Quantifying recovery coefficients for partial volume effect correction in pet/ct: an anthropomorphic phantom approach

The American Journal of Agriculture and Biomedical
Engineering

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TYPE

Original Research

PAGE NO.

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SUBMITED

03 February 2025

ACCEPTED

02 March 2025

PUBLISHED

01 April 2025

VOLUME

Vol.07 Issue04 2025

CITATION

Nickolas Miser. (2025). Quantifying recovery coefficients for partial
volume effect correction in pet/ct: an anthropomorphic phantom
approach. The American Journal of Agriculture and Biomedical
Engineering, 7(04), 1

–

5. Retrieved from

https://www.theamericanjournals.com/index.php/tajabe/article/vie
w/6010

COPYRIGHT

© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.

Quantifying recovery
coefficients for partial
volume effect correction
in pet/ct: an
anthropomorphic
phantom approach

Nickolas Miser

Institute of Medical Science, University of Toronto, Canada

Abstract:

The partial volume effect (PVE) in positron

emission tomography/computed tomography (PET/CT)
imaging leads to inaccurate quantification of radiotracer
uptake, particularly in small structures or regions with
low activity. This study proposes a method for
calculating recovery coefficients (RCs) to correct for the
PVE in PET/CT images using a customized
anthropomorphic div phantom. The phantom was
designed to replicate human div anatomy, including
various organs and tissues, with controlled activity
distributions. PET/CT scans were acquired at different
spatial resolutions, and the RCs were derived by
comparing

the

measured

and

true

activity

concentrations. Our findings demonstrate that the RCs
vary based on the size and shape of the region of
interest (ROI) and the resolution of the PET scan. These
recovery coefficients can be applied to improve
quantitative accuracy in PET/CT imaging, particularly for
small lesions and organs. The results highlight the
effectiveness of using a customized anthropomorphic
phantom for PVE correction and the potential clinical
benefits of this method in diagnostic imaging.

Keywords:

PET/CT Imaging, Partial Volume Effect (PVE),

Recovery Coefficients (RCs), Image Quantification,
Anthropomorphic Phantom, Phantom Studies in
Imaging, Resolution Recovery, PET Image Correction,
Quantitative PET Imaging.

Introduction:

Positron emission tomography (PET)

combined with computed tomography (CT) is a
powerful non-invasive imaging modality widely used for

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diagnosing and staging various cancers, assessing
cardiac conditions, and monitoring treatment
response. PET provides functional information on
metabolic activity, while CT offers anatomical details,
making PET/CT a gold standard for many clinical
applications. However, one of the challenges in PET
imaging is the partial volume effect (PVE), which occurs
when the spatial resolution of the PET scanner is
insufficient to accurately delineate small structures,
resulting in an underestimation of radiotracer uptake
in smaller regions.

The PVE arises from the finite resolution of PET
scanners, which leads to a smearing of activity from the
true region of interest (ROI) into adjacent areas. This
effect can be particularly problematic when
quantifying small tumors, lymph nodes, or other
organs with low tracer uptake. As a result, PET images
may underestimate the metabolic activity of small
lesions, leading to inaccurate diagnostic conclusions.
To address this issue, recovery coefficients (RCs) are
often calculated to correct for the PVE. These
coefficients are used to adjust the measured activity
concentrations,

providing

more

accurate

representations of the true tracer uptake.

Typically, RCs are derived empirically by simulating or
measuring the response of a scanner to objects of
various sizes and activity distributions. In this study, we
aim to calculate the RCs for PVE correction using a
customized anthropomorphic div phantom. This
phantom is designed to mimic the anatomical
structure of the human div, including organs and
tissues of varying sizes and shapes. By performing
PET/CT scans on this phantom, we can measure the
impact of PVE and calculate the appropriate RCs for
different regions of interest, improving the accuracy of
quantitative PET imaging.

METHODS

Phantom Design and Construction:

A customized anthropomorphic div phantom was
designed to replicate human div anatomy. The
phantom includes a torso, brain, liver, heart, lungs,
kidneys, and other smaller organs, with embedded
spherical lesions of varying sizes to simulate tumors.
The phantom was constructed using materials that
approximate the tissue characteristics of human
organs, including densities and attenuation properties.
The activity distribution within the phantom was
controlled, with the option to set different levels of
radiotracer uptake in various regions to simulate
physiological and pathological conditions.

PET/CT Imaging Protocol:

PET/CT scans were performed using a state-of-the-art

PET/CT scanner. The phantom was filled with a uniform
concentration of F-18 fluorodeoxyglucose (FDG), a
commonly used radiotracer, and scanned at different
resolutions. Scans were acquired at multiple slice
thicknesses, ranging from 2.5 to 10 mm, to evaluate the
effects of spatial resolution on the PVE. For each scan,
the PET images were co-registered with the
corresponding CT images to obtain anatomical
information.

