ES3036180A1 - Computer-implemented method for personalized evaluation of the attractive stimulus for bone remodeling models, based on images taken of a patient - Google Patents

Abstract

Computer-implemented method for personalized evaluation of the attractor stimulus for remodeling models, comprising the following steps: obtaining (100) a medical image of a bone structure (E) to be studied; defining (200) representative load states (LS 1 , LS 2 , LS 3) of said bone structure; calculating (300) by structural numerical analysis, the mechanical stresses and/or deformations that appear in the bone structure during the representative load states; selecting (400) a representative stimulus region (RSF) of the bone structure (E); and calculating (500) the attractor stimulus (Ψ A) corresponding to said representative stimulus region (RSF), from the values of the stimulus at the tissue level (Ψ t) which in turn is calculated from the stimulus at the continuous level (Ψ) in the representative stimulus region (RSF). (Machine-translation by Google Translate, not legally binding)

Description

COMPUTER-IMPLEMENTED METHOD OF PERSONALIZED EVALUATION OF THE ATTRACTIVE STIMULUS FOR BONE REMODELING MODELS, FROM

OF IMAGES TAKEN OF A PATIENT

Technical sector

The invention belongs to the technical fields of biomechanics and preventive medicine, and is particularly applicable, for example and without limitation, in the design of bone implants, as well as in clinical practice.

State of the art

One of the most significant needs in biomechanics and preventive medicine is the development of personalized numerical models for each patient. Numerical models for estimating bone reconstruction are particularly important. Due to their precision, low cost compared to experimental methods, and noninvasive nature, they are especially useful in the design of prostheses and implants, and they also allow for individualized medical follow-up for each patient.

Currently, it is possible to create numerical models from existing literature data. However, these models can only be used to describe the generic behavior of a population, but not in the context of personalized prosthetic design and personalized medicine. Furthermore, existing methods for extracting bone remodeling parameters are economically costly and, in some cases, ethically questionable, as in the case described by L.E. Lanyon and colleagues in the article "Bone Deformation Recorded In Vivo From Strain Gauges Attached To The Human Tibial Shaft." Acta Orthopaedica Scandinavica, issue 46, pages 256 to 268, published in 1975, where the placement of a strain gauge directly on the surface of the tibia of a living subject is shown to extract information on the mechanical behavior of the bone.

An essential parameter in the formulation of numerical models of bone remodeling as a function of time is the so-called attractor stimulus, ¥¿, (also known as maintenance, homeostatic or reference stimulus), of bone tissue, measured at the tissue level.

In fact, taking as a basis the attractor stimulus, ¥¿, Beaupré et al., in their article “An Approach for Time-Dependent Bone Modeling and remodelling - Theoretical Development”. Journal of Orthopaedic Research. Issue 8 (1990), pages 651-661, formulated a time-dependent bone remodeling algorithm that allows modeling the process of bone tissue creation/resorption. This algorithm considers that trabecular bone tissue, from a macroscopic point of view, is isotropic and assumes that microstructural phenomena can be modeled by its continuous, average or "apparent" behavior, with said behavior having sufficient spatiotemporal homogeneity for the application of continuum mechanics and its differential equations.

Throughout this description, the most widely accepted definition of this parameter will be used, meaning that the attractor stimulus (¥¿) is essentially the daily amount of tissue-level stimulus, ¥ t , necessary to preserve apparent bone density. To this end, the so-called continuous-level stimulus, ¥ , will be calculated for a load case i, according to the following equation:

where:

nes the number of cycles associated with each of the loads,

m is the effective voltage at continuous level, induced by the load i,y

month the voltage exponent, a parameter that weighs the importance of the frequency and intensity of the load.

The stimulus at the tissue level is calculated using the so-called Power Law, which relates the stimulus at the continuous level ¥ , with the stimulus at the bone tissue level, ¥t :

where:

pes the apparent density;

PCES is the density of cortical bone (fully saturated);

Therefore, it represents the state of stimulation that causes bone density to be maintained, such that, if the mechanical stimulus at the tissue level, Wt, is less than the attractor, the bone tissue would be under little stress and would tend to reabsorb (decrease its density), while, if the mechanical stimulus is greater than the attractor, the bone tissue would be under great stress and would tend to densify (increase its density).

