# Test-beam Performance Results of the FASTPIX Sub-Nanosecond CMOS Pixel
Sensor Demonstrator

Justus Braach  CERN, 1211 Geneva, Switzerland  Institut für
Experimentalphysik, University of Hamburg, 20146 Hamburg, Germany
Correspondence<EMAIL_ADDRESS>Eric Buschmann  CERN, 1211 Geneva,
Switzerland  Dominik Dannheim  CERN, 1211 Geneva, Switzerland  Katharina Dort
CERN, 1211 Geneva, Switzerland  II. Physikalisches Institut, University of
Giessen, 35390 Giessen, Germany  Thanushan Kugathasan  DPNC, University of
Geneva, 1205 Geneva, Switzerland  Magdalena Munker  DPNC, University of
Geneva, 1205 Geneva, Switzerland  Walter Snoeys  CERN, 1211 Geneva,
Switzerland  Peter Švihra  CERN, 1211 Geneva, Switzerland  Mateus Vicente
DPNC, University of Geneva, 1205 Geneva, Switzerland

###### Abstract

Within the ATTRACT FASTPIX project, a monolithic pixel sensor demonstrator
chip has been developed in a modified $180\text{\,}\nm$ CMOS imaging process
technology, targeting sub-nanosecond timing precision for single ionising
particles. It features a small collection electrode design on a
$25\text{\,}\um$-thick epitaxial layer and contains 32 mini matrices of 68
hexagonal pixels each, with pixel pitches ranging from $8.66$ to
$20\text{\,}\um$. Four pixels are transmitting an analog output signal and 64
are transmitting binary hit information. Various design variations are
explored, aiming at accelerating the charge collection and making the timing
of the charge collection more uniform over the pixel area. Signal treatment of
the analog waveforms, as well as reconstruction of digital position, time and
charge information, is carried out off-chip. This contribution introduces the
design of the sensor and readout system and presents performance results for
various pixel designs achieved in recent test-beam measurements with external
tracking and timing reference detectors. A time resolution below
$150\text{\,}\ps$ is obtained at full efficiency for all pixel pitches.

###### keywords:

monolithic pixel sensor, particle detection, fast timing

##  1 Introduction

Vertex and tracking detectors for future high-energy physics experiments face
stringent requirements in view of their spatial and temporal measurement
performance as well as the projected experimental conditions. Within the
ATTRACT FASTPIX project and under the umbrella of CERN’s strategic research
and development programme for future experiments (EP R&D) [Aleksa:2649646], a
monolithic pixel sensor demonstrator chip has been developed in a modified
$180\text{\,}\mathrm{nm}$ CMOS imaging process technology [ATTRACTFASTPIX]. It
targets sub-nanosecond time tagging of hits from single minimum-ionizing
particles, using small pixels of $\leq 20\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ pitch.
For FASTPIX small line width CMOS technologies allow the design of hexagonal
pixels with few-femtofarad collection electrodes and large signal-to-noise
ratios, in favour of detection efficiency and precise timing. Low-field
regions, non-uniform electric field configurations and space requirements for
complex in-pixel circuits introduce timing variation depending on the in-pixel
particle incidence location. In order to face a tradeoff between pixel size
and non-uniform timing, design variations are introduced to accelerate the
propagation of the signal charge and decrease the in-pixel timing variation.
The development of CMOS sensors with small collection electrode design using
Technology Computer Aided Design (TCAD) simulations was presented in
[Munker2019]. The sensor-design optimisation and the circuit design supporting
sensor timing performance in the sub-nanosecond range is presented in
[KUGATHASAN2020164461].
After first results from measurements with two matrices of a sample chip
presented in [instruments6010013], this publication accesses a larger set of
measurement data for a comparison of the various process modifications, sensor
layouts and pixel pitches. The aim is to investigate the potential of targeted
sensor process modifications and design optimisations for the detector
performance.

##  2 The FASTPIX Chip

###  2.1 Sensor Design

Figure 1: Photograph of the FASTPIX chip (left), divided in four quadrants of
matrices with pixel pitches I: $8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$,
II: $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$, III:
$15\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and IV:
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$. An exemplary picture and zoomed in
details of a $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pitch matrix (right).
Modified from [instruments6010013].

The layout of the FASTPIX chip shown in Fig. 1 is partitioned into four groups
of eight matrices each, with pixel pitch I:
$8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$, II:
$10\text{\,}\mathrm{\SIUnitSymbolMicro m}$, III:
$15\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and IV:
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$.

Figure 2: Wafer production process variants for FASTPIX represented by
schematic cross-sections of the pixel unit cells, showing a cut perpendicular
to the sensor surface. The standard $180\text{\,}\mathrm{nm}$ CMOS imaging
process (left) and the modified process variant (right) with added low-dose
n-type implant and optimizations such as a gap in the n-implant, retracted
deep p-well and additional extra-deep p-well implant.

The pixel pitch is the radial distance between two adjacent collection
electrodes or equivalent to the diameter of the incircle of a hexagonal pixel.
The sensor has been produced in multiple versions that are all based on two
variants of the manufacturing process illustrated in Fig. 2. The standard
process sets the baseline with no additional measures to accelerate the
collection of signal charge and with incomplete lateral depletion of the
sensor volume. A timing spread is introduced by a difference in charge
collection time for a hit in the corner compared to a hit in the center of the
pixel. Minimizing the maximum distance between charge generation and
collection is a first step in the optimization for timing uniformity and is
realized by the hexagonal arrangement of collection electrodes and the
$\mathcal{O}($10\text{\,}\mathrm{\SIUnitSymbolMicro m}$)$ pixel pitch. The
geometry also has an effect on charge sharing at the pixel corners with only
three neighboring pixels instead of four, as it is the case for rectangular
geometries. With the modified process, a uniform low-dose n-type implant is
introduced allowing full lateral depletion of the
$25\text{\,}\mathrm{\SIUnitSymbolMicro m}$ epitaxial layer.
In production $12$ process splits were implemented from combinations of
different doping concentration and two different versions of the two
lithographic photomasks that control the feature sizes of n-type and p-type
implantation into the epitaxial layer. Among those, optimizations geared
towards improved timing performance feature an additional extra-deep p-well
implant as well as a gap in the n-implant near the pixel edge.

Figure 3: Overview of 32 matrices implemented on a single FASTPIX chip. The
top-left scheme illustrates the parameter space of wafers produced using the
standard process, below a similar representation of 4 x 8 matrices on a chip
produced in the modified process. The four quadrants are indicated by light
blue roman numeral and are attributed their pixel pitch in the table on the
top right. Within each quadrant two different collection electrode sizes are
represented by white or hatched background. The matrices themselves are
illustrated by geometrical icons colored in yellow, orange, red, or dark-red
with the respective matrix number in bold white. The colorway indicates the
p-well opening size of the pixel cell. The deep p-well opening and extra-deep
p-well opening size is written along the outside edges of each quadrant. In
case of the modified process different deep n-implant (gap) geometries are
represented by the shape of the icon of a given matrix.

Both measures introduce a gradient in the doping profile and with that
increase the strength of the lateral electric field in the corner regions of
the pixel. A more pronounced pull away from the pixel border towards the
collection electrode accelerates charge collection by drift, reduces charge
sharing, maximizes the seed pixel signal and narrows the spread in timing
performance.
Fig. 3 gives an overview of the large parameter space of layout variations
implemented across the 32 matrices on a single FASTPIX chip. The following
sections will discuss FASTPIX samples of three wafers: W03 (standard process),
W15 (modified process), W18 (modified process with higher-dose deep
n-implant).

###  2.2 Frontend and Readout Architecture

The 68 active pixels of a given matrix are grouped into 64 digital and 4
analog channels that each have in-pixel circuitry for reset and leakage
current compensation and one stage of amplification. Due to space constraints
in the $180\text{\,}\mathrm{nm}$ CMOS imaging process, the second
amplification stage is moved to the matrix periphery. Analog channels are
routed through buffers while the signals for digital channels are processed by
a discriminator block with fast-OR logic and two delay lines offering a time-
based encoding of position, time and energy of a hit. The on-chip circuitry is
capable to resolve small differences in charge collection time to support a
detailed characterization of the timing performance of the sensor. Fast
signals need to be buffered to reach the matrix periphery where the
discriminators are implemented, which imposes a penalty on power consumption.
With $\approx 20\text{\,}\mathrm{mW}$ per pixel the circuit reaches a
simulated time jitter of $\approx 20\text{\,}\mathrm{ps}$
[KUGATHASAN2020164461]. The three low voltage differential output signals of
the chip are read out asynchronously and get processed further off-chip.

