars are in the lower left; midpoints
of exposure times in UT hours are at bottom right. These images are color
enhanced to show contrast. The C2 image (a) shows two features, a strong one
in the northwest, and a fainter one in the southeast. The CN image (b) shows
an southeast jet and a discontinuous northwest jet. The OH image (c) is
dominated by a plume to the north ($\sim 350^{\circ}$) not seen in other
filters, as well as a faint east-pointing jet. The dust image (d) is dominated
by a bright northwest jet and a dimmer southeast jet, which is not the
direction of the dust trail.

###  4.4 Dust production

Two jets are visible in the filters representing dust (r′ and BC): one to the
southeast ($120^{\circ}$) and a second, stronger jet toward the northwest
($280^{\circ}$; Figure 6). The dust, CN, and C2 jets are oriented in the same
directions.

We, however, do _not_ see evidence for a large fragment or other repeating
feature in dust wavelengths. Thus, the process producing the repeating CN
feature is creating material only observable in the CN wavelengths. We
therefore conclude that this repeating feature consists primarily of CN. It
may contain some C2 gas, despite images of the latter lacking evidence for the
discontinuities seen in the CN wavelengths.

As the BC images show the same features as the r′ images, we limit the
analysis presented here to r′-filter images, which have more temporal coverage
and better signal-to-noise ratios with shorter exposure times. Although r′ is
a broadband filter and has some gas contamination,the flux in the r′images is
dominated by scattered dust, not by gas, unless the comet is very dust-poor.
The narrowband BC filter was designed to measure the continuum (i.e. by the
dust). The use of r′ as a proxy for dust has been successfully established for
other comets (e.g. Mueller et al., 2013; Knight et al., 2021). Images taken in
r′ require shorter integration times than BC to achieve high SNR, and also
have shorter star trails than BC. Otherwise, the images are indistinguishable.

##  5 Discussion

###  5.1 Possible causes of the repeating jet feature

The repeating CN feature to the northwest represents a short-duration release
of a small quantity of material. If an icy parent molecule, including but not
limited to HCN, is emitted from the nucleus that photodissociates to CN, the
mass of the parent molecules could be substantially larger, depending on the
time of parent molecule release. Considering that an unseen parent such as HCN
could be the majority of the mass in this feature, but we cannot detect HCN in
our filter set, 4.4 kg is the lower limit of the mass required to form this
visible repeating cloud feature. Regardless of whether the CN is emitted
directly from the nucleus in gaseous form, or photodissociates from a icy
parent molecule, the rapid conversion of this material from ice to gas results
in a high production rate for the periodic emission of CN.

Given the small quantity of CN and C2 ($\sim$9.2 kg; Section 4.1) required to
produce the repeating feature, the mechanisms responsible may be simple.
Whatever the source for the repeating jet feature seen during these
observations, it remains the same during the the time span of the
observations, and does not show appreciable depletion during the multiple
rotational cycles in which the inner coma was observed. Thus, a single one-
time event on the comet nucleus is unlikely to cause the repeating feature.

The shape of the nucleus of 45P in Arecibo Observatory planetary radar system
observations (S-band, 12.6 cm) shows varied near-surface topography at the
100-m scale (Figure 7, E.S. Howell, personal communication). The existence of
cliffs, pits, or crevasses would be consistent with the delay-Doppler data
taken of this comet during the same timeframe as the visible-wavelength
observations presented here. Exposed ices on nucleus topography would
sublimate when exposed to the Sun, potentially producing the repeating
northwest-oriented CN feature.

The source region receives enough solar insolation to produce sufficient CN to
create this repeating feature. Formation of the feature may occur either by
heating a high- to medium-thermal inertia region all day, or by near-
instantaneous heating of the source region after being shadowed for the rest
of the rotation period. The all-day scenario requires more topographic relief
in the source region, such as pits or cliffs, than instantaneous release of
CN-bearing material.

Figure 7: A delay-Doppler observation of the 45P comet nucleus taken by the
Arecibo Observatory S-band planetary radar system on 2017 February 12 UT. The
comet is 0.65 km in radius. Each pixel in the vertical direction represents 60
m. The nucleus is illuminated from the bottom. In delay-Doppler projection,
distance increases from the bottom of the image, and rotation velocity of the
object increases from the center horizontally. This image shows vertical
relief at the $\sim 100$-m scale, with steep features deviating from an
ellipsoidal nucleus. Credit: Arecibo Observatory/NSF.

The $\sim 3.31\times 10^{5}$ km scale length of CN molecules at 1.05 au
(Cochran, 1985) is larger than the radial distances from the nucleus to the
edges of our images ($\sim 3\times 10^{4}$ km; e.g., Figure 1). Either the
parent molecule of CN has a short lifetime, or CN originating directly from
the nucleus (Hänni et al., 2020) could explain the repeating jet and other CN
features so close to the optocenters of the images.

The detection of this repeating feature in CN and C2 but not in other
wavelengths may be consistent with heterogeneities in source regions of
volatile species, as has been observed by space missions at other comets. The
EPOXI mission at comet 103P/Hartley 2 observed different source locations for
several volatile species on the nucleus (A’Hearn et al., 2011; Dello Russo et
al., 2011).

