Mathematical Morphology Based Volumetric Analysis of Bone

Density Around Implant in Post-Operational Follow-up of

Per-Trochanteric Fractures

Robertas Petrolis

1,2 a

, Vėtra Markevičiūtė

, Šarūnas Tarasevičius

, Deepak Raina

Lars Lidgren

, Saulius Lukoševičius

and Algimantas Kriščiukaitis

1,2 g

Department of Physics, Mathematics and Biophysics, Lithuanian University of Health Sciences,

Eiveniu str. 4, Kaunas, Lithuania

Neuroscience Institute, Lithuanian University of Health Sciences,

Eiveniu str. 4, Kaunas, Lithuania

Department of Radiology, Lithuanian University of Health Sciences,

Eiveniu str. 2, Kaunas, Lithuania

Department of Orthopaedics and Traumatology, Lithuanian University of Health Sciences,

Eiveniu str. 2, Kaunas, Lithuania

Faculty of Medicine, Department of Clinical Sciences Lund, Lund University, Sweden

Keywords: Femoral Head, Implant, Dynamic Hip Screw, Point Cloud, Mathematical Morphology.

Abstract: Per trochanteric fractures are common in an ageing population with osteoporosis and account for about half

of all hip fractures. Treatment of per trochanteric fractures with extramedullary or intramedullary implants is

challenging especially in unstable fractures. In order to improve the mechanical anchorage of the screw and

prevent re-operations, various attempts have been made to reinforce the fragile bone with polymer based

injectable materials. However, volumetric control of delivered material and/or measurement of bone density

in post-operative follow-up remains challenging. This study presents the basic principles of a new algorithm

for CT based volumetric analysis of the bone density in the region adjacent to the implant in the femoral head

in comparison to the non-operated hip. The method was also used to track long term bone density changes at

3 to 6 months of follow up.

1 INTRODUCTION

Per trochanteric fractures are common in elderly, and

account for about half of all hip fractures (Hermann

et al. 2012). Treatment of per trochanteric fractures

with extramedullary or intramedullary implants is

challenging because of poor bone quality, which

eventually leads to reoperations in up to 5% of the

cases mainly in unstable fractures. Special

mechanical solutions are proposed to cope with the

problem of implant anchorage (Aros et al. 2008). In

https://orcid.org/0000-0003-3487-733X

https://orcid.org/0000-0003-1009-5042

https://orcid.org/0000-0003-1013-3766

https://orcid.org/0000-0001-8767-892X

https://orcid.org/0000-0002-5204-1029

https://orcid.org/0000-0002-8725-4737

https://orcid.org/0000-0003-4392-1937

order to improve the mechanical anchorage of the

screw and prevent re-operations, various attempts

have been made to reinforce the fragile bone with

polymer based injectable materials, such as poly

methyl methacrylate (PMMA) (Stoffel et al., 2008;

Gupta et al., 2012) or Calcium phosphate (CaP)

(Mattsson and Larsson, 2004; Fuchs et al., 2019).

Bioresorbable calcium sulphate/hydroxyapatite

(CaS/HA) is reported as a promising solution of

implant anchoring problem. The compressive

strength of the material is higher than the cancellous

110

Petrolis, R., Markevi

e, V., Tarasevi

cius, Š., Raina, D., Lidgren, L., Lukoševi

cius, S. and Kriš

ciukaitis, A.

Mathematical Morphology Based Volumetric Analysis of Bone Density Around Implant in Post-Operational Follow-up of Per-Trochanteric Fractures.

DOI: 10.5220/0011714600003414

In Proceedings of the 16th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2023) - Volume 2: BIOIMAGING, pages 110-114

ISBN: 978-989-758-631-6; ISSN: 2184-4305

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

bone (Nilsson et al., 2003). A recent study (Kok et al.,

2021) has verified that the CaS/HA material spreads

in the trabecular structures and protects the bone from

fracturing at low loads compared to control trabecular

bone. Special procedures during per trochanteric

fracture surgery and control of the delivery of

CaS/HA at the interface of lag-screw and osteoporotic

bone can enhance the immediate anchorage (Raina et

al. 2022). The biological anchorage can be further

increased by systemically administering zoledronic

acid (ZA), a bisphosphonate that seeks the HA

material placed around the implant and induces

cancellous bone regeneration. However, precise

volumetric control of material delivery and/or bone

density in post operational follow-up remains

challenging. Areal bone mineral density obtained

from dual energy X-ray absorptiometry (DEXA),

currently used in osteoporosis diagnostics, could now

be outperformed by volumetric bone mineral density

estimated by peripheral quantitative computed

tomography (pQCT) (Watcher et al. 2001). In case of

per trochanteric fractures treatment with implants,

pQCT could be used for both: volumetric control of

material delivery and measurement of longitudinal

bone density changes. Volumetric representation and

precise delineation of volume of interest surrounding

the implant in bone allows the follow up of bone

density and implant anchoring during the whole

treatment process.