It is also known to use various generic, reference, i.e. non-subject-specific, attractor stimuli in bone remodeling models, as described, for example, by J. Martínez-Reina et al. in their article “On the Use of Bone Remodeling Models to Estimate the Density Distribution of Bones. Uniqueness of the Solution”, PLoS ONE 1, 11-2 (2015), or J. Martínez-Reina et al. in their article “A bone remodeling model including the directional activity of BMUs”, Biomechanics and Modeling in Mechanobiology, 8, pp. 111-127 (2009). However, the proposed estimates are based on generic, purely theoretical approximations, so their validity may vary significantly from one specific patient to another.

On the other hand, A. Calvo-Echenique et al. in their article “Numerical simulations of bone remodelling and formation following nucleotomy”, Journal of Biomechanics, 88, pp. 128-147, (2019), describe other ways of calculating the attractor stimulus, which are not based on theoretical foundations but on quantitative calculations, although they do not allow an individualized estimate to be made for each patient.

Methods for qualitative approximation of the attractor stimulus based on the patient's age have also been developed, based on theoretical trends and with application in the simulation of bone remodeling, such as those disclosed, for example, by A. Papastavrou et al., in their article “On age-dependent bone remodelling”, Journal of Biomechanics, 103 109701, (2020). However, these estimates are also based on generic and theoretical approximations, so they suffer from the same disadvantages already described above.

Furthermore, other forms of theoretical estimation of the value of the attractor stimulus are known, with application in the simulation of bone remodeling, for example those disclosed by: G. S. Beaupré et al. in the article “An Approach for Time-Dependent Bone Modeling and remodelling - Theoretical Development”, Journal of Orthopaedic Research, 8, pp. 651-661, (1990), or by G. S. Beaupré et al., in their article “An approach for time-dependent bone modeling and remodelling - application: a preliminary remodelling simulation”, J. Orthop Res, 5:663-70, (1990). These other estimates are also based on generic theoretical approximations, so they present the same drawbacks already mentioned.

In view of all the above, it is necessary to develop an alternative solution for the prediction of bone remodeling based on the calculation of the attractor stimulus, which can be performed individually for each patient or subject and without the need to generate heavy numerical models, such as numerical models at the trabecular level, nor data that go beyond those usually obtained in clinical practice.

Summary

The present invention aims to address the aforementioned disadvantages and inconveniences of the aforementioned techniques. To this end, a first object of the invention relates to a computer-implemented method for personalized evaluation of the attractor stimulus for bone remodeling models, characterized in that it comprises the following steps:

a) obtain at least one medical image of a bone structure under study; b) define load states representative of the use of the bone structure;

c) use computer processing means to calculate, by means of structural numerical analysis, the mechanical stresses and/or deformations that appear in the bone structure during representative loading states;

d) using computer processing means to select a representative stimulus region, RSF, of the bone structure shown in the medical image, based on the results obtained in the previous stage; and

e) calculate with the computer processing means the attractor stimulus corresponding to said representative region of stimuli, RSF, from the values of the stimulus at the tissue level W in the representative region of stimuli, RSF.

Thanks to the method according to the invention, it will be possible to predict how the remodeling of a bone structure (object of study) will be, on an individual basis for each patient, since said method bases the prediction on the value of the attractor stimulus obtained from real medical images of the patient's bone structure in question. In contrast, prediction methods already known in the art use, to a greater or lesser extent, mere generic theoretical approximations, which lead to non-personalized, less precise, and less reliable results.

Furthermore, in order to carry out this method, data commonly obtained in clinical practice will be used, such as, but not limited to, a conventional Computed Tomography (CT-scan) medical image. It is not necessary to collect any other data beyond those commonly obtained in clinical practice.

In a first embodiment of the method for personalized evaluation of the attractor stimulus for bone remodeling models according to the present invention, the selection of the representative stimulus region, RSF, of the bone structure comprises the following additional sub-steps:

- calculate the position of the median plane of the bone structure, defined as the transverse plane located halfway along its length;

- locate the point of the bone structure belonging to the median plane, for which the highest value of mechanical deformation is obtained, from all representative loading states; and

- select as the representative stimulus region, RSF, that region that has its center at the point obtained in the previous sub-stage and extends from said center a predefined length along each axis of space;

Furthermore, in the embodiment of the method of the invention described in the previous paragraph, the attractor stimulus is calculated as the average value of the stimulus at the tissue level Wt , in the representative region of stimuli, RSF.

In a second embodiment of the method for personalized evaluation of the attractor stimulus for bone remodeling models according to the present invention, the representative stimulus region (RSF) of the bone structure is that region in which the maximum values of the mechanical deformations caused by the representative loading states are within a certain physiological range, also called adapted window. Furthermore, in the embodiment of the method of the invention described in the previous paragraph, the attractor stimulus is calculated as the average value of the stimulus at the tissue level W in the representative stimulus region RSF of the bone structure.