##  3 Measurement Setup

The chip is mounted on a carrier printed circuit board (PCB) which receives
power, bias and control from the Caribou readout system [Vanat:2020nS]. An
oscilloscope with $\mathcal{O}($\mathrm{GHz}$)$ analog bandwidth and a
sampling rate of
$\mathcal{O}($10\text{\,}\mathrm{GS}\text{\,}{\mathrm{s}}^{-1}$)$ is also
controlled by Caribou and used to record the digital channel signals. For the
test beam measurements presented in the following sections the setup is
installed in the CLICdp Timepix3 beam telescope at the SPS North Area at CERN
[DallOcco:2651308, AlipourTehrani:2270788, AbuslemeHoffman:429703]. FASTPIX
samples are positioned on a x-/y-/rotation-stage in the center of the
telescope between three upstream and three downstream Timepix3 reference
planes. The FASTPIX device under test (DUT) is operated at
$-6\text{\,}\mathrm{V}$ bias at the substrate and p-well electrodes. The
Micro-Channel-Plate Photomultiplier Tube (MCP-PMT) HPK R3809U-50 [R3809U]
provides reference time measurements [BORTFELDT2020163592] and is connected to
a fourth channel of the oscilloscope. To minimize the amount of material in
the telescope acceptance, the MCP-PMT is positioned after the downstream set
of telescope planes and is biased at $2.6\text{\,}\mathrm{kV}$ resulting in a
reference track time resolution of $<10\text{\,}\mathrm{ps}$.
Several FASTPIX samples have been tested in dedicated high-intensity
$120\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\light$ pion beam periods in 2022.
The small active area of the matrices typically yield between $100$ and $500$
hits per $4.8\text{\,}\mathrm{s}$ spill, resulting in average rates of [range-
phrase = – ]525. In preparation for test beam measurement campaigns, FASTPIX
samples have been commissioned, tested and calibrated following the
methodology presented in [instruments6010013]. To allow a good performance
comparison between matrices, the threshold for each matrix has been calibrated
by externally injecting electrical test pulse signals into two digital pixels
of a given matrix.

##  4 Reconstruction and Analysis

Offline reconstruction and analysis of the test-beam data is performed using
the software framework Corryvreckan [Dannheim2021], with extensions for the
time-based decoding of position and pulse height as well as the proper
treatment of the hexagonal pixel geometry.

###  4.1 Data Decoding

For FASTPIX the recorded raw waveforms require offline decoding
[instruments6010013]. The time-of-arrival (ToA) is calculated from the fast-OR
output of the chip providing the first edge of the fastest pixel signal in a
given matrix. The time-over-threshold (ToT) of a pixel signal follows as the
distance between a pair of rectangular pulses. The discriminator outputs a
pulse whenever the pixel signal rises above or falls below threshold. The
pixel position is obtained on the basis of a calibration of the FASTPIX delay
lines.
The temporal positions of the $64$ pixels within a delay line are determined
from a calibration of a given matrix using single-pixel hits. For decoding,
the coordinates of the spatial pixel center are attributed to the designed
order of pixels in the delay line. The spatial position of a recorded pixel
hit is then found by mapping the measured value to the calibrated pixel delays
on the delay line. Overlap between signals from pixels simultaneously crossing
the threshold poses a challenge for this pixel position en-/decoding scheme.
In case of signal overlap the correct position can still be identified, as
long as the relative majority of signal combinations from both delay lines
indicate the correct pixel position value. Hits that can not be completely
decoded are discarded in the data decoding stage.

###  4.2 Event building

The reference telescope planes provide spatial as well as temporal information
for pixel hits and are read out continuously and independently from the DUT.
The oscilloscope triggers on a fast logic OR combination of all pixels in a
FASTPIX matrix, providing the trigger information which is used to synchronize
DUT and telescope planes. The analysis of observables in the spatial and
temporal domain is based on telescope events that are linked to a trigger on
FASTPIX. For a study of detector efficiency the telescope data stream is
divided into $10\text{\,}\mathrm{\SIUnitSymbolMicro s}$ intervals of all
telescope events, independent of FASTPIX triggers. The time intervals are
sized to avoid large hit multiplicities leading to processing intensive amount
of combinations in subsequent reconstruction steps.

###  4.3 Clustering

Direct neighboring pixels collecting charge within a $200\text{\,}\mathrm{ns}$
time window are clustered and the pixel with the earliest timestamp is used to
set the cluster timestamp. Clusters get attributed a center position that is
used to reconstruct the hit position. In case of a single-pixel cluster the
hit position is obtained by using the pixel center. For cluster sizes $>1$ a
charge-weighted interpolation of the cluster geometry is applied, corrected
for non-linear charge sharing using an $\eta$-correction algorithm
[Wennloef2023]. For FASTPIX this correction is conducted in radial coordinates
(r,$\phi$) to account for the different symmetry axes of the hexagonal pixel
grid. Reconstructed cluster position and telescope track position are
translated to radial coordinates where correction parameters are calculated
and stored for each data taking run. The correction is then applied during a
second run of the analysis framework. Currently a first preliminary iteration
of hexagonal $\eta$-correction for cluster size 2 and 3 is implemented, an
addition to the correction module for cluster size 4 is in development. For
larger cluster sizes the charge-weighted interpolation regains cluster
position reconstruction accuracy and a correction for non-linear charge
sharing loses its impact.

###  4.4 Tracking

Straight line tracks are interpolated from combinations of clusters in
telescope planes, as implemented in Corryvreckan [Dannheim2021]. A track is
created as soon as clusters from a minimum $6$ telescope planes have been
associated to a particle trajectory, given they are within a set of spatial
($400\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in projected x-/y-distance) and
temporal cuts ($20\text{\,}\mathrm{ns}$). Cluster information from the device
under test (DUT) is still left out at this point in the reconstruction in
order to avoid a bias on the analysis.

###  4.5 DUT analysis

Tracks are matched to DUT clusters if they occur within a
$20\text{\,}\mathrm{ns}$ time window and if the distance between cluster
center and track impact position is smaller than the pixel pitch of the
investigated matrix. The matching is performed based on the distance between
the cluster center and interpolated track intersect. The analysis is set to
exclude telescope tracks with $\nicefrac{{\chi^{2}}}{{\text{ndf}}}>5$, at the
event edges ($250\text{\,}\mathrm{ns}$), during oscilloscope dead time
($5\text{\,}\mathrm{\SIUnitSymbolMicro s}$), while copying data from the
buffer to the measurement server or close to the oscilloscope frame edge
($>250\text{\,}\mathrm{ns}$). To avoid edge effects on the border of the pixel
matrix, especially for cluster sizes $>$ $4$ in the 4 x 16 pixel matrices,
clusters with track intersect outside of the central 2 x 14 pixels are
discarded.

###  4.6 Timewalk correction

For studies of time measurement precision, the fastest-signal pixel in a
cluster is used to calculate the time residual with respect to the time
reference. Fig. 6 shows the residuals over seed-pixel ToT for all pixels in
the inner $2$ x $14$ pixel region of a FASTPIX matrix.

[t]0.495  [t]0.495

Figure 4: Without correction. Figure 5: With timewalk correction. Figure 6:
Time residuals as function of seed signal for all pixels in the inner $2$ x
$14$ pixel region of a $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pitch
matrix.

[t]0.495  [t]0.495

Figure 7: Mean time residual in relation to in pixel track position. Figure 8:
Mean number of pixels per cluster in relation to in pixel track position.
Figure 9: Time residual and cluster-size maps for in-pixel track incidence
positions in x-/y-plane of a $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel
pitch matrix. Hits from all pixels are projected into one hexagonal pixel
area.

The equivalent in-pixel plot and a related in-pixel cluster-size distribution
is shown in Fig. 9 and presents a dependency of the timing performance and
correlated cluster size on the in-pixel particle incidence location. This
suggests a time-walk correction approach per cluster size applied on subsets
of data. For each cluster size $\leq 5$ an exclusive data set is assembled and
used to evaluate the time residual in relation to ToT on a pixel-by-pixel
level. Clusters $>5$ are grouped into a combined set to retain sufficient
statistics for further analysis. The correction is obtained by calculating the
mean of each ToT bin of one half of a data set and subtracting said mean from
the corresponding entries in the other half of the data set, and vice versa.
Fig. 6 shows the residuals over seed-pixel ToT for all pixels in the inner
region of a FASTPIX matrix after time-walk correction. The cluster-size-
specific subsets have been rejoined after individual correction and are
presented together in a single plot.

##  5 Results

###  5.1 Cluster Size and Efficiency

Figure 10: Cluster-size distributions of a baseline
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrix on W03 and W15.

Fig. 10 shows normalized cluster-size distributions for
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrix number $3$ from
the standard process sample W03 and the modified process sample W15.
On all wafers matrix $3$ features pixels with a
$0.86\text{\,}\mathrm{\SIUnitSymbolMicro m}$ collection electrode,
$4.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ p-well opening and
$16.03\text{\,}\mathrm{\SIUnitSymbolMicro m}$ deep p-well opening.

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Figure 11: W03, matrix 3, $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel
pitch. Figure 12: W15, matrix 3, $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$
pixel pitch. Figure 13: Matrix efficiency maps from a standard process (left)
and a modified process (right) sample at a threshold of
$38\text{\,}\electron$. The color scale shows the efficiency for each track
position bin on the x-/y-plane.

