Over the last years there have been numerous investigations conducted to characterize the mechanical properties of biological tissue systems. Changes in tissue elasticity are, in fact, generally correlated with pathological phenomena. Many cancers, such as scirrhous carcinoma of the breast, appear as extremely hard nodules which are a result of increased stromal density. Other diseases involve fatty and/or collagens deposits which increase or decrease tissue elasticity. Diffuse diseases such as cirrhosis of the liver are known to significantly reduce the elasticity of the liver.

In contrast to engineering materials, biological tissues are not very well behaved, in the sense of being easily described in closed-form mathematical expressions because they are dependent on many parameters. When living, they are metabolically active and exhibit certain mechanical properties, which change soon after death. Moreover, these mechanical properties may be age, strain rate and strain range dependent. A complete and reliable tissue characterization is thus not an easy task to achieve.

The present invention has not the ambitious to solve the general problem of determining the elastic properties of tissues, but aims at providing a smart way to determine parameters related to such elastic properties that can be particularly useful for dynamic evaluation of skeletal muscles functionality.

The performance of skeletal muscles depends on the ability of the same to develop a force and, for that reason, the training is generally focused on muscle mass development. It is also true that the quality of the muscle action depends on many additional factors that are rarely assessed.

The first element of the quality of the development of strength relates to the uniformity of the distribution of muscle tension along the anatomical structure, from bone insertion, through the tendons and along the muscle. It is thus important to be able to verify, from a dynamic point of view, the correct direction of stress and traction on the insertion points and how the muscle shortens according to its contractile ability. A muscle that presents, for example, a reinforced element connected to a less powerful region causes a local increase of the stresses in the areas of connection, with a corresponding increase in the potential risk of injury. These non-uniformities in the muscular function may develop as a result of a rehabilitation program or an athletic intense workload or for individual physiological characteristics of the athlete.

A second element of fundamental importance for the performance of the musculature relates to the presence or not of an adequate dynamic balance between the various muscular structures. Each action of the musculoskeletal system is driven by a number of muscles (agonists) that work together to perform the action in the most appropriate manner with the desired strength in the required time and along the correct direction in space and a corresponding number of muscles (antagonists) that are released so as not to oppose the motion. This is what happens in every joint motion, the flexion of the hips, knees, ankles, as in the movements of the arms, hands and feet, even up to the toes, lumbar and cervical spine to mention only the main ones, or the opening and closing of the jaw.

In simplified terms, every action performed by a muscle element (the agonist) involves a reaction of a second element (antagonist): the contraction of a muscle agonist is necessarily accompanied by the corresponding relaxation of the antagonist muscle. It is therefore evident how necessary it is a balanced development between agonist and antagonist. A very common example in football, caused by normal training techniques, is the imbalance between the quadriceps (agonist of knee extension) and the flexors (antagonist). Excessively enhanced flexors restrain the action of the quadriceps and cause inaccuracy in the shooting besides causing overload on the knee with subsequent risk of muscle and tendon injuries.

It is therefore necessary to develop methods of training and preparation in football and in other disciplines, such as dance, allowing a balanced development of the muscles. This balance is the essential aim in rehabilitation techniques .

The difficulties in the development of such balanced muscle training methods are mainly of a technical nature due to the lack of technology, simple and non-invasive, for a reproducible and objective measurement of the muscular capacity dynamics, i.e. during a muscular action, involving a single or multiple muscle elements at the same time. This technological deficiency has not allowed the development of case studies thus leaving the quality of the training completely in the hands of the individual trainer.

To such extent the inventors have devised a method and a corresponding device that allow to make a quantitative dynamic evaluation of skeletal muscles functionality through sequences of ultrasound images. This is the object of copending Italian patent application N. AQ2013A000003 which is to be considered herein incorporated by reference.

While working on muscle dynamic functionality evaluation, knowing the attempts made in the prior art to try to solve the problem of tissue characterization, the inventors realized that a parameter related to tissue stiffness could be smartly determined with an ultrasound system to allow to make reproducible measurements, for example, to follow up the behaviour of a muscle after a training or a massage.

It is thus an object of the present invention to provide for an method for an improved evaluation of skeletal muscles functionality.