Although we do not observe a periodic, repetitive release of dust from 45P, we
do see a fan of dust extending in the direction of the northwest feature seen
in CN and C2 wavelengths. This implies a possible relationship between the
periodic CN emission and the constant jet of dust. This could be consistent
with larger dust grains drifting at a slower velocity than the smaller CN and
C2 molecules: diurnal variation would effectively “smear” the dust.

For Hartley 2, Knight & Schleicher (2013) detected similar source regions for
CN and other carbon species, as well as OH and NH, but concluded that the
latter were likely derived from smaller grains affected by radiation pressure.
Moretto et al. (2017) observed changes at 9P/Tempel 1 in CO2 abundance while
H2O remained constant, as well as a correlation between the CO2 and dust
distributions; a similar mechanism could be at work for 45P.

The Rosetta mission to comet 67P/Churyumov–Gerasimenko observed that gas
emission and volatile source regions are distributed non-uniformly over the
nucleus surface (Hässig et al., 2015; Bockelée-Morvan et al., 2015; Migliorini
et al., 2016; Fink et al., 2016; Fougere et al., 2016). Further, Rosetta
observations showed that jet formation corresponds to active pits (Vincent et
al., 2015) and dust and gas emission varies with temperature conditions (solar
illumination) (Alí-Lagoa et al., 2015; Lara et al., 2015). The spacecraft also
detected gas-only outbursts from 67P (Feldman et al., 2016).

Other comets exhibit structures in their gas features, particularly CN jets
that can form Archimedean spirals, including 1P/Halley (Klavetter & A’Hearn,
1992), Hale-Bopp (Mueller et al., 1997), and 103P/Hartley 2 (Samarasinha et
al., 2011). At 45P, the motion of the cloud away from the 45P nucleus, and its
expansion, do not resemble an Archimedean spiral. There is precedent for
discontinuities in material emissions into the inner coma: observing on C/1996
B2 (Hyakutake), Harris et al. (1996) reported a “detached sunward facing
plume.” Several jet features could have formed into spirals or repeating
features; the orientation was such that they would have been difficult to
observe from Earth. Further, Wierzchos & Womack (2020) fond that outbursts of
CO do not always correlate with dust.

##  6 Conclusions & Future Work

We analyzed 19 images of comet 45P taken 2017 February 16–17 near perigee in
the CN, C2, OH, and BC Hale-Bopp campaign narrowband filters, as well as r′,
in conjunction with a multi-wavelength observing campaign. We found the
following:

  * •

A bright compact spot adjacent to the nucleus in the CN filter shows comet-
like behavior, indicating a rapid release of a CN parent product material,
with a total mass of $\sim$9.2 kg.

  * •

This small amount of material could be released from changing solar
illumination of surface topology on the nucleus or via another simple process:
due to the low mass, a complex mechanism need not be responsible for the
bright compact spot.

  * •

A high-contrast, repeating CN feature associated with the bright compact spot
retreats away from the nucleus at $\sim 0.8$ km s-1, corresponding to the gas
expansion velocity.

  * •

The time interval between repetition of the feature is similar to the radar-
derived rotation period ($7.6\pm 0.1$ h) for 45P.

  * •

Different position angles for jets from different gas and dust species implies
source region heterogeneity on the nucleus for these species.

The repeating CN feature may represent a process common on JFCs as they
approach the Sun, yet typically obscured from ground-based observations owing
to outer coma species obscuring gases such as CN, which may originate directly
from the nucleus. Owing to the low spatial resolutions of ground-based
observations, investigation of how common repeating features such as this one
are may prove challenging.

Comets 41P/Tuttle-Giacobini-Kresák (41P) and 46P/Wirtanen (46P), two other
small JFCs, passed within 0.14 au of Earth in 2016–2019 and were observed as
part of the coordinated, multi-wavelength campaign in which we observed 45P.
Image reduction, enhancement, and analysis of narrowband visible-wavelength
observations of 41P and 46P are ongoing. Nevertheless, we encourage
coordinated, multi-wavelength campaigns conducted with medium-sized telescopes
for future close approaches of Jupiter-family or other comets to explore
whether features like the one observed at 45P are characteristic of comets as
they approach perihelion, or whether this behavior is unique to 45P.