The pixel edge of the same matrix on W15 is lined by an uninterrupted deep
n-implant and has an $18.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ extra-deep
p-well opening, two modifications that accelerate charge collection by drift,
reduce charge sharing and decrease cluster size. Both cluster-size
distributions follow similar trends and mean cluster size measures $1.83(2)$
pixels per cluster for W03 and $1.78(2)$ pixels per cluster for W15, with
statistical uncertainty.
Fig. 13 shows efficiency maps of matrix $3$ on W03 and W15. The plots present
a consistently efficient area of the matrix without visible structures
introduced by characteristics of the chip or systematic features. A drop in
efficiency along the edge is caused by charge sharing with inactive dummy-
pixels surrounding the matrix edge making the sensitive area slightly larger
than the 4 x 16 active pixels.
Fig. 16 shows in-pixel efficiency maps of the same matrices with no visible
characteristics of the pixel implant geometry or systematic features across
the pixel area.

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Figure 14: W03, matrix 0, $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel
pitch, threshold $38\text{\,}\electron$. Figure 15: W15, matrix 0,
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch, threshold
$38\text{\,}\electron$. Figure 16: In-pixel efficiency maps from a standard
process (left) and a modified process (right) sample. Hits from all pixels are
projected into one hexagonal pixel area. The color scale shows the efficiency
for each triangular track position bin subdividing the hexagonal area on the
x-/y-plane.

For both samples matrix $3$ is able to achieve fully efficient operation at a
similar threshold of $38\text{\,}\electron$ without significant difference in
cluster size or efficiency.
However, this observation changes for the smallest pixel pitch. Fig. 19 and
Fig. 22 show matrix and in-pixel efficiency maps of
$8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ matrix $0$ from the standard
process sample W03 and the modified process sample W15, respectively.

[t]0.495  [t]0.495

Figure 17: W03, matrix 3, $8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel
pitch, threshold $66\text{\,}\electron$. Figure 18: W15, matrix 3,
$8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch, threshold
$51\text{\,}\electron$. Figure 19: Matrix efficiency maps from a standard
process (left) and a modified process (right) sample. The color scale shows
the efficiency for each track position bin on the x-/y-plane.

Across all wafers matrix $0$ features pixels with a
$0.86\text{\,}\mathrm{\SIUnitSymbolMicro m}$ collection electrode,
$3.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$ p-well opening and
$4.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ deep p-well opening. On W15 pixels
in the same matrix have a continuous deep n-implant and a
$7.45\text{\,}\mathrm{\SIUnitSymbolMicro m}$ extra-deep p-well opening, two
modifications that accelerate charge collection by drift, reduce charge
sharing and decrease cluster size.
The efficiency plots present a consistently efficient area of the matrix as
well as pixel area.

[t]0.495  [t]0.495

Figure 20: W03, matrix 3, $8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel
pitch, threshold $66\text{\,}\electron$. Figure 21: W15, matrix 3,
$8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch, threshold
$51\text{\,}\electron$. Figure 22: In-pixel efficiency maps from a standard
process (left) and a modified process (right) sample. Hits from all pixels are
projected into one hexagonal pixel area. The color scale shows the efficiency
for each triangular track position bin subdividing the hexagonal area on the
x-/y-plane.

With respect to the modified process sample W15, the standard process sample
W03 experiences a decrease in efficiency of approximately
$35\text{\,}\mathrm{\char 37\relax}$ for
$8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrix $0$.
Part of the cause of this decrease is a difference in physical threshold for
W03 at $66\text{\,}\electron$ compared to a threshold value of
$51\text{\,}\electron$ for sample W15. A higher threshold reduces the observed
mean cluster size, as lower-signal pixels in the border region of a cluster
fall below threshold and remain undetected. If both samples operated fully
efficient at the same threshold, the standard process sample W03 is expected
to yield larger cluster size compared to the modified process sample W15 due
to the larger amount of charge sharing (see Section 2.1). With a
$15\text{\,}\electron$ higher threshold for the standard process sample W03
the difference in cluster size between both process variants is reduced.
The cluster-size distribution in Fig. 23 shows a 3 times higher mean cluster
size for the modified process sample W15, compared to the the standard process
sample W03.

Figure 23: Cluster-size distributions of a
$8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrix on W03 and
W15.

A cause can be found from the implications of the very small
$8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch. A decrease in pitch
towards smaller pixel size distributes a given amount of generated charge in
the epitaxial layer to a larger number of pixels covering the area above the
particle incidence. This results in an on average smaller signal on each pixel
of a cluster, reducing both the efficiency and the measured cluster size. The
larger amount of charge sharing in the standard process enhances this
reduction of efficiency and measured cluster size. The geometry of the FASTPIX
matrix imposes another effect that alters the registered cluster size in small
pitch matrices. Another effect alters the registered cluster size in the
$8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrices as some
clusters span or even extend beyond the $4$ pixel height of the matrix.
Clusters from tracks traversing a given matrix outside of the center line of
the matrix experience edge effects. A fraction of their charge is deposited
outside of the matrix, is not collected by active pixels and therefore not
accounted for in a cluster size measurement. Consequently, a share of clusters
get misidentified with a smaller size. To mitigate this effect the
reconstructed local intercept position is used to only allow cluster seed
pixel positions in the inner $2$ x $14$ pixels of a matrix. Comparing results
for $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrix $3$ in Fig.
10 and $8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrix $0$ in
Fig. 23, a shift in mean cluster size towards smaller values has been measured
for standard process sample W03 matrix $0$, in contrast to the expected
observation considering the differences in process variants.
The results show how the process modifications of the modified process sample
W15 help to contain the charge within a single pixel and with that give more
margin for efficient detector operation of small-pitch matrices.

###  5.2 Spatial Residuals

An observable closely linked to cluster size is the width of the spatial
residual distribution, shown for a $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$
pitch matrix from modified process sample W18 in Fig. 26.
Similar to modified process sample W15, the sample W18 was produced in the
modified process but with a higher-dose deep n-implant, which accentuates the
achievable depletion and electric field configuration discussed in Section 2.1
even further.
An overview of the width of spatial residuals along the x-axis including all
FASTPIX matrices of wafer $18$ is shown in Fig. 26 in form of the RMS values
between $1.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$4.2\text{\,}\mathrm{\SIUnitSymbolMicro m}$ against matrix number.

[t]0.495  [t]0.495

Figure 24: $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pitch matrix $1$ at a
threshold of $62\text{\,}\electron$. The full distribution yields
$\text{RMS}=$1.89(4)\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ and
$\sigma_{\text{fit, gaus}}=$1.82(5)\text{\,}\mathrm{\SIUnitSymbolMicro m}$$.
Figure 25: Overview of the width of spatial residuals along the x-axis
measured with the W18 sample. The superscript of each data point gives the
threshold in electrons for the respective matrix. Figure 26: Spatial residuals
along the x-axis measured with the W18 sample.

Smaller pitch matrices achieve lower RMS values due to the higher granularity
and since larger mean cluster size and a tendency for lower electron
thresholds allow for a more precise reconstruction of the DUT hit position
with respect to the interpolated track intersect. Sub-threshold and matrix
edge effects previously discussed in Section 5.1 impact the amount of detected
charge and with that have a negative influence on residual width for the
smaller pixel pitches.
The $8.66\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrices achieve
a spatial resolution down to $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ after
unfolding the telescope tracking resolution of
$1.7\text{\,}\mathrm{\SIUnitSymbolMicro m}$ [AlipourTehrani:2270788].

###  5.3 Time Residuals

[t]0.495  [t]0.495

Figure 27: Time residual from matrix $23$ at a threshold of
$74\text{\,}\electron$. The full distribution yields
$\text{RMS}=$107(2)\text{\,}\mathrm{ps}$$,
$\text{RMS}_{$99.7\text{\,}\mathrm{\char
37\relax}$}=$103.0(3)\text{\,}\mathrm{ps}$$ and $\sigma_{\text{fit,
gaus}}=$102(1)\text{\,}\mathrm{ps}$$. The errors represent statistical
uncertainties. Figure 28: Overview of the width of time residual distributions
from all W18 matrices. The superscript of each data point gives the threshold
in electrons for the respective matrix. Figure 29: Time residuals along the
x-axis measured with the W18 sample.

Timing performance is evaluated for the modified process with higher-dose deep
n-implant. The higher dose n-implant of the W18 sample accentuates the
gradient in the doping profile and the lateral component of the field, driving
charges from the pixel border towards the collection electrode maximizing the
seed pixel signal and reducing time-walk effects. The width of the time
residual is shown in Fig. 29 for $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$
pixel pitch matrix $23$. The RMS yields $107(2)\text{\,}\mathrm{ps}$ and is
slightly higher than the width of a Gauss fit
$\sigma=$102(1)\text{\,}\mathrm{ps}$$ performed on the same set of data. The
fit is in good agreement with the RMS${}_{$99.7\text{\,}\mathrm{\char
37\relax}$}=$ $103.0(3)\text{\,}\mathrm{ps}$, for which the outmost
$0.3\text{\,}\mathrm{\char 37\relax}$ of outliers are excluded from the
calculation.
For a selection of FASTPIX matrices of modified process sample W18 a high-
statistic set of data is available, exhibiting less contribution of non-
Gaussian tails in the time residual. With $\approx 30$ times more entries than
in e.g. Fig. 29 the impact of pixel pitch is illustrated by Fig. 32.