Preferably, in the second embodiment of the personalized evaluation method according to the present invention, said predefined range of maximum values (or adapted window) of the mechanical deformations is between 50 and 1,500. Even more preferably, said predefined range of maximum values of the mechanical deformations is between 225 and 1,250^ s.

In a third embodiment of the method for personalized evaluation of the attractor stimulus for bone remodeling models according to the present invention, the representative stimulus region (RSF) of the bone structure is that region in which the total difference in stimulus values at the tissue level ¥ t is minimized. Furthermore, in this third embodiment of the method of the invention described in the previous paragraph, the attractor stimulus is that value that minimizes the bone remodeling rate f r (¥¿) defined by:

where

r is the bone remodeling rate of voxel /; and

Nrel number of voxels in the stimulus representative region.

Throughout this description, it should be understood that a voxel, or volumetric pixel, is the unit with the shape of a rectangular parallelepiped that makes up a three-dimensional element, being in the case described in the previous paragraph, the region representative of stimuli a set of voxels.

A second object of the present invention relates to a computer-readable medium comprising instructions, which, when executed on a computer, cause said computer to carry out the steps of one of the methods of personalized evaluation of the attractor stimulus for bone remodeling models, according to the first object of the invention, described above.

In the context of the present invention, a computer should be understood as any device provided with processing means capable of executing logical instructions such as, for example: laptops, desktop computers, tablets, smart phones (in English, smartphones) and smart watches (in English, smartwatches).

Brief description of the drawings

Figure 1 is a flowchart showing the steps comprising a method for personalized evaluation of the attractor stimulus for bone remodeling models, according to the present invention.

Figure 2 schematically shows representative load states associated with a walking cycle, which are used in a method employed according to Figure 1;

Figures 3a, 3b, 3c and 3d are schematic figures showing the distribution of apparent density in the bone structure under study in the method of Figure 1, obtained during an intermediate sub-stage of the calculation stage of stresses and/or deformations by finite element analysis;

Figure 4a is a schematic figure showing which of the representative load cases produces the maximum principal strains at each point of the bone structure under study in the method of Figure 1.

Figure 4b shows the distribution of the maximum principal deformations of the bone structure under study in the method of Figure 1, obtained with data from each representative loading state;

Figure 5 schematically shows the representative region of RSF stimuli obtained in the method of Figure 1; and

Figure 6a shows the tissue-level stimulus values that appear in the bone structure under study, obtained according to the method in Figure 1, as a result of the third representative loading state;

Figure 6b is an enlarged detail of Figure 6a, in which the representative region of RSF stimuli can be better appreciated, and

Figure 6c is, in turn, an enlarged detail of Figure 6b, in which only the values corresponding to said representative region of RSF stimuli are shown.

Detailed description

Figure 1 schematically illustrates the steps comprising a first embodiment of a method for personalized evaluation of the attractor stimulus for bone remodeling models, according to the present invention.

According to said method, in a first step 100, a medical image of a bone structure (E, shown for example in Figs. 3a and 3b) being studied is obtained. In this particular case, the image obtained is a computed tomography (CT) image and the bone structure E is a human femur of a 75 kg male. However, the method of the present invention contemplates the possibility of using other types of medical images such as, for example and without limitation, magnetic resonance imaging (MRI). Logically, it is also possible to apply the method of the invention to other different bone structures.

Next, in step 200, the load states representative of the use of the bone structure are defined. To do this, the living conditions that give rise to the appearance of loads on the structure and, therefore, generate the appearance of bone adaptation patterns are determined. In this particular case, since the bone structure under study is a human femur, walking at a normal pace is considered the most representative activity in the observed bone tissue, given its relevance in daily life. In fact, the representative mechanical loads of each bone are known to a person skilled in the art. These loads can be obtained using existing musculoskeletal models adapted to each patient or directly measured.

Figure 2 schematically shows the main stages of the gait cycle. As can be seen in this figure, there are two main stages: a heel strike phase, HP, in which the heel of the target leg is in contact with the ground, and a swing phase, SP, in which this contact does not occur.

The heel strike phase, HP, begins the moment the heel makes contact with the ground (instant HP<1>). The sole of the foot then progressively increases its contact with the ground until it reaches a completely flat position (instant HP<2>).