The invention reaches the aim with a method for estimation of elastic properties of tissues, particularly skeletal muscles, subjected to a mechanical stress, the method comprising the following steps:

a) receiving one or more sequences of two-dimensional or three-dimensional echographic images of the tissue under investigation;

b) transforming such sequence or sequences of images in sequences of measurements of deformations and/or strain rates in one or more spatial locations of the tissue;

c) acquiring from at least one sensor at least one signal indicative of the applied stress so as to obtain, through processing of said signal, information on the entity of the stress;

d) calculating stiffness-related parameters as a function of the stress and the deformations and/or strain rates as measured;

e) outputting such stiffness-related parameters in numeric and/or graphical format.

By measuring the applied stress it is thus possible to determine a stiffness- related parameter that can be used to normalize strain / strain rate measurements for different areas of the tissue.

This allows to evaluate with more accuracy the uniformity of muscle activity within same muscles and/or different muscle elements involved in the same action and/or the synchronicity of deformation between agonist and antagonist muscles by measuring deformations and/or strain rates from sequences obtained acquiring with one or more echographic probes one or more zones of the same muscle or of different muscles involved in the same action and operating a comparison between such measurements in terms of intensity and/or synchronicity. Such measurements may be, in fact, normalized by taking into account the pressure exerted by the probe while acquiring the sequences of images so that it is possible to make reproducible measurements not only on different areas of interest but also at different time instants.

The stiffness-related parameters measured according to the present invention may vary from the 81 stiffness constants of the strain tensor as will be defined hereinafter to a simple ratio stress/deformation according to the well- known Hookean formula assuming a pure elastic mono-dimensional behaviour. In any case, whatever are the parameters calculated, they can be used to provide, during the same or different exam, a normalized diagram of deformations and/or strain rates to increase reproducibility and accuracy, particularly in follow-up examinations.

According to an embodiment, the mechanical stress is substantially orthogonal to the surface of the tissue. It is preferably induced by the probe used for obtaining the echographic images of the tissue. The probe comprises at least one sensor capable of measuring such pressure. Such sensor detects pressure components along at least one direction, preferably three orthogonal directions, of a reference system. They are typically piezoelectric sensors, load cells, strain gages or the like.

According to a preferred embodiment step b) comprises determining the distribution of the deformation and/or strain rates through Optical Flow and/or Particle Image Velocimetry techniques for tracking the differential motion of the imaged regions of the tissue. Particularly, the method comprises the step of calculating the main directions of the deformations and the deformation values in such directions, the stiffness-related parameters being calculated as a function of the deformation values in such directions and the applied stress.

According to a variant, the method comprises the following steps:

calculating the velocity of points or zones having the same brightness in subsequent images of the input sequence or sequences of images;

calculating the spatial gradient matrix of said velocities;

- dividing the spatial gradient matrix in a symmetrical matrix of pure deformation and in an asymmetrical matrix of pure rotation;

diagonalizing the symmetrical matrix with calculation of the related eigenvalues;

calculating the stiffness-related parameters as a function of said eigenvalues and the applied stress.

In a particularly advantageous embodiment, for a portion of tissue of depth H that undergoes a deformation ΔΗ when subjected to a pressure stress p, the step of calculating stiffness-related parameters comprises calculating the ratio ρ/ε wherein ε is the strain defined as ΔΗ/Η.

According to another aspect, the invention relates to a device for estimation of elastic properties of tissues, particularly skeletal muscles, subjected to a mechanical stress, comprising:

a) a first input for receiving one or more sequences of two-dimensional or three- dimensional echographic images of the tissue under investigation;

b) a second input for receiving from at least one sensor at least one signal indicative of the applied stress;

c) a processing unit;

d) an output for outputting stiffness-related parameters in numeric and/or graphical format,

wherein such processing unit is configured to transform such sequence or sequences of images in sequences of measurements of deformations and/or strain rates in one or more spatial locations of the tissue, determine the entity of the applied stress and calculate stiffness-related parameters as a function of the stress and the deformations and/or strain rates as measured.

According to an embodiment, the processing unit is configured to calculate the main directions of the deformations and the deformation values in said directions. In this case the device outputs the stiffness-related parameters calculated as a function of the deformation values in said directions and the applied stress.