The aim of this study was to elaborate a

volumetric analysis of region surrounding the implant

in femur and algorithms for evaluation of bone

density changes over time and in regard to non-

operated areas.

2 METHODS

Trochanteric fracture patients undergoing internal

fixation with a dynamic hip screw (DHS) system

were included in the study at the department of

Orthopaedics and Traumatology, Lithuanian

University of Health Sciences. The study was

ethically approved by the hospital ethics board (P1

BE-2-76/2019). In the control group, all patients were

treated per standard care guidelines and were given a

systemic infusion of zoledronic acid, 1-2 weeks post-

surgery. The experimental arm consisted of DHS

augmented with a CaS/HA biomaterial followed by

systemic ZA administration. A volumetric imaging of

pelvic region of 9 patients (3: control, 6: treatment)

was performed by applying a GE Revolution™

Discovery™ HD CT machine (GE Healthcare,

Waukesha, WI). Slice thickness was 0,625 mm,

matrix of 512*512, postprocessing was not applied,

each voxel was representing 0.70312 x 0.70312 x

0.625 mm of space. The intensity of images was 256

levels resolution represented in Hounsfield units.

Points of metal implant had a few fold higher

intensities over the rest of points representing bone or

muscle tissues. Therefore, they were forming an easy

delineable reference object for determination of

volume of interest. Actual volume of interest –

implant surrounding environment – was determined

using 3D mathematical morphology procedure

“dilation” (MatLab function “imdilate”, using

“sphere” structural element):

𝐴

⨂𝐵  𝑧|𝐵







∩ ∅ , (1

)

while 𝐵



is the reflection of the structuring element B.

In other words, it is the set of pixel locations z, where

the reflected structuring element overlaps with

foreground pixels in A when translated to z. The

procedure selects points surrounding the reference

object. We used 7-point radius structural element to

select whole volume of interest, excluding the closest

space to the implant selected by 1-point radius

structural element. The final volume of interest was

14-voxel-thick environment surrounding the implant

and excluding 2-voxel-thick closest points to the

metal implant. Considering the voxels’ size, it

roughly could be estimated as 10 mm – thick

environment around the metal. Such volume of

interest was accepted by experts as most suitable for

implant anchoring and bone density investigations.

Determined volume of interest was transformed into

point cloud representation, where every point at

certain coordinates was carrying information about

original intensity of CT-scan representation in

Hounsfield units.

Reference volume of interest was taken from the

counterpart volume on the other side of the body –

non-operated femur. As far the anatomical pelvis-

femur structures on the left and the right side are

almost symmetric, we identified the vertical axis of

symmetry of pelvis and aligned flipped point cloud

representation of operated pelvis-femur side to the

non-operated one. For this procedure we used sparse

point cloud representation of the structures only by

selected key-points, having empirically selected

intensity of 470 - 480 Hounsfield units. It resulted in

representation of bone structures by roughly 50000

points instead of 13000000 original representation

points. The validity of representation was visually

controlled by the experts. Such reduction in

representation allowed stable and comparatively

quick operation of point cloud alignment procedures

(Matlab functions “pcregistericp”; “pctransform”)

Mathematical Morphology Based Volumetric Analysis of Bone Density Around Implant in Post-Operational Follow-up of Per-Trochanteric

Fractures

111

and gave visually confirmed good result. The

obtained point cloud transformation matrix was used

to transform coordinates of point cloud, representing

determined implant surrounding environment, to

obtain image intensities in reference region of interest

on the unoperated side. The described procedure

allowed to compare the bone density around the

implant to the unoperated reference side. Graphical

representation in form of point cloud of the

differences can reveal detailed changes in bone

density.

Long term follow-up of the bone density changes

around the implant was based on the same principle

of spatial alignment by sparse representations of the

bone structures. At this time, compared CT

volumetric representations were taken in 3- or 6-

months interval, so, spatial point cloud

representations of compared structures eventually can

have certain geometrical differences. Therefore, we

estimated differences in points of compared clouds,

which were pairwise closest to each other by

Euclidean distance in space. Pairs of such closest

points in compared point clouds were found using the

Kd-tree based search algorithm (Muja et al. 2009)

(MatLab function “findNearestNeighbors”).

3 RESULTS

Process of volume of interest determination in CT

scan volumetric lower body representation is

illustrated in Figure 1 by typical real clinical image.

The key-points selected for sparse spatial

representation of left and right parts of pelvis area are

marked by “o” and “+” respectively. Implant, as solid

body, is shown in black. Implant surrounding

environment is shown in blue.

Figure 1: Sparse representation of left and right pelvis for

determination of region of interest surrounding the implant

(blue cylinder body) and its counterpart on the opposite side

(green cylinder body). The number of points representing

structure of pelvis here is reduced for visual clarity.