We are honored to be permitted to conduct astronomical research on Iolkam
Du’ag (Kitt Peak), a mountain with particular significance to the Tohono
O’odham Nation in Southwestern Arizona. We are grateful to the Steward
Observatory TAC for granting us 60+ total nights of observation time in the
spring 2017 semester as part of the larger 41P/45P/46P campaign. We appreciate
the expertise of the Kitt Peak National Observatory and Steward Observatory
staff and faculty, in particular Joseph Hoscheidt, Melanie Waidanz, Scott
Swindell, and Elizabeth “Betsy” Green. We also thank the maintenance/custodial
staff of the telescope buildings and dormitories. The authors thank the
Arecibo Observatory staff and scientists who helped take the delay-Doppler
data, and express our condolences to the greater Arecibo community on the loss
of the extraordinary 305-m William E. Gordon Telescope in December 2020. AS
thanks Ross A. Beyer, Clément Feller, Sierra N. Ferguson, Hamish C.F.C. Hay,
Margaret E. Landis, Tod R. Lauer, Raphael Marschall, Laura C. Mayorga, Henry
Ngo, Timothy E. Pickering, Christopher W. Porter, and Maria E. Steinrueck for
useful science conversations and assistance with data reduction. C. Wolner
provided editing assistance. This research has made use of NASA’s Astrophysics
Data System Bibliographic Services, the AstroBetter blog and wiki, the JPL
Horizons On-Line Ephemeris System, and Astropy, a community-developed core
Python package for astronomy. Observations were supported by NASA Solar System
Observations grant NNX16AG70G; this analysis was supported in part by NASA
FINESST award 80NSSC20K1374.

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Shrajan<EMAIL_ADDRESS>Dejan
<EMAIL_ADDRESS>Zahra
<EMAIL_ADDRESS>Tobias Fechtertobias.fechter@uniklinik-
freiburg.de2 Simon K.B<EMAIL_ADDRESS>Constantinos
<EMAIL_ADDRESS>Anca-Ligia
<EMAIL_ADDRESS>Radu<EMAIL_ADDRESS>Technische Universität Wien, Vienna, Austria Department of Radiation Oncology,
University Medical Centre Freiburg, Germany Segmentation of Prostate Tumours
from PET Images

# Segmentation of Prostate Tumour Volumes from PET Images is a Different Ball
Game

###### Abstract

Accurate segmentation of prostate tumours from PET images presents a
formidable challenge in medical image analysis. Despite considerable work and
improvement in delineating organs from CT and MR modalities, the existing
standards do not transfer well and produce quality results in PET related
tasks. Particularly, contemporary methods fail to accurately consider the
intensity-based scaling applied by the physicians during manual annotation of
tumour contours. In this paper, we observe that the prostate-localised uptake
threshold ranges are beneficial for suppressing outliers. Therefore, we
utilize the intensity threshold values, to implement a new custom-feature-
clipping normalisation technique. We evaluate multiple, established U-Net
variants under different normalisation schemes, using the nnU-Net framework.
All models were trained and tested on multiple datasets, obtained with two
radioactive tracers: [68Ga]Ga-PSMA-11 and [18F]PSMA-1007. Our results show
that the U-Net models achieve much better performance when the PET scans are
preprocessed with our novel clipping technique.

Figure 1: Example of CT (left) and [68Ga]Ga-PSMA-11 PET (right) images with
annotated prostate gland (red) and tumour (green). Center: Cropped pelvic
regions with the prostate and tumour (top: CT and bottom: PET). These images
highlight the importance of correct modality for RT, as the tumour volume is
more pronounced in PET than in CT. Algorithm 1 FCN Algorithm for GTV
Segmentation. The algorithm finds the optimal upper threshold limit based on
the SUV values of all PET images in the training dataset.

Input: data - $x$, labels - $y$

Output: maximum threshold limit - $maxT$

for $p=20\%$ to $70\%$ increment $2\%$ do

for $i=1$ to sample-count($x$) do

threshold $=p~{}*$ max$(x_{i})*0.01$ $\triangleright$ Save threshold value

for $j=1$ to voxel-count$(x_{i})$ do

if $x_{i}(j)\geq$ threshold then

$y^{\prime}_{i}(j)=1$

else

$y^{\prime}_{i}(j)=0$

end if

end for

Calculate DSC$(y^{\prime}_{i},y_{i})$ and NSD$(y^{\prime}_{i},y_{i})$
$\triangleright$ Save DSC and NSD metric results

end for

Calculate average DSC$(y^{\prime},y)$ and average NSD$(y^{\prime},y)$
$\triangleright$ for each p

end for

Find $p_{max}DSC$ where, $p_{max}=p$ for highest average DSC

Find $p_{max}NSD$ where, $p_{max}=p$ for highest average NSD

Find average SUV threshold ($t_{max}DSC$) value at $p_{max}DSC$

Find average SUV threshold ($t_{max}NSD$) value at $p_{max}NSD$

return maxT = average of $t_{max}DSC$ and $t_{max}NSD$

Figure 2: Left and Center: Performance of semi-automatic contouring approaches
on the intra-prostatic SUV, of the PET images for 68-Ga and 18-F tracers. All
voxels with uptake values equal-to and above the SUVmax$\%$ threshold, are
considered as tumour, and the rest as background. For Dice coefficient (DSC)
and normalised surface dice (NSD), the higher their value the better the
prediction, whereas, for the Hausdorff Distance 95% percentile (HD-95) is the
other way around. The best performance for all three metrics is achieved
between 30%-40%. Right: The absolute threshold uptake values of all images for
a given percent. Most of the average threshold values lie in the range 3-10.