The device may be provided in combination with a sensor associated to an ultrasound probe for acquiring sequences of two-dimensional or three- dimensional echographic images of a tissue. The sensor is connected or connectible to the second input of the device for acquiring information related to the pressure exerted by the probe on the surface of the tissue.

The probe is preferable of the hand-held type having an emitting surface for transmitting and/or receiving ultrasonic signals when placed in contact with the surface of the tissue under investigation. The emitting surface is adapted to exert a mechanical pressure on the surface of the tissue when the probe is moved back and forth, while the pressure sensor is rigidly coupled to the probe to contact the surface of the tissue to detect the pressure exerted by the emitting surface on the surface of the tissue.

According to an embodiment, the at least one pressure sensor is coupled to an enlargement or frame of the probe, typically coplanar with the emitting surface, which surrounds the emitting surface containing the array of electro- acoustic transducers, such enlargement or frame having a surface adapted to rest on the surface of the tissue.

In case the emitting surface of the probe has a rectangular shape, the pressure sensors may be advantageously located on the enlargement or frame in proximity of each side of the emitting surface, particularly in proximity of the middle of each side. To increase accuracy, at least two pressure sensors may be located on the enlargement or frame in proximity of each longest side of the emitting surface.

The device may be advantageously provided in combination with an echographic apparatus having at least a probe for acquiring sequences of two- dimensional or three-dimensional echographic images of a tissue to be transferred to the first input of the device, the probe comprising, or being associated to, at least a sensor connected or connectible to the second input of the device for acquiring pressure-related information.

According to another aspect, the invention relates to an echographic apparatus for estimation of elastic properties of tissues, particularly skeletal muscles, subjected to a mechanical stress, comprising the above device configured to measure deformations and/or strain rates from sequences obtained acquiring with at least one echographic probe one or more zones of a tissue, determine the entity of the applied stress and calculate stiffness-related parameters as a function of the stress and the deformations and/or strain rates as measured.

In a particularly advantageous configuration, the processing unit of the device is one of the processing unit of the apparatus and the second input of the device is a port of the apparatus connected or connectible to the sensor associated to the probe for acquiring information related to the pressure exerted by the probe on the surface of the tissue. The apparatus is advantageously configured to:

- read pressure data from such second input while acquiring sequences of two-dimensional or three-dimensional echographic images of the tissue under investigation;

- transform such sequences of images in sequences of measurements of deformations and/or strain rates in more spatial locations of the tissue;

- show, as stiffness-related parameter, a normalized diagram of deformations and/or strain rates for different areas of the tissue.

The apparatus typically outputs a pressure curve, which is used to normalize the measurements of deformations and/or strain rates, particularly by dividing the values of such measurements by the value of the measured pressure at the corresponding time instant.

The apparatus is particularly advantageous when configured to evaluate the uniformity of the muscle activity within same muscles and/or different muscle elements involved in the same action and/or the synchronicity of deformation between agonist and antagonist muscles by measuring deformations and/or strain rates from sequences obtained acquiring with one or more echographic probes one or more zones of the same muscle or of different muscles involved in the same action and operate a comparison between such measurements in terms of intensity and/or synchronicity, such measurements being normalized by taking into account the pressure exerted by the probe while acquiring the sequences of images.

Further improvements of the invention will form the subject of the dependent claims.

The characteristics of the invention and the advantages derived therefrom will be more apparent from the following description of non-limiting embodiments, illustrated in the annexed drawings, in which:

Fig. 1 shows a simplified sketch of a tissue subjected to an orthogonal force with related relationship stress/deformation.

Fig. 2 shows exemplary normalized curves of longitudinal (upper part) and radial (lower part) strain calculated with a method and device according to the invention.

Fig. 3 shows, in its upper part, the echographic image of a muscle subjected to a pressure by the same ultrasound probe used for acquiring the image. The lower part shows the same figure of the upper part with superimposed a diagram of deformation as obtained with the method and device of the present invention.

Fig. 4 shows how different zones of the same muscle may have differences in the entity and time of the contraction. The curves have been obtained by normalizing the diagrams of the deformation with stiffness-related parameters calculated applying a pressure with the same probe used for the imaging.