[t]0.495  [t]0.495

Figure 30: Matrix $1$, $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch
at a threshold of $62\text{\,}\electron$. The distribution yields
$\text{RMS}=$140.7(2)\text{\,}\mathrm{ps}$$,
$\text{RMS}_{$99.7\text{\,}\mathrm{\char
37\relax}$}=$128.0(2)\text{\,}\mathrm{ps}$$ and $\sigma_{\text{fit,
gaus}}=$121.5(2)\text{\,}\mathrm{\SIUnitSymbolMicro m}$$. Figure 31: Matrix
$3$, $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch at a threshold of
$80\text{\,}\electron$. The distribution yields
$\text{RMS}=$138.2(2)\text{\,}\mathrm{ps}$$,
$\text{RMS}_{$99.7\text{\,}\mathrm{\char
37\relax}$}=$109.0(2)\text{\,}\mathrm{ps}$$ and $\sigma_{\text{fit,
gaus}}=$104.4(2)\text{\,}\mathrm{\SIUnitSymbolMicro m}$$. Figure 32: Time
residual distributions for two matrices of modified process sample W18. The
errors represent statistical uncertainties.

Both matrices differ in pixel pitch while the other pixel design modification
parameters are equal, except deep p-well and extra-deep p-well opening which
both have a specific size for each pixel pitch in the quadrants of the FASTPIX
chip (see Fig. 3). The $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch
matrix achieves $15\text{\,}\mathrm{\char 37\relax}$ better timing performance
compared to the $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch.

The timewalk-correction approach presented in Section 4.6 enables an
investigation of the contribution of seed pixel signals of different size
clusters to the time measurement precision of the chip. In case of a cluster
size $>1$ less signal is collected by the seed pixel, giving way to time-walk
effects. Moreover, for large cluster size it is more likely that a particle
hit falls on the corner of the pixel, where charge collection is slower and
exhibits more spread in collection speed.
Fig. 35 shows the width of time residuals from subsets of data sorted by
cluster size. Time difference values
$\Delta\text{t}=\text{t}_{\text{DUT}}-\text{t}_{\text{MCP}}$ for cluster sizes
$\leq 5$ are sorted in exclusive data sets while clusters $>5$ are grouped in
a combined set.

[t]0.495  [t]0.495

Figure 33: Matrix $1$, $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch
at a threshold of $62\text{\,}\electron$. The distribution for single-pixel
clusters yields: $109.2(1)\text{\,}\mathrm{ps}$
RMS${}_{$99.7\text{\,}\mathrm{\char 37\relax}$}$ Figure 34: Matrix $3$,
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch at a threshold of
$80\text{\,}\electron$. The distribution for single-pixel clusters yields:
$103.2(1)\text{\,}\mathrm{ps}$ RMS${}_{$99.7\text{\,}\mathrm{\char
37\relax}$}$ Figure 35: Time residual width
(RMS${}_{$99.7\text{\,}\mathrm{\char 37\relax}$}$) per cluster size for two
matrices of modified process sample W18. The error bars represent the
statistical uncertainties. The superscript of each data point gives the number
of entries in the subset of the underlying time residual distribution.

In both cases, independent of pitch, single pixel clusters reach the best
performance with a higher probability of collecting the majority of deposited
charge in a singular pixel. Doubling the pixel pitch yields an improvement of
$6\text{\,}\mathrm{\char 37\relax}$, from an
RMS${}_{$99.7\text{\,}\mathrm{\char 37\relax}$}$ of $109\text{\,}\mathrm{ps}$
for the $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrix to
$103\text{\,}\mathrm{ps}$ in case of the
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch matrix. Large pixel
pitch is in favor of timing performance as a large part of the signal charge
is collected by the seed pixel, reducing time-walk effects.

Fig. 29 shows an overview of the time residual RMS of all FASTPIX matrices
based on a low-statistic set of data. The impact of different pixel design
modifications can be discussed by isolating all matrices of equal pitch from
the overview in Fig. 29.
The data points for matrices with $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$
pixel pitch are colored in pink. In this subset the baseline is matrix $3$
which achieves a time residual RMS of $138\text{\,}\mathrm{ps}$. Following
Fig. 3, this matrix features pixels with a
$0.86\text{\,}\mathrm{\SIUnitSymbolMicro m}$ collection electrode,
$4.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ p-well opening,
$16.03\text{\,}\mathrm{\SIUnitSymbolMicro m}$ deep p-well opening and
$18.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ extra-deep p-well opening. The
pixel edge is lined by an uninterrupted deep n-implant without modifications
of the deep n-implant geometry.
For matrix $7$ a hexagonal $2.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$ corner
gap gets added to the deep n-implant while the other parameters remain
unchanged. The gap increases the strength of the lateral electric field in the
corner regions of the pixel which accelerates charge collection by drift,
reduces charge sharing and maximizes the seed pixel signal. The improved
timing performance yields a time residual RMS of $118\text{\,}\mathrm{ps}$.
Another variation of the deep n-implant is found in matrix $23$ where the
corner gap is changed to a $3.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$
triangular geometry. The larger gap produces an even more pronounced pull away
from the pixel corner towards the collection electrode and further narrows the
spread in timing performance, resulting in a time residual RMS of
$106\text{\,}\mathrm{ps}$.
Matrix $19$ differs from matrix $3$ in terms of p-well opening size, while the
remaining parameters stay the same. Reducing the area of the p-well benefits a
uniform depletion over the full pixel area, favours charge collection but also
cuts into the area available for in-pixel circuitry and its complexity. The
smaller p-well area of matrix $19$ with a
$6.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$ p-well opening achieves a time
residual RMS of $123\text{\,}\mathrm{ps}$.
The collection-electrode size is another parameter that is changed throughout
these eight matrices. Increasing the size of the collection electrode has
similar beneficial effects as the change in p-well opening but comes with a
penalty for signal-to-noise ratio and power consumption. Comparing matrix $19$
($123\text{\,}\mathrm{ps}$) and $27$ ($112\text{\,}\mathrm{ps}$) shows the
impact of a change in collection electrode size from
$0.86\text{\,}\mathrm{\SIUnitSymbolMicro m}$ to
$2.0\text{\,}\mathrm{\SIUnitSymbolMicro m}$ with an uninterrupted deep
n-implant geometry. Comparing matrix $7$ ($118\text{\,}\mathrm{ps}$) and $15$
($110\text{\,}\mathrm{ps}$) yield slightly less gain in timing performance
from the same difference in collection electrode size with a hexagonal
$2.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$ corner gap.
In comparison with matrix $3$, an approximate doubling of the collection
electrode size and a $\approx 50\text{\,}\mathrm{\char 37\relax}$ increase in
p-well opening size brought improvements in timing performance of $\approx
9\text{\,}\mathrm{\char 37\relax}$ and $\approx 12\text{\,}\mathrm{\char
37\relax}$, respectively. The larges improvement was observed with the
addition of corner gaps, especially the triangular corner gaps could yield a
decrease in time residual width of $\approx 17\text{\,}\mathrm{\char
37\relax}$ compared to the baseline matrix $3$.

##  6 Conclusions

FASTPIX was successfully integrated in the Timepix3 telescope, the Caribou DAQ
and Corryvreckan-based reconstruction and analysis framework. Large data sets
allowed the comparison of the various process modifications, sensor layouts
and pixel pitches.
The process modifications have shown to be essential to maintain efficient
operation for small pixel pitch matrices. FASTPIX reaches a spatial resolution
down to $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$\mathcal{O}($100\text{\,}\mathrm{ps}$)$ timing precision for the modified
process with higher-dose deep n-implant.
The impact of sensor design optimization was presented in context of timing
performance results for $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch
matrices from a modified process sample with higher-dose deep n-implant. The
largest relative improvement was observed for additional triangular corner
gaps, followed by improvements from a change in collection electrode and
p-well opening size.
The obtained FASTPIX results with $180\text{\,}\mathrm{nm}$ technology
demonstrate the large potential of targeted sensor process and TCAD
simulation-based design optimisations for the detector performance. Similar
optimisations are also applicable in $65\text{\,}\mathrm{nm}$ process
technology, which enables higher circuit density and thereby allows to include
advanced readout circuitry for precise timing inside a larger pixel matrix.