##  1 Introduction

Prostate Cancer (PCa) is an ubiquitous malignancy in men that accounts for
nearly 30% of all diagnosed cancers in the USA and Europe [Sung et al. (2021),
Marhold et al. (2022), Siegel et al. (2024)]. Radiotherapy (RT) is one of the
primary treatment approaches, that demands precise localization of gross-
tumour volumes (GTV) and organs at risk (OAR) [Kerkmeijer et al. (2021),
Zamboglou et al. (2022)]. Common medical imaging modalities, such as computed
tomography (CT) and magnetic resonance imaging (MR) provide detailed
anatomical information. However, GTV segmentation from CT and MR volumes is
challenging [Eiber et al. (2016), Spohn et al. (2020)].

Recently, positron-emission tomography (PET) scans demonstrated a significant
potential for identifying tumour volumes, particularly intra-prostatic lesions
using prostate-specific membrane antigen (PSMA). PET images excel in
characterizing metabolic activity using the standardized uptake value (SUV),
which is directly proportional to the intensity of radioactive tracer uptake
by cancer cells. This phenomenon is evident in the PET scans in Figure 1.

To remedy the challenges posed by manual segmentation [Draulans et al. (2021),
Spohn et al. (2020)], deep-learning-based (DL) approaches, such as U-Nets
[Ronneberger et al. (2015), Çiçek et al. (2016)], have been investigated to
automatically segment PCa from PET scans [Kostyszyn et al. (2020), Xu et al.
(2023), Holzschuh et al. (2023)]. In spite of these works, research on tumour
delineation from PET images is relatively limited compared to other clinical
modalities. Hence, there is a scarcity of well-established configurations and
preprocessing pipelines for PET segmentation tasks. Current research works
rely upon normalisation schemes tailored for CT and MR volumes [Kostyszyn et
al. (2020), Xu et al. (2023), Holzschuh et al. (2023), Isensee and Maier-Hein
(2023), Murugesan et al. (2023), Hadlich et al. (2023)]. These preprocessing
techniques may not be suitable for PET images, since they factor SUV values
from the full image. Whereas, PET scans illustrate intensity values based on
the localised and concentrated metabolic activities of the body region
[Zamboglou et al. (2019), Spohn et al. (2020), Zamboglou et al. (2022)]. Since
the network performance is reliant on normalisation methods [Litjens et al.
(2017), Isensee et al. (2021)], there is an urgent need for robust
preprocessing steps in PET segmentation.

In this work, we overcome the shortcomings of the existing research in two
steps. First, we investigated the various normalisation techniques currently
in use, and scrutinised their impact on the performance of GTV segmentation
from PET images. Additionally, we leveraged the insights of the physicians
during manual annotation, by incorporating SUV-threshold values in our
preprocessing steps. This novel normalization method is called as feature-
clipping normalisation (FCN). The FCN algorithm helps to find all-encompassing
optimum threshold value for different datasets, especially when dealing with a
specific type of PSMA-tracer.

In the second step, to assess the benefits of our new FCN method, we compared
four U-Net variants: Classic U-Net, Attention-U-Net, and their inductive-bias
extensions, IB-U-Net, and IB-Attention-U-Net, respectively. We conducted our
experiments with multiple PCa datasets with different tracers, namely
[68Ga]Ga-PSMA-11 (68-Ga) and [18F]PSMA-1007 (18-F), and objectively evaluated
the models. The results showed that our SUV threshold-based normalisation
improves the accuracy of all the networks. In summary:

  * •

Our main contribution in this paper, is to develop a novel feature-clipping
normalisation method, we call FCN, that provides custom clipping limits
according to the threshold values used by physicians while performing the
manual segmentation.

  * •

Another contribution in this paper is to empirically demonstrate that our new
feature-clipping normalisation improves the accuracy of the networks for PCa
segmentation from PET images, irrespective of the PSMA tracer and SUV-
threshold values.

  * •

Finally, we also implemented our FCN method and all the U-Net variants used
(U-Net, IB-U-Net, Attention U-Net and IB-Attention U-Net) in the popular
state-of-the-art nn-Unet framework. The code is open source, and the framework
is easy to use.

##  2 Literature Review

###  2.1 U-Net variants

Since the release of the 2D U-Net architecture in 2015 [Ronneberger et al.
(2015)], numerous revisions and variants have been proposed [Punn and Agarwal
(2022)]. Many of these variations propose extensions and advances, and have
achieved state-of-the-art (SOTA) performances: V-Net [Milletari et al.
(2016)], Attention U-Net (Oktay et al., 2018), U-Net++ (Zhou et al., 2019),
and SegResNet (Myronenko, 2019). Bhandary et al. (2022) compared the
performances of these models using the nn-UNet framework Isensee et al. (2021)
on multiple medical segmentation tasks. Inspired by the inner workings of the
vertebrate retina, the authors also introduced inductive biased (IB) On-and-
Off convolutional filters in the second encoder of the U-Net architecture. The
addition of IB filters in the network structure improved the accuracy of
segmentation networks, and made them robust against artefacts. They
demonstrated superior performance for small-sized datasets, especially in
tasks pertaining to the prostate gland Bhandary et al. (2022).