Fig. 5 shows an exemplified block diagram of a first embodiment of the device according to the invention;

Fig. 6 shows an exemplified block diagram of a second embodiment of the device according to the invention;

Fig. 7 shows a longitudinal section of an ultrasound probe according the invention;

Fig. 8 and 9 show a view taken from the emitting side of the probe head respectively in a first and a second embodiment. In solid mechanics, the relationship stress/strain is a so-called constitutive law, i.e. it's not a physical law, but characterizes the type of material. Stiffness- related parameters are part of such a constitutive law for each material.

In the simplest case of an elastic relationship between strain and stress, there's a linear dependence according to the well-known Hooke law

τ = Ε - ε

where τ is the stress, ε the strain and E the Young's module. Fig. 1 shows how this relation applies to the deformation ΔΗ of a tissue of initial length H subjected to an external pressure increase p. The relationship pressure/strain becomes

AH _ p

H ^~ E

In soft tissues the relationship stress/strain is not linear and can be empirically considered of the type

τ = C ^■ (e ^bE - 1)

where τ is the stress, ε the strain, C and b stiffness constants that vary with age, pathologies and training. This not linear relationship is due to a sort of self- compensating mechanism which is triggered to avoid too high deformations which could lead to a rupture of the tissue.

When a tissue is subjected to a force per unity of surface (stress), its elements undergo a deformation (strain), i.e. modify their position. The Law of Continuous Media implies the existence of a function M that maps the original coordinates of the position of tissue elements X = (X1 , X2, X3) at some initial time, say t=0, into the novel position of the same tissue elements at current time t, t>0, located at x = (x1 , x2, x3). In formulae this deformation of tissue elements is written as x=M(X, t); and these elements move through space with a velocity v = dx/dt = G(X, t) where G is the time-gradient map, i.e. the time derivative of the map M.

The mapping information M can be determined using several methods. Particularly advantageous is the usage of image processing tracking procedures, such as "Optical Flow" or "Particle Image Velocimetry" (OF-PIV). See, for example, Singh A. Optic Flow Computation: A Unified Perspective. Piscataway, NJ: IEEE Comput. Soc. Press, 1992, Barron JL, Fleet DJ, Beauchemin S. Performance of optical flow techniques. International Journal of Computer Vision 1994; 12:43-77, Adrian RJ Twenty years of particle image velocimetry. Experiments in Fluids 2005; 39, 159-169.

Once the displacement map M is determined, tissue deformation can be defined by the displacement gradient tensor, F, obtained by the gradient of the displacement map F = VM, in indexing notation F = dM dX _j . Similarly the velocity gradient tensor is defined by L = VG, in indexing notation L = dG/dXj = dv dX _j . The deformation gradient is commonly best suited for Lagrangian analysis (i.e. referring all measurements on particles moving with the tissue), while the velocity gradient is usually preferred for Eulerian analysis (i.e. using reference points fixed in space).

From the basic mathematics of linear algebra, these tensors can be decomposed into two other tensors, R and U, that represent two phenomena R, for the rotation, and U for pure deformation where U is a symmetric matrix. Alternatively, the velocity gradient can be decomposed into its rotation-rate Ω and rate-of-deformation D components. The deformation U, or rate-of-deformation D, tensors are those that are related with the applied forces and the tissue elastic properties. The elastic properties of a tissue are parameters that enter in a relationship between stress and strain. There are numerous strain measures that can be constructed from matrix U or D, such as, for example, Green Strain Tensor

S = -(u - U ^< - i)

2 ^;

as disclosed in Green AE, Adkins JE (1960) Large Elastic Deformations. Oxford at the Clarendon Press or Humphrey JD (2002) Cardiovascular Solid Mechanics. Springer, New York.

Other Strain Tensors can be equally used, such as, for example, Kirchoff,

Cauchy, Piola, Almansy, etc without departing from the teaching of the present invention. It is, in fact, not relevant the type of stiffness-related parameters that are calculated, but the consistent application of the same type of parameters during the same or a different exam to obtain a normalization of the deformation and/or strain rate measurements.

Once the external forces, i.e. the stress, and the deformation, i.e. the strain, are both known then the elastic parameters that enter in a stress-strain relationship can be estimated.