## Acknowledgments

Author Contributions:

J.B.: Investigation, Software, Visualization and Writing-Original Draft; E.B.:
Investigation, Software and Visualization; D.D.: Investigation, Supervision,
Writing-Review and Editing; K.D.: Investigation; T.K.: Investigation; M.M.:
Investigation; W.S.: Conceptualization and Funding Acquisition; P.S.:
Investigation; M.V.: Investigation. All authors have read and agreed to the
published version of the manuscript.

Funding:

This project has received funding from the ATTRACT project, funded by the
European Commission under grant agreement 777222.
This work has been sponsored by the Wolfgang Gentner Programme of the German
Federal Ministry of Education and Research (grant no. 05E15CHA).

Institutional Review Board Statement:

Not applicable.

Informed Consent Statement:

Not applicable.

Data Availability Statement:

The data supporting the findings of this study are available within the
article.

Infrastructure:

We would like to gratefully acknowledge the CERN SPS beam physicists and
accelerator staff for the reliable and efficient test beam operation. We thank
Eraldo Oliveri for his help with providing and operating the MCP-PMT.

Conflicts of Interest:

The authors declare no conflicts of interest.


:
ML4H Extended Abstract Arxiv Index 2021 2021 Machine Learning for Health
(ML4H) 2021

# Using Deep Learning to Identify Patients with Cognitive Impairment in
Electronic Health Records

Tanish Tyagi1 Authors contributed equally Colin G. Magdamo11footnotemark: 11
Ayush Noori1 Zhaozhi Li1 Xiao Liu1 Mayuresh Deodhar1 Zhuoqiao Hong1 Wendong
Ge1 Elissa M. Ye1 Yi-han Sheu1 Haitham Alabsi1 Laura Brenner1 Gregory K.
Robbins1 Sahar Zafar1 Nicole Benson1 Lidia Moura1 John Hsu1 Alberto Serrano-
Pozo1 Dimitry Prokopenko1 Rudolph E. Tanzi1 Bradley T. Hyman1 Deborah Blacker1
Shibani S. Mukerji1 M. Brandon Westover1 Sudeshna Das1
1{ttyagi, cmagdamo, anoori1, zli39, xliu61, mdeodhar, zhong1, wendong.ge,
emye, ysheu, halabsi, lnbrenner, grobbins, sfzafar, nbenson, lidia.moura,
john.hsu, aserrano1, dprokopenko, dblacker, rtanzi, bhyman, smukerji,
mwestover, sdas5} @mgh.harvard.edu  Massachusetts General Hospital and McCance
Center for Brain Health Boston  MA

###### Abstract

Dementia is a neurodegenerative disorder that causes cognitive decline and
affects more than 50 million people worldwide. Dementia is underdiagnosed by
healthcare professionals — only one in four people who suffer from dementia
are diagnosed. Even when a diagnosis is made, it may not be entered as a
structured International Classification of Diseases (ICD) diagnosis code in a
patient’s charts. Indeed, information relevant to cognitive impairment (CI) is
often found within electronic health records (EHR) but manual review of
clinician notes by experts is both time consuming and often prone to errors.
Automated mining of these notes presents an opportunity to label patients with
cognitive impairment in EHR data. We developed natural language processing
(NLP) tools to identify patients with cognitive impairment and demonstrate
that linguistic context enhances performance for the classification task. We
fine-tuned our attention based deep learning model, which can learn from
complex language structures, and substantially improved accuracy (0.93)
relative to a baseline TF-IDF (term frequency-inverse document frequency) NLP
model (0.84). Further, we show that deep learning NLP can successfully
identify dementia patients without dementia-related ICD codes or medications.

###### keywords:

EHR, NLP, Dementia

##  1 Introduction

Dementia is the most common neurodegenerative disease affecting older adults,
progressing from mild cognitive impairment (MCI) to mild, moderate, and severe
dementia. Dementia is underdiagnosed (AlzheimerAssociation, 2021): dementia is
not formally diagnosed or coded in claims data for over 50% of older adults
living with probable dementia. Often, a diagnosis is given once patient has
reached moderate dementia, and irreversible damage has already been done to
the brain. The early detection of the first signs of cognitive impairment,
however, is important for improving clinical outcomes and patient management.
Tools that can efficiently and effectively analyze medical records for warning
signs of dementia and recommend patients for follow up with a specialist can
be critical to obtaining an early diagnosis for dementia. We aim to use NLP to
detect signs of cognitive impairment from unstructured clinician notes by
using deep learning techniques. Such a tool could also be useful in recruiting
into clinical trials as well as a variety of research studies. We apply our
deep learning algorithm to patients in Mass General Brigham (MGB) Healthcare
who have genotype data available from the MGB BioBank. An overview of our
project can be found in Appendix 3.

##  2 Related Works

Prior works have used NLP techniques to detect various diseases from EHR.
(Rajkomar et al., 2018) used recurrent neural networks (long short-term memory
(LSTM)) among others to predict inpatient mortality using EHR data from the
University of California, San Francisco (UCSF) from 2012 to 2016, and the
University of Chicago Medicine (UCM) from 2009 to 2016. (Glicksberg et al.,
2018) performed phenotyping for diseases such as Attention Deficit
Hyperactivity Disorder (ADHD) by clustering on word2vec embeddings from EHR of
the Mount Sinai Hospital (MSH) in New York City. These studies have shown that
the application of NLP techniques to EHR have improved disease detection, and
that NLP techniques can be applied to dementia detecton to achieve similar
results. Our work uses deep learning NLP techniques, which has achieved
impressive results when applied to general text due to the use of word
embeddings and attention-based models (Vaswani et al., 2017; Mikolov et al.,
2013; Pennington et al., 2014; Peters et al., 2018; Devlin et al., 2018), but
have had limited applications in healthcare, particularly in dementia
research.

##  3 Dataset, Preprocessing, and Annotations

### Dataset

Our dataset consisted of a cohort (N = 16,428) of patients from the Mass
General Brigham (MGB) HealthCare (formerly Partner’s Healthcare, comprising
two major academic hospitals, community hospitals, and community health
centers in the Boston area) system who were older than 60 years (as of July
13, 2021), had APOE genotypes—the biggest genetic risk factor for Alzheimer’s
disease (Mahley and Rall Jr, 2000)—available from the MGB BioBank, and at
least one clinician note with a dementia-related keyword. tab:table1 shows
demographics of the cohort of patients.

### Preprocessing

For each patient in our dataset, we extracted unstructured clinician notes,
identified matches to 18 dementia-related keywords (Appendix
LABEL:app:keywords, including those related to memory, cognition,
neuropsychological tests, and dementia diagnoses. We constructed sequences
from the note text spanning each of these matches (of length 800 characters).
Our cohort of 16,428 patients had 279,224 sequences with dementia-related
keywords in total.

tab:table1  Characteristic (N = 16428) Age (years) mean (SD) 73.01 (7.96)
Gender Male, _n_ (%) 8740 (53.2) Race, _n_ (%) White 14896 (90.7) Other/Not
Recorded 608 (3.7) Black 570 (3.5) Hispanic 170 (1.0) Asian 168 (1.0)
Indigenous 16 (0.01) APOE Genotype, _n_ (%) APOE ${\bm{\varepsilon}}$2 2028
(12.3) APOE ${\bm{\varepsilon}}$3 10177 (62.0) APOE ${\bm{\varepsilon}}$4 4223
(25.7) Average Speciality Visits (SD) 1.67 (4.6) Average PCP Encounters (SD)
5.25 (5.63)

Table 1: Demographics of Data

### Annotations

A subset of sequences was annotated for indication of cognitive impairments.
We defined cognitive impairment as evidence of MCI, where one cognitive domain
is involved, or dementia, where more than one cognitive domain is involved and
activities of daily living are affected. Concern from the family of the
patient or the patient was not considered as cognitive impairment. Experts
annotated sequences using a web-based annotation tool (Appendix B) and labeled
them as 1) Yes, i.e., patient has CI; 2) No i.e., Patient does not have CI;
and 3) Neither (NTR) i.e., sequence has no information on patient’s cognition.
Appendix 6 shows example sequences for all 3 classes.

We assigned 5,000 diverse sequences containing at least one match to every
keyword from 5,000 unique patients for labeling. In order to expedite
annotations, we utilized an “always pattern” scheme. An always pattern is
defined as a phrase or regex expression that in any context indicates the
phrase will be labeled with a particular class (i.e. yes, no, or neither).
Once an always pattern is defined, all other sequences that match the pattern
are automatically labeled with that always pattern’s class. For examples of
always patterns for all three classes (Yes, No, Neither), see Appendix 6.

The final dataset of 8,656 annotated sequences from N = 2,487 unique patients
was split between train (90%) and holdout test (10%) sets, stratified across
label and proportion of sequences annotated manually and through always
patterns. Validation datasets were split from the train set using techniques
described in the Methodology section.

tab:table2  Model AUC Accuracy Sensitivity Specificity Micro F1 Macro F1
Weighted F1 TF-IDF 0.95 0.84 0.83 0.92 0.84 0.81 0.84 ClincialBERT 0.98 0.93
0.91 0.96 0.93 0.92 0.93

Table 2: Model Performance

##  4 Methodology

We developed two NLP models for the classification task and compared them to
each other.