###  2.2 GTV segmentation

Before we discuss various DL-based algorithms, we first evaluate threshold-
based PET image segmentation approaches. Zamboglou et al. (2019) examined $20$
patients with PCa who underwent 68-Ga PSMA-11-PET/CT followed by radical
prostatectomy. They carried out manual and semi-automatic segmentations, and
concluded that SUV capping ($SUV$min-max $0$–$5$) or thresholding ($20\%$ of
$SUV$max) could provide high sensitivity, and should be considered for PSMA-
PET-based focal therapy approaches. The study by Spohn et al. (2020) subjected
$10$ patients to 18-F PSMA-1007 PET, and then performed radical prostatectomy.
They observed that manual contouring with PET scaling of $SUV$min-max
$0$–$10$, or a semi-automatic approach with a threshold of $20\%$ of $SUV$max
offer the best results.

Tamal (2020) conducted a review of different fixed and adaptive threshold-
based PET image segmentation approaches under a common mathematical framework.
The author highlighted the advantages and disadvantages of the threshold-based
methods from the perspectives of diagnosis, treatment planning, and response
assessment. In their experiments, they also observed that a fixed threshold-
based method is dependent on the tumour, to background ratio, and the size of
the tumour, and therefore, recommended adaptive threshold-based methods. Tamal
(2020) advocated that SUV-based threshold methods hold merit, and proposed
that advanced adaptive approaches such as DL algorithms could improve GTV
segmentation.

Over the past decade, convolutional neural networks (CNNs), such as the
U-Nets, have demonstrated their ability as an invaluable tool that can adapt
automatically to complex medical segmentation tasks. However, depending upon
image modality, segmentation of the prostate gland and the associated tumour
volumes is extremely challenging. For example, some of the works that
performed PCa segmentation from MR images did not achieve good results Bressem
et al. (2022); Saha et al. (2022). On the other hand, there are some instances
where U-Net based GTV segmentation have been moderately successful.

One of the earliest works on prostate tumour delineation from PET images by
Kostyszyn et al. (2020), employed a 3D U-Net Çiçek et al. (2016). The dataset
consisted of 68-Ga PSMA-11-PET images, and were normalised with global
intensity values. Likewise, Holzschuh et al. (2023) trained a 3D U-Net on a
18F-PSMA-PET dataset, and evaluated the resultant model on internal and
external test sets. In the preprocessing steps, although the authors cropped
the PET images to the pelvic region, an arbitrary $SUV$max value of $15$ was
used to clip the data. The overall segmentation performances in Kostyszyn et
al. (2020) and Holzschuh et al. (2023) were good. However, in both instances,
we also observed a lack of meaningful comparison with other networks, and did
not find a rationale behind choosing the normalisation methods.

Recently, AutoPET-II challenge Gatidis et al. (2023) was organized with the
goal to segment cancer lesions, such as malignant melanoma, lymphoma, and lung
cancer. In spite of large and multifaceted network architectures, the
segmentation accuracies of the top ranking submissions were low. A possible
explanation could be that the participants in the competition utilised various
normalisation schemes, normally applied to CT and MR images Isensee and Maier-
Hein (2023); Murugesan et al. (2023); Hadlich et al. (2023).

These studies highlight the rapid advancements in the field of PET imaging,
particularly PSMA-PET, for prostate cancer. Although the integration of deep
learning networks has enabled a more accurate and efficient segmentation of
GTV, there is still considerable room for improvement, and standardisation.

##  3 Methods and Materials

###  3.1 Datasets

In this paper, we used two in-house prostate-specific membrane antigen (PSMA)
PET datasets. Simultaneously, CT scans were also captured to locate OARs. The
datasets comprised of PET images that were collected using two unique tracers:
Gallium (68-Ga) gozetotide or Gallium (68-Ga) PSMA-11, and piflufolastat
(18-F).

The multi-institutional 68-Ga dataset consists of a combined total of 168
scans collected at Centres A (n = 142), and B (n = 26). Out of the 168
volumes, 151 collated from Centres A (n = 125) and B (n = 26), respectively,
were used during training. The remaining 17 volumes from Centre A were used
for final testing. The second, 18-F PSMA-PET data consists of 131 training
images from Centre A. Testing was done on 50 patient images that were
collected from an independent internal cohort from Centre A (n = 19), and from
an independent external cohorts obtained from Centre C (n = 14).

In both datasets, the manual segmentation of the prostate on CT, and the
tumour volumes on the PET images were generated by expert physicians of the
respective groups in consensus. To decrease the inter-observer variability,
validated techniques were used to annotate the tumour on PET. For the 68-Ga
PSMA-PET dataset, a scaling range of $SUV$min$-SUV$max of [$0-5$] was used by
the physicians during annotations, whereas, $SUV$min$-SUV$max of [$0-10$], was
used for the 18-F dataset. The scaling was applied uniformly cross all the
images based on the type of tracer, including in-house and external sets.