When the loading is of short enough duration that the viscous nature of the material can be ignored, the tissue can be assumed to behave elastically. This means that the state of the tissue only depends on the current loading, i.e. there's not effect from the previous loading. By idealizing the tissue as an elastic material, the task of describing its behaviour is reduced to a matrix E of 81 stiffness constants as follows:

^F ij = ∑ ^E ijhk ^S IA 0 )

k,h

1,2,3

Where F is the Stress tensor, S the Strain tensor and E the stiffness matrix.

When deformation is one-dimensional, rotation is absent and deformation is immediately computed by differential displacements from the relation

^ll ^— ^llll^ll

If the tissue can be considered homogeneous and isotropic, it is possible to demonstrate that among the 81 Ej _jk h coefficients only two are independent, namely Young's module E and Poisson's module v.

In incompressible materials the Poisson's module is almost constant, thus the only unknown in (1 ) remains the Young's module.

It is thus possible, with several degrees of approximation, to determine stiffness-related parameters from the knowledge of the deformations caused by a known stress.

According to an embodiment, deformations are calculated using image processing tracking procedures, such as "Optical Flow" or "Particle Image Velocimetry" (OF-PIV), that allow to evaluate instantaneous velocity or displacements of points or particles by comparing images taken at successive moments of time assuming that the brightness of each point of the original image moves rigidly in the images of the sequence. The images can be either two- dimensional three-dimensional. The following will, however, only deal with the two-dimensional case. Obviously, this should not be construed as limiting the scope of protection, but represents only an exemplification for an immediate grasp of the mathematical concepts used.

Indicating by B ( x , y, t ) the brightness of a point P of coordinates (x , y) at the time instant t, with Vx, Vy the velocity components, respectively along the x axis and along the y axis, it can be shown that the above assumption on B implies that the following equation has to be satisfied:

There are several ways to solve this equation. The document Barron JL, Fleet DJ, Beauchemin S. Performance of optical flow techniques, International Journal of Computer Vision 1994; 12:43-77 makes an overview of these possible ways of resolution.

Although any resolution technique may be employed, the inventors have found that in the particular case of the detection of deformations muscle via echo images, the techniques of windowing and error minimization are the most appropriate in terms of complexity of calculation, and thus processing speed, and accuracy of the results.

Specifically, the speed for each point of the image can be advantageously estimated by defining a window of pixels W and minimizing the quantity:

Posing the derivative to zero, i.e.

dE

0

dV _x

dE

0

We obtain

That provides the following linear system

from which we can derive the unknowns Vx and Vy and, therefore, the field of velocities.

The deformation rates calculated by the method and the device according to an embodiment of the invention are represented by the changes of velocities in space i.e. by the gradient of the velocity vectors

dV _r dV _x

dx dy

vv

dV _y dV _y

dx dy

This matrix can be written as a sum of a symmetric matrix U and an antisymmetric matrix R in the following way

The symmetric matrix U is a pure deformation, while the asymmetric matrix R a pure rigid rotation.

According to a particularly advantageous implementation form, the invention comprises the step to diagonalize the symmetric matrix U to determine the lengthening / shortening (eigenvalues) along the principal directions (eigenvectors), i.e. the amount of pure deformation without shear. This new diagonalized matrix is the basis for the calculation of the Strain Tensor S, which, from the knowledge of the stress tensor F, allows to calculate the stiffness parameters that in their simplest form are represented by the ratio between the stress and the corresponding strain in the principal directions.

The entity and the direction of the stress is advantageously calculated by using sensors in the ultrasonic probe used for acquiring the sequences of two- dimensional or three-dimensional echographic images upon which the deformations are derived. If, in fact, it is the same imaging probe that is advantageously used also for exerting a force on the tissue by transaxially moving the transducer to compress or displace a proximal region of the tissue, by placing pressure sensors in the probe is thus possible to monitor the curve of pressure and thus strain in time.

Fig. 7 shows an ultrasound probe 3 of the hand-held type having an emitting surface 203 for transmitting and/or receiving ultrasonic signals when placed in contact with the surface of the tissue under investigation. The emitting surface 203 is composed of a series of ultrasound transducer placed side by side in an array configuration. By acting on the grip of the probe 3, the physician can use the same emitting surface 203 to exert also a mechanical pressure on the surface of the tissue.