### (1) Logistic Regression with TF-IDF Vectors

We performed TF-IDF (term frequency-inverse document frequency) vectorization
on the annotated sequences and selected features based on a term’s Pearson
correlation coefficient with the cognitive impairment outcome. L1 Regularized
logistic regression (Tibshirani, 1996) was applied with the annotated
cognitive impairment labels. We used 10-fold cross validation to determine the
optimal lambda value and correlation coefficient threshold to select features.

### (2) Transformer Based Sequence Classification Language Model

We utilized a pre-trained language model called ClinicalBERT (Alsentzer et
al., 2019), which was trained on the MIMIC II (Saeed et al., 2011) database
containing EHR records from ICU patients. We used the implementation in the
Huggingface Transformers (Wolf et al., 2019) and Simpletransformers
(Rajapakse, 2020) packages. After text preprocessing, input texts were
tokenized with the default tokenizer and converted to embeddings. The model
was initialized with pre-trained parameters and later fine-tuned on our
labeled training set. Optuna (Akiba et al., 2019) was used to perform a
20-trial study and tune the learning rate, Adam epilson, and the number of
train epochs on the held-out validation set to maximize AUC. An early stopping
rule was used to prevent overfitting by ensuring that training stopped if the
loss did not change substantially over 3 epochs.

##  5 Results

We evaluated each model based on sequence level class assignments. Model
performance for each model on the held-out test set are shown in Table 2. To
compute each metric, we used the threshold that maximized accuracy. The TF-IDF
model achieved an AUC of 0.95 and accuracy of 0.84. The 20 words with the
highest correlation coefficients using TF-IDF word vectorization are shown in
Appendix E. While TF-IDF was able to identify the presence of a keyword or
always pattern in a sequence, it was unable to the leverage the context around
each keyword match. The context of the keywords and the agents within the
sentence often contained useful information regarding a patient’s cognitive
status. For example, the sentence ”Patient is caregiver for wife who has
dementia” has the keyword dementia, but does not pertain to the patient’s
cognitive diagnosis. This led the baseline TF-IDF model to incorrectly predict
sequences as evidence of cognitive impairment, resulting in a large count of
false positives.

fig:umap

Figure 1: UMAP Clustering of ClinicalBert Embeddings

ClinicalBERT, with its more complex architecture, was able to leverage the
context of the keyword matches within the sequences and overcome these issues.
Indeed, using a small dataset of manually annotated sequences (n=150) which
did not match an always-pattern, the ClinicalBERT embeddings were able to able
accurately discriminate between all three classes (see Figure LABEL:fig:umap).
The fine-tuned ClinicalBERT model achieved an AUC of 0.98 and substantially
improved accuracy to 0.93 (specificity of 0.96, sensitivity of 0.91, micro F1
of 0.93, macro F1 of 0.92, and weighted F1 of 0.93).

In order to generate patient level class assignments, we applied ClinicalBERT
to all 186,730 sequences from the N = 13,941 unique patients that were not
patient of our training/validation/set sets. With these sequence level
predictions, we generated patient level class assignments by assigning
patients a cognitive impairment label if their number of sequences predicted
positive was greater than an empirically tuned threshold. We identified the
most optimal threshold (from a range of 1 - 10) by comparing the percentage of
patients being predicted as having cognitive impairment stratified by APOE
allele to the percentages of patients with cognitive impairment related
Meds/ICD codes stratified by APOE allele (M/I code column in tab:bert).
tab:bert shows the comparison of Med/ICD codes to ClinicalBERT patient level
class assignments with a sequence threshold of 2. As shown, ClinicalBERT was
able to identify a significant proportion of patients that went undetected by
current clinical methods, highlighting the utility of such a tool in a
clinical setting.

tab:bert  Count Yes (%) No/Ntr (%) M/I (%) APOE ${\bm{\varepsilon}}$2 1754
0.17 0.83 0.11 APOE ${\bm{\varepsilon}}$3 8751 0.17 0.83 0.11 APOE
${\bm{\varepsilon}}$4 3436 0.21 0.79 0.17

Table 3: Comparison between Other Indicators of Cognitive Impairment and
ClinicalBERT

M/I = Med/ICD Code

Figure 2: Confusion Matrix Patient Level Prediction Counts for ClinicalBERT

##  6 Conclusion and Future Work

We applied NLP algorithms to identify patients with cognitive impairment in
EHR and compared a baseline TF-IDF model with an attention based deep learning
model on performance of sequence level class assignment predictions. Our work
can help address the underdiagnosis of dementia and alert primary care
physcians to do a formal cognitive evaluation or refer to specialists. Such a
tool can be used to generate cohorts for dementia research studies to identify
risk and protective factors of dementia as well as recruit patients into
observational studies or clinical trials.

The deep learning model’s performance was significantly better than the TF-IDF
model as it was able to fully leverage the context of sequences. Our work
illustrates the need of more complex, expressive language models for the
nuanced task of detecting dementia in electronic health records.

We used the sequence level class assignments of the deep learning model to
generate patient level classes. For a few patients, we manually verified that
our model can successfully identify patients with cognitive impairment who
lack dementia-related ICD codes or medications in their records. However, a
lack of patient level annotations prevents us from measuring the true accuracy
of these results. In order to address this issue, we plan to generate 1000
patient level class assignments using our annotation tool. We also plan to
further improve the generalizability of our models by labeling more sequences
that do not match an always pattern. An active learning loop will be used to
pick particular patients and sequences by using entropy scores to label
uncertain cases and UMAP clustering (McInnes et al., 2018) of ClinicalBERT
word embeddings on the sequences of the N = 13,941 patients. The new gold-
standard dataset will serve as the basis for the next iteration of the active
learning loop to further improve model performance and detect patients with
cognitive impairment with improved accuracy.

## References

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##  Appendix A Overview

Figure 3: Overview

##  Appendix B Pictures of UI Interface for Annotations

Figure 4: Annotation UI Figure 5: Always Pattern List Generated by Annotations

##  Appendix C Example Sequences

Figure 6: Example Sequences

##  Appendix D Keywords

app:keywords  Keyword Match Count Memory 109218 Cognition 87655 Dementia 51034
Cerebral 45886 Cerebrovascular 36370 Cerebellar 26863 Cognitive Impairment
20267 Alzheimer 20581 MOCA 9767 Neurocognitive 7711 MCI 3889 Amnesia 3695 AD
2673 Lewy 2561 MMSE 2134 LBD 224 Corticobasal 147 Picks 41

Table 4: Keywords indicative of Cognitive Impairment

##  Appendix E Top TF-IDF Word Features

Word | Corr | Word | Corr
---|---|---|---
Intact | 0.56 | Experiences | 0.36
Oriented | 0.43 | Associations | 0.36
Concentration | 0.42 | Homicidal | 0.36
Orientation | 0.41 | Observation | 0.36
Sensorium | 0.40 | Knowledge | 0.36
Perceptions | 0.40 | Abstract | 0.36
Judgement | 0.39 | Suicidal | 0.35
Fund | 0.38 | Attention | 0.35
Insight | 0.36 | Content | 0.34
Ideation | 0.36 | Thought | 0.34
Table 5: Top 20 TF-IDF Word Features and their Correlation Coefficient


# On the flat transverse momentum dependence of the single-spin asymmetry in
inclusive neutral pion production

S.M. Troshin, N.E. Tyurin
Institute for High Energy Physics,
Protvino, Moscow Region, 142281, Russia

We discuss recent experimental results from RHIC where the flat transverse
momentum dependence of a single-spin asymmetry has been found in the inclusive
production of neutral pions. This dependence takes place in a wide region of
the transverse momenta up to $p_{T}=10$ GeV/c. We emphasize that similar
dependence has been predicted in the nonperturbative spin filtering mechanism
for the single-spin asymmetries in hadron interactions and present some
implications for this mechanism from the new experimental data.

## Introduction

It should be noted that decrease with transverse momentum $p_{T}$ of
single–spin asymmetries (SSA) is a common feature of perturbative QCD
approaches including those based on account for the various modifications
implemented into the calculation scheme originally grounded on collinear
factorization. The most recent progress in this field is described in [1, 2].
The decreasing dependence has not been directly observed experimentally, but
the experimental data were not very conclusive due to large statistcal errors.
However, the existing data are consistent with the flat transverse dependence
of SSA in inclusive processes. This conclusion is valid for the old data on of
$\Lambda$–hyperon polarization [3], for example, and for the most recent data
obtained at RHIC [4]. It is essential that the new data cover the wide region
of the transverse momentum values up to $p_{T}\simeq 10$ GeV/c. In [6] it was
noted that experimental data at higher values of $p_{T}$ would be needed to
perform a more conclusive test of various pQCD theoretical approaches and
their predictions. The model proposed in [6] provided flat $p_{T}$ -dependence
of SSA. The new data which have appeared very recently[4, 5] are consistent
with the observed earlier trend, i.e. flat dependence on transverse momenta
can be extended to the region of higher values of $p_{T}$. Since such high
values of transverse momenta have been reached experimentally, one forced to
conclude that the mechanism of the SSA’s generation can have a nonperturbative
origin. Of course, presence of the significant statistical errors in the
current experimental data (cf. e.g [4, 5]) is the serious obstacle on the way
of derivation of a completely unambiguous final conclusion on the
impossibility of a decreasing dependence of the SSA with $p_{T}$.

