A method for automated masking and plantar pressure analysis using segmented computed tomography scans

Abstract

Background.

Plantar pressure, a common gait and foot biomechanics measurement, is typically analyzed using proprietary commercial software packages. Regional plantar pressure analysis is often reported in terms of underlying bony geometry, and recent advances in image processing and accessibility have made computed tomography, radiographs, magnetic resonance imaging, or other imaging methods more popular for incorporating bone analyses in biomechanics.

Research Question.

Can a computed tomography-based regional mask provide comparable regional analysis to commercial plantar pressure software and can the increased flexibility of an in-house method obtain additional insight from common measurements?

Methods.

A plantar pressure analysis method was developed based on bony geometry from computed tomography scans to calculate peak pressure, pressure time integral incorporating sub-peak values, force time integral, pressure gradient, and pressure gradient angle. Static and dynamic plantar pressure were acquired for 4 subjects (male, 65 ± 2.4 years). Plantar pressure variables were calculated using commercial and computed tomography-based systems.

Results.

Dynamic peak pressure, pressure time integral, and force-time integral computed using the bone-based software was 5% (9kPa), 7% (0.3kPa-s) and 13% (0.3 N-s) different than the and commercial software on average. Region masks of the metatarsals and toes differed between commercial and computed tomography-based software due to subject-specific bone geometry and toe shape. Pressure time integral values incorporating sub-peak pressure were higher and demonstrated higher relative hindfoot values compared to those without. Removing step-on frames to static pressure analysis decreased forefoot pressures. Regional maps of peak pressure and maximum pressure gradient demonstrate different peak locations.

Significance.

Computed tomography-based regional masks are comparable to commercial masks. Inclusion of static step-on frames and sub-peak pressures may change regional plantar pressure patterns. Differences in location of maximum pressure gradient and peak pressure may be useful for assessing subject specific injury risk.

Introduction

Plantar pressure, a contact-area normalized measure of the force exerted through the foot during various activities, is a common metric in biomechanical analysis of gait, foot bone deformities, and plantar soft tissue pathology. Changes in peak plantar pressure have been associated with peripheral neuropathy [1,2], diabetes-related ulceration [3,4], and bony deformities [5], and has been suggested as a predictive clinical tool [4]. Additional metrics have also been derived from plantar pressure, such as pressure time integral (PTI), which is used to estimate the cumulative spatial load [6], and plantar pressure gradient (PPG) and pressure gradient angle (PGA), which are used to estimate shear stress or complex loading [7,8]. Increased PPG and decreased PGA have also been associated with diabetes [8].

Plantar pressure changes both spatially and temporally over the course of gait and standing, and as such has been summarized in several ways, including a single peak value over spatial and temporal dimensions [9], a temporal progression of the spatial center of pressure [10,11], and spatial deviations from a standard over normalized gait progression [12–14]. However, plantar pressure is most commonly subdivided into plantar regions. These regional analyses are typically performed using commercial software packages associated with plantar pressure collection systems. However, these packages can be inflexible to developing and using new metrics like PPG and PGA, new masking schemes, or changing the method of calculation for a predefined metric. In particular, some commercial systems calculate the PTI using only peak pressures, making it strongly correlated with the calculated peak pressure [15]. The lack of flexibility in these commercial software packages, while reducing risk of user error, increases difficulty when comparing metrics calculated using different systems or attempting to extend plantar pressure evaluations with new measurements.

Many regional plantar pressure analyses use regions defined by underlying bone geometry such as the forefoot (distal metatarsals and proximal phalanges), toes (distal phalanges), hindfoot (calcaneus), and medial and lateral midfoot (proximal metatarsals, cuboid, navicular, and cuneiforms). Therefore, an automated plantar pressure analysis based on registered bony anatomy could be useful for studies, such as geometric bone analysis or biplanar fluoroscopy, where medical images are already acquired and processed. This work aims to create a flexible, automated, and platform-independent method of analyzing plantar pressure data based on segmented computed tomography (CT) scans.

Methods

Four subjects (male, age 65 ± 2.4 years) were recruited for an IRB-approved study through the Veteran Affairs Puget Sound Health Care System. At least one static plantar pressure trial and three dynamic plantar pressure trials (self-selected speed) were taken using the emed-X plantar pressure platform (novel, St. Paul, MN, USA).