The time interval between instants HP<i> and HP<2> is called the load response phase, RP. The heel contact phase, HP, ends at instant HP<3>, when the heel begins to lift off the ground. The heel swing phase, SP, in turn, begins at instant SP<1>, when the toes begin to lift off the ground, and continues until instant SP<2>, before the heel makes contact with the ground.

In the personalized evaluation method of the attractor stimulus for bone remodeling models illustrated in the Figures, three representative loading states of the walking cycle described above are considered to exist: LS<1>, LS<2>, and LS<3>. The first representative loading state, LS<1>, occurs shortly after the instant HP<2> at which the sole of the foot assumes a completely flat position (at an instant corresponding to 13% of the walking cycle). The second representative loading state, LS<2>, occurs between the instant HP<3> (at which it ends in heel contact) and the instant SP<1>, at which point the toes begin to lift off the ground, more specifically, at an instant corresponding to 37% of the walking cycle. Finally, the third representative load state, LS<3>, coincides with the instant SP<1>, in which the toes begin to lift off the ground and which corresponds to 66% of the walking cycle.

The next step of the personalized evaluation method of the attractor stimulus for bone remodeling models illustrated in the figures, i.e., step 300, consists of calculating by finite element analysis, the mechanical stresses and/or deformations that appear in the bone structure during the representative loading states: LS<1>, LS<2>, and LS<3>.

To this end, in this particular embodiment of the method of the invention, the computer processing means use the medical image obtained in step 100 to create a numerical model using a Cartesian mesh finite element method (cgFEM). This finite element method (cgFEM) also incorporates a 3D slicing sub-step to segment the femur tissue visible in the medical image. The present invention, however, contemplates the possibility of using other different numerical simulation methods.

Subsequently, in this specific embodiment of the invention and without limitation, the value in Houndsfield units (Hüvoxei) of each voxel of the femur tissue (obtained from the CT Scan medical image) is transformed into the apparent bone density value in each voxel.

For this purpose, as an example, each value (Hüvoxei) obtained is converted, in turn, into a pvoxel apparent density value, through the following linear relationship:

where:

Pw= 0.022 g/cm3 and Hüw= 0 are, respectively, the assigned density and the assigned Houndsfield units for tissue other than bone; and

Pc= 2.1 g/cm3 is the density of cortical bone and Hüc= 1,950 is the maximum value of Houndsfield units, measured in the CT scan medical image.

However, the present invention also expressly contemplates the use of other methods already known in the art to calculate the pvoxel apparent density value.

The results obtained in this sub-stage are shown in Figures 3a, 3b, 3c and 3d, where Figures 3a and 3b are images of the complete femur under study, while Figures 3c and 3d correspond to different sections of it.

The Young's modulus of each voxel is then calculated from its apparent density value using the following relationship:

However, the present invention also expressly contemplates the use of other methods already known in the art to calculate Young's modulus from the apparent density of each voxel.

Then, in carrying out the method of the invention illustrated by the figures, the computer processing means obtain the maximum principal deformations for each load state ei, i5 l,e2l ls2i ,ls3 using the following equation:

where:

'1,LS is the maximum principal strain corresponding to the voxel and the representative loading state LS; and

\e¡|, \e¡¡ |, \e¡¡¡\are the principal deformations obtained by solving the eigenvalues of the deformation tensor.

Figure 4a schematically illustrates the maximum principal strains occurring in bone structure E during the representative loading states LS<1>, LS<2>, and LS<3>. These strains were obtained using the equation described in the previous paragraph during calculation stage 300 by means of finite element analysis. In Fig. 4a, each shade of gray identifies one of these most representative loading states.

Figure 4b shows the distribution of the maximum principal strains '<1>,^ using data from each representative loading state. In this embodiment of the invention, the maximum principal strains e1¡ max are calculated using the expression:

where LSI represents each of the representative charge states.

It is important to note that the sub-steps of step 300 described in the preceding paragraphs, namely the sub-step of segmenting the bone structure tissue; the sub-step of assigning a Houndsfield units (Hüvoxe) value to each voxel; the sub-step of converting said Hüvoxe values to an apparent density value, pvoxei, and the sub-step of calculating the Young's modulus of each voxel from its apparent density value, are nevertheless applicable to any embodiment of the method for personalized evaluation of the attractor stimulus for bone remodeling models according to the invention.

Next, in the personalized evaluation method described in the figures, step 400 takes place, in which the computer processing means, based on the results obtained in the previous step, select a representative region of RSF stimuli, from the bone structure E visible in the medical image.