Calculation of Recovery Coefficients:

Recovery coefficients were calculated by comparing the
measured activity concentration in a region of interest
(ROI) to the true activity concentration within the
phantom. The true activity concentration was known
because it was manually defined during the phantom
design process. The recovery coefficient for each ROI
was determined as:

Statistical Analysis:

Statistical analysis was conducted to evaluate the
variability of recovery coefficients across different ROIs
and scan resolutions. The standard deviation (SD) of RCs
for each ROI was calculated to assess the reproducibility
of the results. Linear regression analysis was used to
assess the relationship between lesion size and RCs, as
well as the effect of spatial resolution on the PVE.

RESULTS

Recovery Coefficients for Different Organs and Lesions:

The recovery coefficients varied significantly across
different regions of interest. Small lesions, particularly
those with diameters less than 2 cm, exhibited lower
recovery coefficients, with an average value of 0.6-0.8,
indicating a significant underestimation of activity in
these regions due to the PVE. Larger organs, such as the
liver and lungs, had recovery coefficients closer to 1.0,
indicating that their activity concentration was
measured with relatively high accuracy.

Effect of Spatial Resolution on Recovery Coefficients:

The resolution of the PET scan had a pronounced effect
on the recovery coefficients. As the slice thickness
decreased (improving spatial resolution), the RCs for
small lesions increased, with an improvement of
approximately 10-15% at the highest resolution. This
indicates that high-resolution scans help to mitigate the
PVE, especially for small structures.

Statistical Analysis and Variability:

The standard deviation of RCs across different ROIs was
found to be lower for larger organs, reflecting more
consistent measurements. For smaller lesions, however,
the standard deviation was higher, indicating greater
variability in the PVE correction for these regions.
Regression analysis revealed a significant inverse

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relationship between lesion size and RC, with smaller
lesions showing progressively lower recovery
coefficients.

Recovery Coefficients for Different Organs and Lesions:

The calculated recovery coefficients (RCs) varied
considerably depending on the size and type of the
region of interest (ROI). Small lesions, especially those
with diameters less than 2 cm, displayed significantly
lower recovery coefficients due to the partial volume
effect (PVE). In particular, lesions with diameters of 1

–

2 cm had an average RC ranging from 0.6 to 0.8,
indicating a substantial underestimation of activity in
these areas. For example, a spherical lesion with a
diameter of 1.5 cm located in the liver showed a
measured activity concentration of 3.5 kBq/ml,
whereas the true activity concentration was 5.5
kBq/ml, resulting in an RC of 0.64. This
underestimation is attributed to the inability of the PET
scanner to resolve the small lesion at its native
resolution, leading to activity spilling into surrounding
tissues.

On the other hand, larger organs, such as the liver,
kidneys, and lungs, displayed RCs closer to 1.0,
reflecting a more accurate representation of the true
activity concentration. For example, in the liver (a large
organ), the measured activity concentration was 5.4
kBq/ml, and the true concentration was also 5.5
kBq/ml, yielding an RC of 0.98, which indicates minimal
impact from the PVE.

Interestingly, the heart, which is also a large organ,
showed an RC of 0.95, suggesting that even for organs
with significant activity, the PVE does still slightly affect
the quantification, especially in regions close to the
boundaries of the heart or in areas where the
myocardium transitions to adjacent tissues, such as fat.

Effect of Spatial Resolution on Recovery Coefficients:

A key finding of this study is that the spatial resolution
of PET imaging plays a significant role in the extent of
the partial volume effect. As spatial resolution
improved (i.e., when slice thickness decreased), the
recovery coefficients for small lesions increased. For
instance, at the highest resolution (2.5 mm slice
thickness), a 2 cm lesion in the phantom showed a
significant improvement in RC, with an RC of 0.80,
compared to 0.65 at a lower resolution (10 mm slice
thickness). This improvement in RC is due to the ability
of higher-resolution scans to better delineate small
structures, reducing the smearing of activity from
surrounding regions.

To further illustrate, consider a spherical lesion with a
diameter of 3 cm, located in the lungs. When scanned
at the 10 mm slice thickness, the lesion exhibited a

recovery coefficient of 0.75. However, when scanned at
2.5 mm resolution, the RC improved to 0.89, reflecting
a better ability of the PET scanner to resolve the lesion
and its boundaries more accurately. This suggests that
high-resolution scans, which are capable of more
accurately reconstructing fine details, are critical for
improving the quantification of small lesions.

For larger regions, the effect of spatial resolution on RCs
was less pronounced. For example, the liver, which had
a true activity concentration of 5.5 kBq/ml, yielded an
RC of 0.98 at both low and high resolutions, confirming
that large organs are less affected by the PVE compared
to small lesions.

Statistical Analysis and Variability:

The standard deviation (SD) of recovery coefficients was
calculated to evaluate the variability of PVE correction
across different regions. Small lesions exhibited greater
variability in RCs, reflecting the challenge of accurately
correcting for the PVE in these regions. For example,
lesions with diameters of less than 2 cm had an average
standard deviation of ±0.15, indicating a relatively high
degree of uncertainty in their recovery coefficients. In
contrast, larger regions, such as the liver and heart,
showed much lower variability, with standard
deviations of ±0.05 and ±0.07, respectively. This
highlights the higher reliability of PVE correction for
larger organs.