Regional plantar pressure analysis was performed using both commercial software (novel, St. Paul, MN, USA) and the custom CT-based software. For the commercial analysis, the 11-region ‘novel’ mask was applied to each static and dynamic trial using the automask program. The peak pressure, PTI, and force-time integral (FTI) were calculated for each mask using the multimask evaluation program. Regional variables were exported to a text file and an additional variable, PTI_F was calculated as FTI divided by contact area as previously reported [15].

Partial weight-bearing CT scans were acquired using the CurveBeam LineUP (Hatfield, PA, USA) with the Large patient Large FOV preset (120 kV, 5mA). Bone masks (all toes, all metatarsals, all cuneiforms, calcaneus, navicular, and cuboid) were segmented from each CT scan using Mimics (Materialise, NV Leuven, Belgium). Bone masks were exported to .bmp file format as opaque colorations overlaid on the original coronal plane images. These images were converted into a three-dimensional bone label map using custom MATLAB code. The three-dimensional bounding box and centroid of each bone were calculated from the label map using the built-in function regionprops. The transverse plane coordinates of the bounding boxes and centroids for each bone (Figure 1, left) were used to compute 11 regional masks (Figure 1, right) as follows.

Figure 1:

Left: Bone centroids and bounding boxes overlaid on project of CT intensity values through the interior-superior axis. Right: Plantar pressure mask defined by bony landmarks in the CT scan.

The medial-lateral boundaries of the hallux mask were defined as the midpoint between the hallux and second phalangeal centroids and the medial limit of the hallux bounding box. The anterior-posterior boundaries were defined as the centroid of the hallux and the anterior extent of the hallux and second phalangeal bounding boxes. The medial-lateral boundaries of the lesser toes mask were defined as the midpoint between the hallux and second phalangeal centroids and the lateral limit of the fifth phalangeal bounding box. The anterior-posterior boundaries were defined as the centroids of the second to fifth toes posteriorly and the anterior extent of the second, third, and fifth phalanges.

The first metatarsal head mask was defined medial-laterally as the midpoint between the first metatarsal and second metatarsal centroids and the medial limit of the first metatarsal bounding box. The anterior-posterior boundaries were defined as the midpoint between the first metatarsal and second metatarsal centroids and the midpoint between the hallux and second phalanx centroids. The boundaries of metatarsal heads two to four were defined as the midpoints between adjacent centroids of metatarsals and phalanges. The boundaries of the fifth metatarsal were mask were defined as the midpoint between the fourth and fifth metatarsals or phalanges, and the lateral extent of the fifth metatarsal and fifth phalanx bounding boxes.

The boundaries of the lateral midfoot mask were defined by the lateral extent of the fifth metatarsal bounding box and the midpoint between the lateral extent of the fifth metatarsal and calcaneus bounding boxes laterally and the centroid of the intermediate cuneiform and the midpoint between the centroids of the second and third metatarsal medially. The anterior-posterior boundaries were defined by the midpoints between centroids of third to fifth metatarsals and the lateral bounding box of the fifth metatarsal anteriorly and the centroid of the intermediate cuneiform and the anterior extent of the cuboid bounding box posteriorly. The boundaries of the medial midfoot mask were defined by the centroid of the intermediate cuneiform and the midpoint between the centroids of the second and third metatarsal laterally and the bounding boxes of the first metatarsal and the calcaneus medially. The anterior-posterior boundaries were defined by the midpoints between centroids of second and third metatarsal heads and the anterior bounding box of the navicular anteriorly and the anterior bounding box of the calcaneus posteriorly.

The boundaries of the hindfoot were defined by the medial, lateral, and posterior extents of the calcaneus bounding box, the centroid of the intermediate cuneiform, and the posterior extent of the cuboid bounding box. Some of the boundaries were extended by a small empirically determined factor in order to account for the extension of the soft tissue past the bone (Figure 1, right).

Plantar pressure trials were exported from the commercial software, imported into MATLAB, and registered to the summation of the CT along the superior-inferior axis. The summation was binarized using Otsu’s method [16] to obtain the soft tissue area, and the plantar pressure was binarized using a threshold of pressure measurements over zero. Angular registration was performed by calculating the sum of absolute differences (SAD) metric across angles between - 14 and 10 degrees in increments of 1 degree and selecting the angle for which the metric was minimized. Translations and scale were calculated as the difference between the bounding boxes of the binarized, rotated CT and binarized plantar pressure map. The registration was applied to the CT-generated masks to calculate the plantar pressure masks. These masks were used to calculate peak plantar pressure, FTI, PTI, pressure gradient (PPG) and pressure gradient angle (PGA) as follows.