Any type of ultrasound probe can be adapted for the aim. It can be a classical mono-dimensional probe, i.e. with transducers placed side by side along one direction, or a more sophisticated bi-dimensional probe with transducers placed in a matrix array configuration. It can be of the linear, convex or phased array type, although for the specific application to muscular analysis the linear probe seems more appropriate to better follow the longitudinal extension of the muscles.

The head of the probe has typically a rectangular or square shape following the structure of the array of transducers. Square shapes are generally employed in bi-dimensional probes for volume acquisitions. The invention advantageously provides for pressure sensors coupled to the probe.

According to an embodiment, the pressure sensors 103 can be advantageously placed on an enlargement or frame 303 of the probe 3 which surrounds the emitting surface containing the array of electro-acoustic transducers as shown in Fig. 8 and 9. The enlargement or frame 303 has a surface, typically coplanar with the emitting surface 203, which is adapted to rest on the surface of the tissue. The surface of contact is thus increased with a resulting effect of a more uniform mechanical pressure exerted when the probe is moved back and forth.

When the emitting surface 203 of the probe 3 has a rectangular shape, the pressure sensors 103 can be, for example, located on the enlargement or frame 303 in proximity of each side of the emitting surface, particularly in proximity of the middle of each side. To increase sensitivity and accuracy, two pressure sensors may be located on the enlargement or frame 303 in proximity of each longest side of the emitting surface 203.

It is to be noted that the configurations of sensors mentioned above are not to be considered limitative of the scope of protection. Just one sensor capable to detect pressure components along at least one direction, or better along three orthogonal directions, of a reference system could, in fact, suffice for the purpose. As far as pressure sensors are concerned, they may be of any known type such as piezoelectric sensors, load cells, strain gages or the like.

In the simplest actuating form shown in Fig 5, the probe 3 is connected to an ultrasound apparatus 2 capable of acquiring sequences of images of the tissue under investigation. The ultrasound apparatus exchanges data, particularly in the form of sequences of images, with the device 1 according to the invention which is also directly connected to the sensors 103 of the probe 3 to read the value of the pressure.

The ultrasound machine 2 is connected in a physical manner or through wireless connections through an input 101 . It is also possible to provide that the exchange of data between the ultrasound apparatus 2 and the device 1 is carried out through mass memories in a completely transparent way with the operation mode of the ultrasound system that, for this reason, can be of any type. The processing unit 201 of the device 1 reads the input sequences and process them to assess the deformation and/or strain rate and show the results of the analysis, for example in the graphics form of fig. 2, on a monitor 301 . The processing unit 201 may be a dedicated microprocessor system or, more generally, a PC of the general purpose type. The characteristics of the processing unit 201 will obviously reflect on the processing speed.

Through input 401 , the device 1 can read the information coming from the pressure sensors 103 of the probe 3. The processing unit 201 is configured to transform the sequences of images coming from the ultrasound apparatus 2 in sequences of measurements of deformations and/or strain rates, determine the entity of the applied stress and calculate stiffness-related parameters as a function of the stress and the deformations and/or strain rates as measured.

The stiffness-related parameters are used, for example, to normalize subsequent measurements of deformations, for example to determine the behaviour of different zones of a contracting muscle as shown in fig. 4.

A more sophisticated embodiment is shown in Fig 6, where the device 1 is integrated within the ultrasound apparatus 2. The device 1 , in this case, may be part of the processing system of the ultrasound images with the monitor 301 that coincides with the same main monitor of the ultrasound apparatus. Also the second input 401 of the device 1 can be a port of the ultrasound apparatus 2 that can be used to read the exerted pressure through an auxiliary channel as it normally happens for EKG, EMG signals. This results in a very compact system that can be dedicated, for example, to the analysis of muscle deformations.

It is, in fact, possible to configure such compact system to evaluate the uniformity of the muscle activity within same muscles and/or different muscle elements involved in the same action and/or the synchronicity of deformation between agonist and antagonist muscles by measuring deformations and/or strain rates from sequences obtained acquiring with one or more echographic probes one or more zones of the same muscle or of different muscles involved in the same action and operate a comparison between such measurements in terms of intensity and/or synchronicity. All that thanks to the possibility to normalize the measurements by taking into account the pressure exerted by the probe while acquiring the sequences of images.