In this particular case, as graphically illustrated in Figure 5, to obtain the representative region of RSF stimuli, the position of the median plane S<m> of the bone structure is first calculated. Next, point C of the bone structure E belonging to the height of the median plane S<m> is located, for which the highest value of the mechanical deformation is obtained, of all the representative loading states.

The position of the central point C is defined by the angle a<g p ,>which is the angle formed between the coronal plane P<c>(i.e. the intersection between the center of the femoral head and the upper lateral point of the greater trochanter) and the plane P<g>(i.e. the plane that contains said point C and that also cuts the femoral axis).

Next, in the method according to the invention, described in the figures, the representative region of RSF stimuli shown, for example, in Figure 5, is chosen as that region that has its center at point C obtained in the previous sub-step and extends from said center a predefined length along each axis of space.

Finally, in the last step of the method according to the invention shown in the figures, step 500, the attractor stimulus ^ is calculated as the average value of the tissue-level stimulus W in the region representative of RSF stimuli. To do this, the following equations are used:

where:

nes the number of cycles associated with the load. In this particular case, 10,000 load cycles,7 is the effective stress, induced by the load in the voxel considered, and

month the stress exponent. In this particular case m = 4, and

n

The choice of the stress exponent m = 4 is based on the recommendation given by R.T. Whalen et al. in their academic article “Influence of physical activity on the regulation of bone density,” published in the Journal of Biomechanics, Volume 21, Issue 10, 1988, pages 825–837.

Figure 6a shows the tissue-level stimulus values ¥ t that appear in the bone structure E under study, calculated based on the previous equation, as a result of the third representative loading state.

Figure 6b is an enlarged section of Figure 6a, which better shows the region representative of RSF stimuli. Finally, Figure 6c is, in turn, an enlarged detail of Figure 6b, which shows only the tissue-level stimulus values Wt , corresponding to said region representative of RSF stimuli.

Claims (5)

CLAIMS 1. A computer-implemented method for personalized evaluation of the attractor stimulus for bone remodeling models, characterized in that it comprises the following steps: a) obtaining (100) at least one medical image of a bone structure (E) under study; b) defining (200) load states (LS<1>, LS<2>, LS<3>) representative of the use of the bone structure (E); c) using computer processing means to calculate (300), using numerical structural analysis, the mechanical stresses and/or deformations that appear in the bone structure (E) during the representative load states (LS<1>, LS<2>, LS<3>); d) selecting (400) using the computer processing means a representative stimulus region (RSF) of the bone structure (E) shown in the medical image, based on the results obtained in the previous step; and e) calculate (500) using the computer's processing means, the attractor stimulus (¥¿) corresponding to said representative stimulus region (RSF), based on the tissue-level stimulus values W in the representative stimulus region (RSF). 2. The method of claim 1, wherein the step of selecting the representative stimulus region (RSF) comprises the following substeps: - calculating the position of the median plane (S<m>) of the bone structure (E); - locating the point of the bone structure (E) belonging to the median plane for which the highest value of mechanical deformation is obtained from all the representative loading states; and - selecting as the representative stimulus region (RSF) that region having its center at the point obtained in the previous substep and extending from said center a predefined length along each axis of space; and furthermore, the attractor stimulus (¥¿) is calculated as the average value of the tissue-level stimulus W in the representative stimulus region (RSF). 3. Method according to claim 1, wherein the representative stimulus region (RSF) of the bone structure is the region in which the maximum values of the mechanical deformations caused by the representative loading states (LS<1>, LS<2>, LS<3>), are within a predefined range and in the attractor stimulus (¥4) is calculated as the average value of the stimulus at the tissue level ¥ in the representative stimulus region (RSF). 4. Method according to claim 3, wherein the predefined range of maximum values of the mechanical deformations is between 50 and 1,500^s and more preferably, between 225 and 1,250. 5. Method according to claim 1, wherein the representative stimulus region (RSF) of the bone structure is the region in which the total difference of the stimulus values at continuous level (¥ ) is minimized and in which, in addition, the attractor stimulus (¥4) is the value that minimizes the bone remodeling rate ( / f ( ¥<4>)) defined by: where f is the voxel's bone remodeling rate; and N is the number of voxels in the representative stimulus region (RSF). <6>. A computer-readable medium comprising instructions which, when executed on a computer, cause said computer to perform steps of a method for personalized evaluation of the attractor stimulus for bone remodeling models, according to any one of claims 1 to 5.