The PTI was calculated as the spatial and temporal sum of all sensors in a region multiplied by the time step.

$$PTI={\sum }_{v=1}^T{\sum }_{i=1}^N{\sum }_{j=1}^{M}P\left(x_{i,v},y_{j,v}\right)\left(t_v-t_{v-1}\right)$$ (1)

Which reduces with uniform time steps to

$$PTI=\Delta t{\sum }_{t=1}^T{\sum }_{i=1}^N{\sum }_{j=1}^{M}P\left(x_{i,v},y_{j,v}\right)$$ (2)

Similarly, the FTI was calculated as the spatial and temporal sum of the force measured by all sensors in a region multiplied by the time step, where the force is the product of the pressure and the sensor area, making it sensitive to region definition.

$$FTI=\Delta t{\sum }_{t=1}^T{\sum }_{i=1}^N{\sum }_{j=1}^{M}P\left(x_{i,v},y_{j,v}\right)\ast A_{\mathit{\text{sensor}}}$$ (3)

A prior investigation used the FTI to compute an alternative PTI within the confines of commercial software [15]. Their definition of the FTI divided by the contact area is equivalent to the average pressure time integral over the mask area.

$$PT{I}_F=\frac{FTI}{CA}=\frac{\Delta t{\sum }_{t=1}^T{\sum }_{i=1}^N{\sum }_{j=1}^{M}P\left(x_{i,v},y_{j,v}\right)\ast A_{\mathit{\text{sensor}}}}{{\sum }_{i=1}^N{\sum }_{j=1}^M{A}_{\mathit{\text{sensor}}}}=\frac{{\sum }_{\mathit{\text{sensor}}=1}^{N}PT{I}_{\mathit{\text{sensor}}}}{N}$$ (4)

Initial dynamic frames within static trials (where subjects stepped onto the pressure mat) were removed by calculating the number of active sensors in each frame, and removing frames before the steady-state point, defined as the frame where the time derivative of the number of active sensors falls below 0.001. For dynamic trials, all frames were used.

The PPG and PGA were calculated for dynamic trials as previously reported [8,17,18]. The pressure gradient was calculated as the maximum of the difference between a pressure value and its surrounding 8-sensor neighborhood normalized by the distance between the centers of the sensors, with a buffer to remove the high gradient at the transition to the non-activated sensors outside the plantar area. The pressure gradient angle was calculated as the difference between the direction of the pressure gradient at each time step and the direction of the pressure gradient at the same sensor for the previous time step. The maximum value over the trial duration within a region is reported as the max pressure gradient (MPG) and max pressure gradient angle (MPGA) for each subject. In order to avoid selection of the border pixels of the plantar pressure map, these pixels are removed from the analysis.

CT-based mask overlays were compared visually to the 11 region built-in mask calculated by the commercial software. Mean differences and mean percent error between methods were calculated for the peak pressure, PTI_F, FTI, and PTI from each region of each static and dynamic trial, across all trials for each subject, and across subjects. Differences between methods were qualitatively compared.

Results

The SAD-based registration of plantar pressure and CT soft tissue binary maps was qualitatively acceptable. Visually, the CT-based and commercial automasking created similar masking areas. The first metatarsal, fifth metatarsal, and midfoot regions were the most different between methods (Figure 2, Table 1).

Figure 2:

Comparison of auto-generated masks between commercial and CT-based (grey background) systems. Left. CT-based 2^nd-4^th metatarsal masks are narrower and the Hallux-toes boundary is more rigid. Right. The commercial mask mislabels toes as part of the metatarsal region, which is unlikely to happen with the CT-based mask.

Table 1:

Average differences between the commercial method and the CT-based method by region and overall for both static and dynamic peak pressure, PTI, PTI_F, and FTI.