After determination of implant surrounding

environment, the sparsely represented spatial

structure (marked by “o”) is flipped and aligned to its

counterpart on the other side (marked by “+”). The

corresponding volume in the unoperated side is

marked in green as control volume of interest. The

whole procedure can be visually controlled.

Figure 2: Histograms of intensity values of implant

surrounding environment together with counterpart

environment from unoperated side.

Histogram of intensity values of implant and the

surrounding cancellous bone compared with the

unoperated side is presented in Figure 2. As one can

notice, bone density adjacent to implant is

significantly higher than in control volume from the

unoperated side. Detail spatial distribution of

differences across the whole volume of interest is

obtained by 3-D presentation of points in actual space

positions where differences are represented by colour

and marker size. Such representation is illustrated in

Figure 3 and revealed a noticeably bigger differences

are situated close to the implant surface in patient

where CaS/HA filling was used to enhance anchorage

of the implant (see right side of the graph). There is

no such clearly visible difference in case when

CaS/HA filling was not used.

Histograms of bone density differences in cases

illustrated in Figure 3 are presented in Figure 4. This

is preliminary, yet promising result, showing the

increased bone density when CaS/HA filling was

used.

Example of investigation results of long-term

changes in bone density during three months follow-

up is shown as histograms of spatial points intensity

in implant surrounding environment immediately

after operation and after three months (Figure 5).

Slightly visible difference in histogram

supplemented by spatial representation of pairwise

comparison of intensities in each point of point cloud

of implant surrounding environment gives much

more detailed diagnostic information (Figure 6).

BIOIMAGING 2023 - 10th International Conference on Bioimaging

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Most visible positive changes in bone density

after three months are in the implant surrounding

area, at the tip of the implant. It is a promising result

showing that bone density increased at the region

where most of CaS/HA filling was delivered.

Figure 3: 3-D presentation of points of implant surrounding

environment in actual space positions in the patient when

CaS/HA filling was used (right side) and in the contralateral

side of the same patient where no filling was used (left

side). The differences between intensity of implant

surrounding environment and counterpart unoperated side

are represented by colour and marker size as indicated on

the right side of the graph.

Figure 4: Histograms of bone density differences in case

when CaS/HA filling was used compared with un-

augmented controls. The data are from cases illustrated in

Figure 3.

4 DISCUSSION

Dual energy X-ray absorptiometry (DEXA),

routinely used for evaluation of bone mineral density

in osteoporosis diagnostics gives Ca concentrations

estimates in absolute values. However, the region of

interest for estimates could not be defined so

precisely as we show for CT-scan volumetric images.

Usage of calibrating technics, as in peripheral

quantitative computed tomography, could offer

acceptable precision for Ca concentration estimation.

Figure 5: Histograms of intensity values of implant

surrounding environment immediately after operation and

after 3 months.

Figure 6: 3-D presentation of differences between intensity

of implant surrounding environment immediately after

operation and after three months.

On the other hand, we are mostly interested in

changes of Ca concentration than absolute values

during post operational follow up, therefore CT-scan

volumetric imaging supplemented with algorithms of

precise determination of volumes of interest, as we

present here, could outperform DEXA in diagnostic

value.

The presentation of volume of interest as point

cloud gives us the new possibilities of facile data

management and evaluation using comparatively

small computational resources. Methods of spatial

transform and alignment allow to perform detailed

Mathematical Morphology Based Volumetric Analysis of Bone Density Around Implant in Post-Operational Follow-up of Per-Trochanteric

Fractures

113

comparison of intensity in every particular spatial

point of real investigated object. Point-to-point

comparison of intensities revealed detail dynamics in

bone density caused by implant insertion and special

chemical means to reinforce implant anchorage.

Detail 3D representation of differences in bone

density gives us a visual control for selection of

difference estimates to be used for evaluation of

effect of chemical reinforcement materials used. In

this study we have very limited amount of patient data

and we show only preliminary results. However, the

aim of this study was to show the technical means to

be used in such studies and to reveal the directions of

further development.

One of the challenging tasks revealed in this

process was determination of volume of interest in the

particular anatomical structures (counterpart volume

of interest in the unoperated side) – determination of

reference points. In this work we selected the points

in the lower body CT scan according the intensity,

which was empirically selected by visual control. The

expert was aiming to have as much as possible area

of pelvis to be represented with minimal number of

points. After several attempts we ended up with

roughly 50000 points selected out of 13000000

original representation points. Changing the number

of selected points even by 2-folds up or down from

the used one did not have any significant impact on

accuracy of spatial representation and subsequent

alignment procedures. Nevertheless, additional

investigation of optimal number of points and

methods of their selection is needed. We simply

selected the existing original points of volume

representation, but construction of new reference

points in regard to local geometric properties of

special anatomic structures would be a promising

direction of investigations.

5 CONCLUSION

Point cloud presentation of objects or volumes of

interest in volumetric CT-scan data reveals the new

possibilities of facile data management and

evaluation using comparatively small computational

resources at the same time giving the valuable

diagnostic results.

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