All the images (PET volume, prostate contour and PCa ground-truth labels) were
resampled to a voxel size of $2\times 2\times 2$ $mm^{3}$. The PET scans were
resampled with B-spline interpolation, while the annotated prostate and tumour
contours were resampled using nearest neighbour interpolation technique. The
PET volumes and the GTV ground-truth labels were cropped around the prostate,
and we added a second channel, consisting of the prostate mask, along with the
PET image as input. This improved overall segmentation performance. Finally,
all of these volumes were converted to the nnU-Net framework format for the
experiments.

###  3.2 Existing Normalisation Schemes

One of the crucial aspect of this study is the evaluation of different
normalisation schemes on PET-based tumour segmentation performance. The nnU-
Net framework, by default, offers two of the most popular normalisation
techniques, namely $Z$-score for MR and other non-CT images, and global
normalisation with percentile clipping for CT images. Equation (1) gives the
formula for computing the $Z$-score using local (single image) parameters:

$\begin{array}[]{l@{\
}l}x^{\prime}_{i}(j)&=\frac{x_{i}(j)-\mu_{i}}{\sigma_{i}},\qquad x_{i}\in
x={x_{0},...,x_{N}-1}\end{array}$ (1)

where, $x$ is the full training set with $N$ samples, $x_{i}$, the $i$th
sample, $x_{i}(j)$, the raw value at voxel $j$, $\mu_{i}$, the mean of all
voxels in sample $i$, $\sigma_{i}$, the standard deviation of all voxels in
sample $i$, and $x^{\prime}_{i}$, the standardized value of the $i$th sample.

Generally, for CT images, each voxel intensity of an image is first clipped to
a minimum of $0.5$ percentile and a maximum of $99.5$, of all voxels in the
entire training dataset, as given by Equation (2). Then Equation (3) is used
to standardize the clipped voxel value, using the global parameters (across
all images). Thus:

$\begin{array}[]{l@{\ }l}x(J)_{\text{0.5percentile}}~{}\leq x_{i}(J)~{}\leq
x(J)_{\text{99.5percentile}}\end{array}$ (2) $\begin{array}[]{l@{\
}l}x^{\prime}_{i}(j)&=\frac{x_{i}(j)-\mu_{J}}{\sigma_{J}},\qquad x_{i}\in
x={x_{0},...,x_{N}-1}\end{array}$ (3)

where, $x$ is the full training set with $N(0-n)$ samples, $J$, represents all
the voxels in all images $x$, $x_{i}$ is the $i$th sample, $x_{i}(j)$ is the
raw value at voxel $j$, $\mu_{J}$, the mean of all voxels in $x$,
$\sigma_{J}$, the standard deviation of all voxels in $x$, and
$x^{\prime}_{i}$ is the standardized value of the $i$th sample.

In addition to $Z$-score and CT( global normalisation with clipping), we added
a clipping-based normalisation, based on the uptake threshold limits applied
during manual delineation in Holzschuh et al. (2023). We call this fixed clip,
and the minimum threshold (min$T$) was $0$, whereas, the maximum limit
(max$T$) was set to $15$ Holzschuh et al. (2023). However, it should be noted
that normalisations were applied to only the first channel consisting of PET
images, as the second is a binary mask of the prostate contours.

###  3.3 Feature Clipping Normalisation (FCN)

The motivation and idea behind the algorithm is based on the combination of
the manual and semi-automatic contouring technique recommended by the
physicians in Zamboglou et al. (2019) and Spohn et al. (2020), and the review
by Tamal (2020). As mentioned in Section 3.1, both 68-Ga and 18-F PSMA-PET
datasets were manually annotated after scaling them to a particular fixed
value ($5$ and $10$ for 68-Ga and 18-F, respectively). Instead of using these
fixed maximum bounds to scale the intensity values, our FCN method
automatically finds the upper clipping value (max$T$) for preprocessing a
specific dataset. Since the least voxel SUV is for most PET images is usually
$0$, the lower clipping value (min$T$) was set to $0$.

The method to find the optimal upper bound is illustrated in Algorithm 1. We
decided to use a search range from 20% to 70% of $SUV$max with an increment of
2. As mentioned in Algorithm 1, if the SUV for a voxel was greater than the
threshold value, then it was considered as a tumour, otherwise normal. Using
this, a prediction image was obtained and compared against the ground-truth
label using NSD ($\uparrow$), HD-95 ($\downarrow$) and DSC ($\uparrow$)
metrics. The evaluation results between the ground-truth labels, and
predictions using the metrics, are showcased in Figure 2 (left and centre).
The percentage-wise absolute threshold ($t$) value from Algorithm1 for each
image is displayed as a box plot (right) in Figure 2.