		Toes	Forefoot	Midfoot	Hindfoot	total	overall average
Difference between commerical and CT-based methods
Peak pressure (kPa)	dynamic	31.7	11.6	−19.0	−2.2	−11.5	8.9
	static	−41.3	−24.7	−40.8	−50.8	−52.1	−35.0
PTI (kPa.s)	dynamic	939	2183	1167	5157	4996	2411
	static	2072	7540	6494	43735	43719	13579
PTIF (kPa.s)	dynamic	−0.44	−0.49	−0.51	5.96	0.41	0.28
	static	−4.9	−5.7	−7.0	59.5	−2.5	1.2
FTI (N.s)	dynamic	1.2	2.8	−19.6	4.7	−4.0	−0.3
	static	−18.4	−71.7	−233.4	−365.0	−999.6	−199.4
Contact Area (cm2)	dynamic	−2.2	0.4	−10.1	5.8	−6.9	−1.3
	static	−2.6	−1.2	−13.4	1.6	−23.0	−3.2
		Percent difference of CT-based method relative to commercial method
Peak pressure	dynamic	18%	5%	−14%	−1%	−1%	5%
	static	−41%	−23%	−43%	−25%	−25%	−29%
PTI	dynamic	1735%	2209%	2230%	7205%	2199%	2615%
	static	674%	1805%	1839%	5372%	5271%	2066%
PTIF	dynamic	−18%	−10%	−36%	175%	12%	7%
	static	−61%	−25%	−65%	142%	−10%	−18%
FTI	dynamic	46%	15%	−40%	4%	−1%	13%
	static	−36%	−25%	−71%	−27%	−34%	−33%
Contact Area	dynamic	−17%	10%	−37%	15%	−5%	−1%
	static	−44%	−3%	−60%	3%	−20%	−18%

Overall, dynamic peak pressures using the commercial method were about 4.8% higher than dynamic peak pressures using the CT-based method (Table 1). Differences varied by region, but regional trends remained similar (Figure 3). FTI and PTI_F, which are calculated similarly between the two metrics, were 13.1% and 6.6% higher on average, respectively, in dynamic trials using the CT method compared to the commercial method. Again, the deviation varies by region but regional trends remain intact (Figure 3). In contrast, static peak pressure, FTI, and PTI_F calculated using only frames occurring after step-on were on average 18–33% lower than those calculated by the commercial software including step-on frames.

Figure 3:

Per-subject regional peak pressure (top), FTI (top middle), PTI_F (bottom middle) and PTI (bottom) demonstrating similar trends for comparable dynamic metrics and differences in trends for static metrics and the different PTI definitions.

The PTI calculated including sub-peak pressures was 1610–2615% higher than those calculated using peak pressures alone. The regional trends of both static and dynamic PTI differed between the two methods, with the heel sustaining qualitatively higher total loads relative to the rest of the foot over the loading time in the CT-based method compared to higher summed peak pressures in the forefoot in the commercial method. The differences in regional PTI trends and average static contact area may also reflect the removal of the step-on frames in the static trials.

The calculated maximum peak pressure gradient and maximum pressure gradient angle (Table 2) are not available to calculate in the commercial software and therefore cannot be compared in the same way as peak pressure, PTI, and FTI. Locations of high peak pressure are similar to locations of high PTI and FTI (Figure 4). However, the locations of high MPGA and MPG are not always consistent with the location of the peak pressure (Figure 4).

Table 2:

MPPG (kPa/mm) and MGPA (degrees) by region, averaged across all subjects

	HA	Toes	M1	M2	M3	M4	M5	LM	MM	HF
MPPG	55.2	41.7	31.4	28.2	27.1	23.8	42.7	13.5	3.6	35.2
MPGA	43.0	50.0	78.0	80.3	84.3	74.6	80.4	64.4	14.1	22.2

Figure 4:

Spatial heat maps of peak pressure, PTI, FTI, MPPG, and MPGA for subjects A (top), B (middle), and D (bottom). Locations of peak values are sometimes but not always correlated between MPPG, MPGA, and peak pressure. Location of peak pressure is often correlated with location of peak PTI and FTI values

Discussion

This work presents a novel method to perform automated regional masking and plantar pressure analysis using segmented CT scans. Differences in peak pressure, PTI, and FTI calculated using the two different methods were 4.7–13.1% of the total value on average. Outliers among these differences were often clustered in the values at the toes, the first and fifth metatarsals, and the midfoot-heel boundary, likely due to differences in the way that the masks are defined. The metatarsal head masks calculated with the commercial automasking software appear evenly distributed along the width of the forefoot. However, the metatarsal heads are not always distributed evenly in the soft tissue, particularly under load. The CT-projection method creates more variable widths in the metatarsal head masks and tends to place the first and fifth metatarsals closer to the sagittal midplane of the foot than the commercial software, creating larger first and fifth metatarsal areas and smaller second through fourth metatarsal areas. Additionally, the CT-based method calculates the midfoot-hindfoot border as the anterior boundary of the calcaneus, placing this boundary farther anterior than the commercial software. As a result, using the CT-based method, variable values are often lower in the midfoot and higher in the hindfoot than those calculated using the commercial method. Such regional differences affect FTI more than PTI more than peak pressures due to decreasing dependence on contact area.