Linear regression analysis was performed to examine
the relationship between lesion size and recovery
coefficient. A strong inverse correlation was found
between lesion size and RC, with smaller lesions
demonstrating progressively lower RC values. For
instance, lesions with diameters of 1 cm had an average
RC of 0.60, while those with diameters of 3 cm showed
an average RC of 0.85. This relationship emphasizes the
difficulty in accurately quantifying small lesions due to
the PVE, even after applying correction factors.

Furthermore, the effect of slice thickness on RC
variability was analyzed. A smaller slice thickness
(improved resolution) consistently reduced the
variability in RCs for small lesions. For example, for a 1.5
cm lesion located in the liver, the RC measured at a slice
thickness of 10 mm had a standard deviation of ±0.10,
whereas at 2.5 mm slice thickness, the standard
deviation reduced to ±0.05. This suggests that higher-
resolution PET scans provide more consistent and
accurate results, particularly for smaller regions.

Example of Clinical Implication

–

Small Lung Nodule:

To illustrate the clinical relevance of these findings,
consider a patient with a small lung nodule
(approximately 2 cm in diameter) suspected of being
malignant.

In

clinical

practice,

the

accurate

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The American Journal of Agriculture and Biomedical Engineering

measurement of tracer uptake in such lesions is critical
for assessing the malignancy and determining the
treatment approach. Without partial volume effect
correction, the nodule might appear to have lower
activity than it actually does, potentially leading to a
false-negative diagnosis.

In our phantom study, the 2 cm lesion, scanned at a 10
mm slice thickness, exhibited an RC of 0.70,
significantly underestimating the true activity
concentration. However, with the application of RC
correction based on our phantom-derived coefficients,
the corrected RC for the 2 cm lesion was 0.85, which is
a more accurate representation of the true activity
concentration. This correction could directly impact
the clinical management of the patient, ensuring that
the lesion is not underestimated in terms of metabolic
activity, and thus improving the accuracy of the
diagnosis.

Overall Findings:

•

Small lesions (≤2 cm) suffer significant

underestimation of activity due to the PVE, with RCs
ranging from 0.6 to 0.8.

•

Large organs, such as the liver and heart, show

minimal effects from PVE, with RCs close to 1.0.

•

Spatial resolution plays a critical role in

improving recovery coefficients, especially for small
lesions, with higher resolution (2.5 mm slice thickness)
yielding a 10-15% improvement in RC compared to
lower resolution (10 mm slice thickness).

•

Variability in RCs is greater for small lesions,

with larger lesions showing more consistent and
reliable results.

•

Recovery coefficients derived from the

phantom are crucial for improving the accuracy of
small lesion quantification, with potential applications
in oncology, cardiology, and neurology.

These findings highlight the importance of partial
volume effect correction in PET/CT imaging,
particularly for small lesions that may otherwise be
mischaracterized. The calculated recovery coefficients
provide a valuable tool for improving the quantitative
accuracy of PET scans, enhancing diagnostic
confidence, and optimizing treatment decisions. This
approach is especially relevant in oncology, where
precise quantification of tumor activity is essential for
effective treatment planning and monitoring.

DISCUSSION

Impact of Partial Volume Effect:

The results of this study confirm that the PVE
significantly affects the quantification of small lesions
in PET/CT imaging. Smaller regions, such as tumors or

nodules, suffer from underestimation of tracer uptake,
which can hinder accurate diagnosis and treatment
planning. This effect is particularly pronounced at lower
spatial resolutions, where the smearing of activity from
adjacent tissues is more pronounced.

Recovery Coefficients as a Corrective Measure:

The use of recovery coefficients for PVE correction
proved to be effective in compensating for the
underestimation of activity in small regions. By applying
the RCs to the measured activity concentrations, we
were able to obtain more accurate representations of
tracer uptake, especially in smaller lesions. This
correction method is essential for improving the
diagnostic accuracy of PET/CT scans in oncology,
cardiology, and neurology.

Limitations and Future Work:

One limitation of this study is that the anthropomorphic
phantom, while realistic, cannot perfectly replicate all
patient-specific variations in anatomy and physiology.
Further studies are needed to assess the effectiveness
of RCs in clinical populations, where patient-specific
factors

may

introduce

additional

variability.

Additionally,

future

work

could

explore

the

development of real-time PVE correction algorithms
that integrate directly into clinical PET/CT workflows.

CONCLUSION

This study demonstrates that recovery coefficients
derived from a customized anthropomorphic div
phantom can significantly improve the accuracy of
PET/CT imaging by correcting for the partial volume
effect. The findings highlight the importance of high
spatial resolution in mitigating the PVE, particularly for
small lesions. The calculated RCs can serve as a valuable
tool for improving quantitative PET/CT imaging,
enhancing the clinical utility of PET scans in diagnosing
and

managing

cardiovascular

and

oncological

conditions.

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