As shown in the metrics graphs of Figure 2 (left and centre), our FCN semi-
automatic contouring method achieved the highest performance, for percentages
between $30$ to $40$. Above $40\%$, the accuracies dip, and this is true for
both datasets. The top NSD value is $0.30$ for the 68-Ga tracer, and $0.38$
for the 18-F tracer. Similarly, the top DSC value is $0.45$ for the 68-Ga
tracer, and $0.54$ for the 18-F tracer. From the box plots of Figure 2, the
average SUV-threshold for the percent range $30$ to $40$ is between $3$ and
$10$ for both the 68-Ga and 18-F datasets. The final max$T=5.142$ for 68-Ga,
and max$T=8.736$ for 18-F training datasets. This is approximately equal to
the SUV limits used during manual segmentation. We would like to point that,
we did not consider the results of HD-95 metric to determine the upper
threshold limit (max$T$). This is because, hausdorff distance does not have an
upper bound (range: $0-\infty$), and therefore, gives inaccurate measurements
for empty volumes Maier-Hein et al. (2022).

###  3.4 Implementation of our framework

We used the versatile and robust data pipeline of the nnU-Net framework
(version $2$) Isensee et al. (2021) to build our tumour-segmentation solution.
As mentioned in Section 3.2, $Z$-score and CT( global normalisation with
percentile clipping) are already available in the nnU-Net framework. The fixed
clip and FCN normalisation methods implemented by us can be utilised by
specifying the type of normalisation scheme (when required) in the
dataset.json file. For a given PSMA-PET dataset, the upper bound (max$T$) is
calculated during the experiment planning and dataset fingerprint extraction
phases. Finally, all the PET images are clipped to min$T=0$ and the max$T$
value obtained previously. We evaluated four different 3D models (did not use
2D versions), namely the U-Net, IB-U-Net, Attention-U-Net, and IB-Attention-U-
Net. The IB-extended versions were chosen for their robustness abilities
against distribution shifts Bhandary et al. (2022). The new normalisation
schemes (including the FCN) and the additional network architectures were
implemented in PyTorch Paszke et al. (2019), in accordance to the nnU-Net
framework Isensee et al. (2021) guidelines.

The nnU-net framework has data pipelines that carry out various data
augmentations. For both 68-Ga and 18-F datasets, a mini-batch size of 6 was
used. In addition to the final prediction, the outputs of deep supervision
layers were used for the final loss calculation. We used a compound loss
function, which is a combination of cross-entropy loss and dice loss Milletari
et al. (2016), to optimise the networks. All the models were trained for 1000
epochs, and a sliding window technique with an overlap size of $50\%$ was used
during inference. Due to the possibility of multiple tumour lesions in a given
image, the default post-processing step (retain only the largest connected
component) was not applied.

###  3.5 Experiments and Results

We conducted our GTV segmentation experiments in two ways with U-Nets using
the nnU-Net framework. The first procedure used existing normalisation schemes
($Z$-score, CT and fixed clip); whereas, the second method used the automatic
FCN mentioned in Section 3.3. For both stages, we investigated the different
U-Net variants using 5-fold cross-validation (CV) experiments. Each model was
trained on both the 68-Ga and 18-F PSMA-PET datasets with four different
normalisation schemes. The experiments were run on an NVIDIA Titan RTX with 24
GB memory. We evaluated the overall performances using three metrics: NSD
($\uparrow$), HD-95 ($\downarrow$) and DSC ($\uparrow$), however, for brevity
we only present the results using NSD in this paper. Segmentation performances
using DSC and HD-95 are given in the appendix.

PSMA | Training | Testing | Model | Z-score | CT | fixed clip: | FCN
---|---|---|---|---|---|---|---
tracer | data | data | name |  Isensee et al. (2021) |  Isensee et al. (2021) |  $0$-$15$ Holzschuh et al. (2023) | (ours)
68-Ga |  |  | UNet | $0.579$ | $0.609$ | $0.637$ | $\mathbf{0.661}$
Centres A + B | Centre A | IB-UNet | $0.616$ | $0.637$ | $0.668$ | $\mathbf{0.699}$
n = 151 |  n = 17 | Att. UNet | $0.553$ | $0.650$ | $0.652$ | $\mathbf{0.666}$
|  | IB-Att. UNet | $0.601$ | $0.664$ | $0.671$ | $\mathbf{0.705}$
18-F |  |  | UNet | $0.657$ | $0.713$ | $0.700$ | $\mathbf{0.738}$
| Centre A | IB-UNet | $0.686$ | $0.720$ | $0.718$ | $\mathbf{0.747}$
|  n = 19 | Att. UNet | $0.656$ | $0.726$ | $0.701$ | $\mathbf{0.741}$
Centre A |  | IB-Att. UNet | $0.677$ | $0.751$ | $0.685$ | $\mathbf{0.761}$
n = 131 |  | UNet | $0.545$ | $0.587$ | $0.601$ | $\mathbf{0.644}$
| Centre C | IB-UNet | $0.598$ | $0.596$ | $0.616$ | $\mathbf{0.657}$
|  n = 14 | Att. UNet | $0.543$ | $0.605$ | $0.608$ | $\mathbf{0.653}$
|  | IB-Att. UNet | $0.603$ | $0.600$ | $0.627$ | $\mathbf{0.667}$
Table 1: Comparison of U-Net variants all implemented by us in the same nnU-
Net framework, for different normalisation methods, using NSD metric
($\uparrow$). Z-score standardises voxels using local mean and standard
deviation. CT first does percentile clipping and then standardises voxels
using global mean and standard deviation. fixed clip limits intensities to
pre-defined lower and upper bounds. Statistical significance difference
between best performing FCN preprocessing scheme against the rest of the
normalisations is in bold.