The PTI calculated using all pressure values was two orders of magnitude higher than the value calculated by the commercial software using only peak values at each time step. There was qualitatively observable variation in regional trends between the two methods. Using the sub-peak pressures, the maximum PTI occurred at the hindfoot in both static and dynamic conditions, with lower values at the lateral foot and toes, while the maximum commercially calculated PTI occurred at the hindfoot for static acquisitions and the hallux or metatarsals for dynamic conditions. Differences between high and low regional PTI were more pronounced using the CT-based sub-peak pressures method. Furthermore, the regional pattern of the PTI and peak pressure using the commercial method are similar while using the CT-based method, the PTI is more similar in regional patterns to the FTI. These results indicate that there is an accumulation of higher sub-peak pressures at the hindfoot that are not captured by the commercial PTI metric, supporting the assertion of Melai et. al [6]. Such high sub-peak loads could be indicative of cumulative damage during quiet activities of daily living that are not captured by the peak summation method.

Removing step-on frames from static load acquisitions moderately affected overall and regional peak pressure values as well as regional contact area in this small sample. The reduced peak pressures at the forefoot indicate that when these frames are not removed they may artificially increase the measured peak pressure for static acquisitions and may not reflect pressures commonly experienced during daily life as the static acquisition protocol is not a common motion. Measurement of these frames could incorrectly flag forefoot areas as high risk using static pressure thresholds or disrupt secondary calculations using static data. Applications where static plantar pressure is used for stiffness calculations [19] or other applications where true quiet stance is important should take care to ensure these frames are not included.

Prior work has calculated pressure gradient and pressure gradient angle only at the location of the peak pressure [17,18,20]. However, the maximum pressure gradients and angles did not always occur within the 8-pixel neighborhood of the peak plantar pressure. Use of a matrix approach for calculating MPG and PGA allows visualization of MPG and PGA ‘maps’ which may better illustrate how the plantar pressure changes both spatially and temporally. Location of peak pressure and peak pressure gradient or peak pressure gradient angle taken together may explain more ulcer risk than location of peak pressure alone.

In some cases, the commercial automasking software incorrectly labeled toe regions (Figure 2). While the pre-defined CT-based mask regions are more box-like and less adaptable to the curves of regions like the toes, complete mislabeling of entire pressure regions is less likely. However, the CT-based method does suffer occasionally from assigning pixels on the borders of the regions incorrectly due to the rigid lines. In particular, the CT-based method assigned pixels associated with the hallux in the commercial mask to the lesser toes region due to the substantial tissue curvature at that location.

There are several limitations to this work. First and foremost, this sample is too small to validate statistical equivalence (peak pressure, FTI) or difference (PTI, removal of step-on frames). However, the calculated percent error and regional trends support the utility of this method. The use of segmented CTs limits the broader, particularly clinical, applicability and practicality of this method and contributes additional cost and patient risk. However, in cases where CT scans or MRI are already acquired and segmented for other outcomes of interest and where there is a desire for additional flexibility computing plantar pressure variables of interest, this methodology represents an efficient method for producing those results. As fields such as biplanar fluoroscopy and medical image processing advance, or in patient populations with medically required imaging such as pedal athroplasty, it may be more common to have bony anatomy available. Segmentation itself is also a significant time investment. However, automated tools are rapidly reducing the time required for this task and could be implemented for this method, as the calculation of bounding boxes does not require a high-quality segmentation. Finally, this method was only tested against a single commercial system and with normal foot anatomy. Many commercial systems calculate similar metrics using similar methods, making it likely that the CT-based method performs well relative to these methods as well. Bony deformities, such as claw toe and partial foot amputations that are common with diabetes, can create issues in masking regions of plantar pressure as there may be changes in the plantar pressure shape used to define the masks. Use of the weighted CT scan reflects the subject-specific relationship between soft tissue area and underlying bone geometry, which may be more robust to these challenges. However, the current software relies on presence of all 16 segmented bones and would need to be adapted for the case of missing bones.

Conclusion

This work contributes an alternative automated method for plantar pressure analysis and spatially extends two variables to further explore the explanatory power of plantar pressure. This method could make newer variables like MPG and MPGA more accessible, and provides a framework from which to build additional plantar pressure-based analysis.

Highlights.

• Plantar pressure masks can be automatically generated from computed tomography

• Locations of peak pressure gradients and peak pressures may be different

• Including sub-peak pressures in pressure-time integral may change regional trends