## Highlights of the filtering mechanism of SSA generation and new
large-$p_{T}$ experimental data

A nonperturbative QCD dynamics is closely interrelated with the two well–known
phenomena, namely, color confinement and spontaneous breaking of chiral
symmetry ($\chi$SB)( cf. e.g. [7]). The $\chi$SB–mechanism resulting in
transition of current into constituent quarks is directly responsible for
generation of their masses and appearance of quark condensates. Constituent
quarks are colored objects, they appear to be quasiparticles and a hadron is
often represented as a loosely bounded system of the constituent quarks.
Simultaneously, the Goldstone bosons which are the excitations of the
condensates appear and mediate interactions of the constituent quarks.

This interaction is mainly due to a pseudoscalar pion field and has therefore
a spin–flip nature. Spin states filtering results from the unitarization
process in the $s$-channel and connects SSA with asymmetries in the position
(impact parameter) space [6].

The common features of SSA measurements at RHIC and Tevatron (linear increase
of asymmetry with $x_{F}$ and flat transverse momentum dependence at large
transverse momentum, $p_{T}>1$ GeV/c) are reproduced and described in the
framework of the semiclassical picture based on the further development of the
chiral quark model suggested in [8] and results of its use for the treatment
of the polarized and unpolarized inclusive cross-sections including those
obtained at RHIC [9].

We summarize now the essential features of the mechanism. Valence constituent
quarks are scattered simultaneously (due to strong coupling with Goldstone
bosons) and in a quasi-independent way by the effective strong field. In the
initial state of the reaction $pp_{\uparrow}\to\pi^{0}X$ the proton is
polarized and for the wave function of the proton we use the simple SU(6)
model. The constituent quark $Q_{\uparrow}$ with transverse up spin fluctuates
into Goldstone boson and another constituent quark $Q^{\prime}_{\downarrow}$
with down spin, performing spin-flip transition [10]:

$Q_{\uparrow}\to GB+Q^{\prime}_{\downarrow}.$ (1)

It should be noted that $\pi^{0}$-fluctuation of constituent quark does not
change its flavor and color. Assuming the equal probabilities of the processes
with $U$ and $D$ quarks:

$U_{\uparrow,\downarrow}\to\pi^{0}+U_{\downarrow,\uparrow}\quad\mbox{and}\quad
D_{\uparrow,\downarrow}\to\pi^{0}+D_{\downarrow,\uparrow},$ (2)

the production of $\pi^{0}$ by the polarized proton $p_{\uparrow}$ in this
simple $SU(6)$ picture can be treated as a result of the fluctuation of the
constituent quark $Q_{\uparrow}$ ($Q=U$ or $D$) in the effective field into
the system $\pi^{0}+Q_{\downarrow}$ (Fig. 1).

Figure 1: Chiral mechanism of $\pi^{0}$–production in polarized proton-proton
interaction.

Since the total angular momentum is conserved, the compensation of quark spin
flip should occur, i.e. to compensate quark spin flip $\delta{\bf S}$, an
orbital angular momentum $\delta{\bf L}=-\delta{\bf S}$ should be associated
with the final state of reaction (1). The introduction of $\delta{\bf L}$
implies a shift in the impact parameter value of the pion $\pi^{0}$:

$\delta{\bf S}\Rightarrow\delta{\bf L}\Rightarrow\delta\tilde{\bf b}.$

Note, that outside the hadron interior the Goldstone bosons are the usual
pions and kaons. Due to different strengths of interaction at the different
impact distances, i.e.

$\displaystyle p_{\uparrow}\Rightarrow Q_{\uparrow}$ $\displaystyle\to$
$\displaystyle\pi^{0}+Q_{\downarrow}\Rightarrow\;\;-\delta\tilde{\bf b},$
$\displaystyle p_{\downarrow}\Rightarrow Q_{\downarrow}$ $\displaystyle\to$
$\displaystyle\pi^{0}+Q_{\uparrow}\Rightarrow\;\;+\delta\tilde{\bf b}.$ (3)

the processes of transition $Q_{\uparrow}$ and $Q_{\downarrow}$ to $\pi^{0}$
will have different probabilities. It eventually leads to nonzero asymmetry
$A_{N}(\pi^{0})$. When the shift in impact parameter is negative,
$-\delta\tilde{\bf b}$, the interaction is stronger than that with the
positive shift, $+\delta\tilde{\bf b}$, and therefore the asymmetry
$A_{N}(\pi^{0})$ is positive too. The shift in $\tilde{\bf b}$ (the impact
parameter of final pion) is correlated with the shift of the impact parameter
of the collision according to the relation between impact parameters in the
multiparticle production process:

${\bf b}=\sum_{i}x_{i}{\tilde{\bf b}_{i}}.$ (4)

The production of $\pi^{0}$ with impact parameter $\tilde{\bf b}$ is
considered in the fragmentation region, i.e. at large $x_{F}$ the approximate
relation

${\bf b}\simeq x_{F}\tilde{\bf b},$ (5)

which results from Eq. (4) has been used with additional assumption on the
small values of Feynman $x_{F}$ for the other particles.

It should be noted that direction of spin of the proton is chosen to be along
or opposite to the impact parameter vector ${\bf b}$. The integration over the
asimuthal angle $\varphi$ selects therefore the finctions $I$ (see below)
corresponding to the respective directions of the proton spin. The mechanism
is illustrated in Fig. 2.

Figure 2: Schematic illustration of the SSA’s generation mechanism due to spin
flip of the constituent quark Q.

An essential feature of the mechanism is an account of unitarity in the direct
channel of reaction. The corresponding formulas for inclusive cross–sections
of the process

$p^{\uparrow,\downarrow}+p\to\pi^{0}+X,$

have been obtained in [11]:

${d\sigma^{\uparrow,\downarrow}}/{d\xi}=8\pi\int_{0}^{\infty}bdb{I^{\uparrow,\downarrow}(s,b,\xi)}/{|1-iU(s,b)|^{2}},$
(6)

$b$ is the collison impact parameter. The function $U(s,b)$ is the generalized
reaction matrix (averaged over initial spin states) which is determined by the
basic dynamics of the elastic scattering. The elastic scattering amplitude in
the impact parameter representation $F(s,b)$ is then given [8] by the
relation:

$F(s,b)=U(s,b)/[1-iU(s,b)].$ (7)

The equation (7) allows one to obey unitarity for the elastic scattering
amplitude provided the inequality $\mbox{Im}\,U(s,b)\geq 0\,$ takes place. The
model [8] has been used for construction of the functional dependence of
$U(s,b)$, namely, this function was chosen as a product of the factors
corresponding to the averaged amplitudes of the individual valence quarks. The
strong interaction radius of the quarks is determined by its mass,

$r_{Q}=\zeta/m_{Q}$

The parameter $\zeta$ was extracted from the experimental data for the
differential cross-section of the elastic $pp$-scattering. In the region of
medium values of $t$ this model provides[8] the familiar Orear-type behavior:

$\frac{d\sigma}{dt}\sim\exp\left(-\frac{2\pi\zeta}{M}\sqrt{-t}\right),$

where $M$ is equal to the total mass of the constituent quarks in the two
colliding protons, i.e. $M=6m_{Q}\simeq 2$ GeV/c, and the value of parameter
$\zeta\simeq 2$ since from the experimental data $m_{Q}/\zeta=150-200$ MeV and
to reproduce the standard constituent quark masses the value of $\zeta$ should
be around 2.

The functions $I^{\uparrow,\downarrow}$ in Eq. (6) can be expressed through
the functions $U_{n}^{\uparrow,\downarrow}$ – the multiparticle analogs of the
function $U$ [11] in the polarized case. The set of the kinematical variables
$\xi$ ($x_{F}$ and $p_{T}$ for example) describe the state of the produced
pion.

We assume that the shift $\delta\tilde{b}$ can be connected with the radius of
quark interaction $r_{Q}^{flip}$, which is responsible for the quark
transition flipping its spin, i.e.:

$\delta\tilde{b}\simeq r_{Q}^{flip}.$

Asymmetry $A_{N}$ can be written in terms of the functions $I_{-}$, $I_{0}$
and $U$:

$A_{N}(s,\xi)=\frac{\int_{0}^{\infty}bdbI_{-}(s,b,\xi)/|1-iU(s,b)|^{2}}{2\int_{0}^{\infty}bdbI_{0}(s,b,\xi)/|1-iU(s,b)|^{2}},$
(8)

where $I_{0}=1/2(I^{\uparrow}+I^{\downarrow})$ and
$I_{-}=(I^{\uparrow}-I^{\downarrow})$ and $I_{0}$ obey the sum rule

$\int I_{0}(s,b,\xi)d\xi=\bar{n}(s,b)ImU(s,b),$

here $\bar{n}(s,b)$ stands for the mean multiplicity in the impact parameter
representation.