Table 1 showcases the segmentation accuracy of all the four models for both
datasets across four different normalisation methods. It is clearly evident
that the networks that we preprocessed with FCN are superior to the existing
normalisation schemes. We also conducted model-wise statistical significance
tests (Wilcoxon-signed rank test) to compare the differences in performance
between the top ranking normalisation scheme (FCN) versus the remaining three
(Z-score, CT and SUV clip). This is highlighted in bold face in Table 1, and
please refer to the appendix for the detailed results. The low $p$ values
($p\,{<}\,0.05$) for the NSD metric in Table 1 indicate our feature-clipping
technique is the best normalisation scheme for the both the tracers, 68-Ga and
18-F. For both tracers, the IB-variants have surpassed the original versions,
and the highest segmentation accuracy is attained by the IB-Attention U-Net.
Figure 3 shows the qualitative behaviour of the four models, for their best
normalisation schemes, respectively. The rank of the normalisation methods in
descending order is FCN, CT (68-Ga) or fixed clip (18-F), and $Z$-score.

Figure 3: A qualitative accuracy comparison of U-Net and Attention U-Net and
their IB extended variants on the prostate tumour segmentation task. All the
PET images were scaled using the FCN algorithm, and then trained using the
U-Net models. As one can observe, the IB-versions perform better (fewer
instances of false positives), with the IB-Attention-Net, achieving the best
performance. Furthermore, the results show that the tumours are prominently
differentiable from the background with 18-F tracer, in contrast to 68-Ga.

##  4 Discussion and Conclusion

In this paper, we have successfully demonstrated the effectiveness and the
practical applicability of U-Net-based CNN architectures in the segmentation
of tumour volumes from PSMA-PET images. More importantly, we have shown that
our FCN approach offers a significant advancement over semi-automatic
delineation methods, and other diverse normalisation techniques. We have also
investigated four different U-Net variants across two different PSMA tracers.
Our results indicate that the FCN algorithm helps to provide a more accurate,
more efficient, and more reproducible means of tumour volume analysis. The FCN
algorithm was developed to encapsulate the intuition of the physicians and
doctors to improve segmentation from PET images. By clipping the PET images,
the networks are able to better focus of on the local information around the
prostate. This advantage is not present in other normalisation techniques,
such as $Z$-score and CT.

Despite these advancements, our study acknowledges certain limitations, such
as the size and diversity of the dataset used. Our work is currently limited
to PCa segmentation, that is localized to the pelvic region. None of the
models achieved superior performance (NSD$\,{>}\,0.8$), and this is because
like CT and MR scans, PET images are highly diffused. It is difficult to
estimate the tumour growth, prostate whole-gland, and zonal boundaries with
high certainty due to imaging limitations. Furthermore, the high degree of
inter-observer heterogeneity, during manual segmentation of tumours from PET
images, could further exacerbate the difficulties of supervised learning
approaches, such as the U-Net. Because of this, it is possible that the models
start replicating the subjective errors of the annotators.

On the positive note, prostate GTV segmentation from PET images is better when
compared to CT and MR scans, as the SUV intensities are extremely beneficial
in locating the lesions in the images. As shown in Figure 3, the models are
quite adept in segmenting the tumour volumes, prominently from PSMA-PET images
for the 18-F tracer. In our future work, to ensure generalizability and
robustness, we aim to validate the proposed normalisation techniques, and
segmentation algorithms on larger and more heterogeneous datasets, such as the
AutoPET-III Gatidis et al. (2023). Additionally, we will also explore the
integration of these CNN-based techniques, into open-source software for
medical image computing, such as the 3D Slicer software Fedorov et al. (2012).
Another avenue of future research, would be to take advantage of the trained
model weights, and use them to classify the tumour grades based on Gleason
Scores.

In conclusion, this paper demonstrates the effectiveness of U-Nets, and their
inductive biased versions, in accurately delineating intra-prostatic GTV in
PSMA-PET images. Our results show that by employing an appropriate
normalisation technique, in conjunction with the labelling protocols used by
the physicians, helps to improve the segmentation performance. Moreover, when
compared to their seminal architectures, the IB-extended UNets are more
versatile and robust in accurately delineating PCa from PET images.

## Acknowledgement

This research was funded in part by the Austrian Science Fund (FWF): I 4718,
and the Federal Ministry of Education and Research (BMBF) Germany, under the
frame of the Horizon-2020 ERA-PerMed call JTC-2019 Project Personalized
Medicine: Multidisciplinary Research Towards Implementation (PersoRad). Z. B.
was supported by the Doctoral College Resilient Embedded Systems, which is run
jointly by the TU Wien’s Faculty of Informatics and the UAS Technikum Wien.

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