With the above relation for the shift in the impact parameter due to the
transition flipping quark spin the following expression for asymmetry
$A_{N}^{\pi^{0}}$ can be written

$A_{N}^{\pi^{0}}(s,\xi)\simeq-
x_{F}r_{Q}^{flip}\frac{1}{3}\frac{\int_{0}^{\infty}bdbI^{\prime}_{0}(s,b,\xi)db/|1-iU(s,b)|^{2}}{\int_{0}^{\infty}bdbI_{0}(s,b,\xi)/|1-iU(s,b)|^{2}},$
(9)

where $I^{\prime}_{0}(s,b,\xi)={dI_{0}(s,b,\xi)}/{db}$. It is evident that
$A_{N}^{\pi^{0}}(s,\xi)$ should be positive because
$I^{\prime}_{0}(s,b,\xi)<0$.

In the model [8] the function $U(s,b)$ is chosen to be a product of the
averaged quark amplitudes under assumption of the the quasi-independence of
valence constituent quark scattering in the self-consistent mean field. The
function $U(s,b)$ in a pure imaginary case for the elastic scattering
amplitude, which we consider here for simplicity has been written in the
following form

$U(s,b)=i\tilde{U}(s,b)=ig(s)\exp(-Mb/\zeta),$ (10)

where the factor $g(s)$ increases at large values of $s$ like a power of
energy:

$g(s)=\left[1+\alpha\frac{\sqrt{s}}{m_{Q}}\right]^{N},$

$M$ is the total mass of $N$ constituent quarks with mass $m_{Q}$ in the
initial hadrons and parameter $\zeta$ determines a universal scale for the
quark interaction radius without flipping its spin, i.e. $r_{Q}=\zeta/m_{Q}$.

To evaluate asymmetry dependence on $x_{F}$ and $p_{T}$ the semiclassical
correspondence between transverse momentum and impact parameter has been used.
Integrating by parts, we can rewrite the expression for the asymmetry in the
form:

$A_{N}^{\pi^{0}}(s,\xi)\simeq
x_{F}r_{Q}^{flip}\frac{M}{3\zeta}\frac{\int_{0}^{\infty}bdbI_{0}(s,b,\xi)\tilde{U}(s,b)/[1+\tilde{U}(s,b)]^{3}}{\int_{0}^{\infty}bdbI_{0}(s,b,\xi)/[1+\tilde{U}(s,b)]^{2}},$
(11)

At small values of $b$ the values of $U$-matrix are large, and we can neglect
unity in the denominators of the integrands. Thus the ratio of the two
integrals (after integration by parts of nominator in Eq. (11)) is of order of
unity, i.e. the energy and $p_{T}$-independent behavior of asymmetry
$A_{N}^{\pi^{0}}$ takes place at the values of transverse momentum $p_{T}\gg
x_{F}/R(s)$:

$A_{N}^{\pi^{0}}(s,\xi)\simeq x_{F}r_{Q}^{flip}\frac{M}{3\zeta}.$ (12)

This flat transverse momentum dependence of asymmetry results from the
similarity of the rescattering effects for the different spin states, i.e.
spin-flip and spin-nonflip interactions undergo similar absorption at short
distances and the relative magnitude of this absorption does not depend on
energy. It can be considered as a one of the manifestations of the unitarity.
The numerical value of polarization $A_{N}^{\pi^{0}}$ can be significant.
Indeed, there is no small factor in (12). The function $R(s)$ is the hadron
interaction radius ($R(s)\sim\ln s$), the typical numerical falue of $R$ has
been taken to be equal to 1 fm. Thus, the typical value of $x_{F}/R(s)$ is 0.1
GeV/c and the Eq. (12) which is valid at $p_{T}\gg x_{F}/R(s)$, should be
applicable in the region $p_{T}>1$ GeV/c. The value of $r_{Q}^{flip}$ is of
order $\sim 10^{-1}$ fm on the basis of the model estimates [6, 8, 11]. The
radius of quark interaction $r_{Q}^{flip}$ responsible for the transition
$Q_{\uparrow}\to Q_{\downarrow}$ changing quark spin. The linear increase of
asymmetry with $x_{F}$ follows from the above considerations which, of course,
are approximate and valid at $x_{F}$ around unity. Therefore, at smaller
values of $x_{F}$ the linear dependence is distorted.

Thus, Eq. (12 is valid in the region of large $x_{F}$. The flat dependence of
asymmetry on $p_{T}$ provided by this relation is consistent with the new data
from RHIC (we have used data available at the largest values of $x_{F}$ due to
approximation made in the model and discussed above) [4, 5] (cf. Fig. 2,3).

Figure 3: $p_{T}$ -dependence of the asymmetry $A_{N}$ in the process
$p_{\uparrow}+p\to\pi^{0}+X$ at RHIC, preliminary data from [4, 5] correspond
to pion isolation of 70 mR, $\sqrt{s}=500$ GeV and $0.32<x_{F}<0.40$.

Figure 4: The same plot as in Fig.3, but with data corresponding to pion
isolation of 30 mR.

Comparison with the data allows one to estimate the value of $r_{Q}^{flip}$
more precisely , namely $r_{Q}^{flip}\simeq 0.05$ fm. Similar mechanism
generates SSA in the inclusive production of charged pions. It should be noted
that dependencies of SSA on $p_{T}$ consistent with the flat ones have also
been observed at lower values of $x_{F}$, namely, in the two regions
$0.16<x_{F}<0.24$ and $0.24<x_{F}<0.32$ [4, 5]. The data demonstrate increase
of SSA with $x_{F}$. Due to limitation of the model for the large $x_{F}$
region, we have not used those data, but, in principle, the model is in
agreement with them too. To be honest, one should not compare the predictions
of the model which are valid for $x_{F}$ in the vicinity of unity with the
experimental data wich have highest value of $x_{F}$ around 0.4. However, the
data demonstrate similar flat dependence on transverse momentum in the the
rather wide range $x_{F}$ from 0.16 to 0.4. We therefore assume that the
similar dependence will be valid at $x_{F}$ values around unity and perform
comparison with the experiment. It should be clarified, that the above
agreement with the data has a qualitative value only and for the quantitative
analysis the data at higher values of $x_{F}$ are required.

The mechanism of chiral quark fluctuation in the effective field with spin
flip is suppressed compared to the direct elastic scattering of quarks and,
therefore, it should not play a significant role e.g. in the reaction
$pp_{\uparrow}\to pX$ in the fragmentation region, but evidently it is not the
case for the reaction $pp_{\uparrow}\to nX$. The above features can be
observed experimentally: asymmetry $A_{N}$ is consistent with zero for proton
production and significantly deviates from zero for the neutron production in
the forward region.

In ref. [14] an important issue has been raised, namely a model when trying to
explain spin asymmetries should simultaneously describe the data for the
unpolarized inclusive cross-sections. In this approach with the effective
degrees of freedom – constituent quarks and Goldstone bosons – unpolarized
inclusive cross–section at high transverse momenta fllows a generic power-like
dependencies on $p_{T}$ . At high $p_{T}$ the power-like dependence
$p_{T}^{-n}$ with $n=6$ takes place. It originates from the singularity at
zero impact parameter $b=0$. The exponent $n$ does not depend on $x_{F}$. This
$p_{T}^{-6}$–dependence of the unpolarized inclusive cross–section is
consistent with the respective data dependence on the transverse momentum
(Fig. 5) [6].

Figure 5: Transverse momentum dependence of unpolarized inclusive
cross–section, experimental data from [9].

## Conclusion

It was shown that prediction of the spin filtering mechanism [6] on the flat
$p_{T}$-dependence of single-spin asymmetries is consistent with the new
experimental data from RHIC. As it often happens, this interpretation is not
unique. Such flat dependence can result from finite size of a constituent
quark and a presence of the orbital angular momentum of the current quarks
residing inside the constituent one [12, 13]. This mechanism is based on the
similar ideas as the spin filtering one but is, in principle, different and
has no predictive power for $x_{F}$ dependence of SSA. Thus, we would like to
treat the seemingly flat $p_{T}$-dependence of SSA in favor of the spin
filtering mechanism, while the presence of the internal orbital momentum in
the structure of constituent quarks still remains to be an interesting option
and cannot be excluded at the moment (cf. e.g. [15]).

Finally, we would like to stress again that the experimental data set [4, 5]
is the preliminary one and we hope that the final data will show smaller error
bars and allow one to provide a quantitative discrimination of the model
predictions for SSA.

## Acknowledgment

We are grateful to Yuri Kovchegov for the information on the new experimental
data from RHIC and the interesting discussions.

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