Method and system for simulating intervertebral disc pathophysiology

A computer-implemented method and system for modeling the pathophysiology of a human intervertebral disc may comprise an anatomic dataset and a biophysical model disposed in connection with a simulation program. The biophysical model may comprise a plurality of subsystems, including, without limitation, governing equations, constitutive equations, boundary conditions, initial conditions, and parameter values. By altering certain subsystems of the biophysical model, a user may selectively solve for certain pathophysiological metrics using at least one of a plurality of algorithms disposed within the simulation program. Moreover, such selective altering of the subsystems, such as, for instance, the boundary conditions, may allow a user to impose certain conditions on the computer-implemented method system, thereby allowing a user to dispose the intervertebral disc of the model at, for instance, in vivo human conditions, and subsequently initiate simulated degeneration conditions thereto, for the efficient and accurate modeling of such an intervertebral disc.

BACKGROUND OF THE INVENTION

Field of the Invention

The present invention is directed to a method and system for simulating the pathophysiology of intervertebral discs including a computer-implemented program for implementing such simulation.

Description of the Related Art

An intervertebral disc is a fibrocartilaginous structure which lies between each of the vertebrae in the spinal column, functioning to both transfer loads and provide flexibility. Each intervertebral disc consists of a complex structure disposed in three distinct parts: (1) a fibrocartilaginous annulus fibrosus, comprising outer and inner regions and composed of concentrically orientated layers of fibrous tissue; (2) a central nucleus pulposus; and (3) two cartilaginous endplates. Each of these will be briefly discussed in greater detail hereafter.

The annulus fibrosus consists of a series of concentric rings, or lamellae, with aligned parallel collagen fibers disposed within each lamella, and elastic fibers disposed therebetween. Such a structural arrangement allows the annulus fibrosus to react to the tensile and compressive forces associated with spinal movement, thereby allowing an intervertebral disc to return to its original shape following such flexion and/or extension of the spine.

The nucleus pulposus comprises a gelatinous tissue composed primarily of proteoglycan aggrecan, with type II collagen fibers randomly arranged therein. Such an elastic structure disposed at the inner core of the intervertebral disc allows such intervertebral disc to withstand forces of compression and torsion, playing an essential role in the flexibility and stability of the spine.

The cartilaginous endplates are composed of osseous and hyaline-cartilaginous layers and are located between the vertebral endplates and the nucleus pulposus. Such cartilaginous endplates function to transmit compressive loads across the disc-bone interface, pressurize the nucleus pulposus, and support nutrient transport for the intervertebral disc.

As may be understood, degeneration of the intervertebral disc, which is associated with lower back pain, may significantly affect an individual's quality of life. Typically, degeneration of the intervertebral disc may alter various physiological aspects of the spine, such as the disk height of each intervertebral disc and the mechanics which stem therefrom, wherein such degeneration commonly leads to chronic segmental spinal instability. Specifically, as disk height decreases, the mechanics of the affected spinal segment is altered, which subsequently may lead to acceleration of the degeneration of adjacent spinal segments, as well as other spinal structures, such as small joints, ligaments, and muscles. Accordingly, as may be generally understood, the disruption in the normal architecture of any of the aforementioned structures from which the intervertebral disc is comprised, may lead to altered mechanics, and perhaps other physiological problems, such as disc herniation, a protrusion of the inner nucleus pulposus, or the application of pressure on the spinal cord or a nerve root.

It is generally understood cells play a significant role in the degeneration of intervertebral disc. Specifically, disc cells live in a complicated mechano-electrochemical environment, and their activities and viability are regulated by mechanical signals (e.g., deformation, stress, fluid flow, and solute transport), electrical signals (e.g., streaming potential and current), and biochemical signals (e.g., nutrition level, pH, and growth factor level). The cells function to maintain the balance between anabolism and catabolism of tissue; that is, they synthesize both the macromolecules, for the extracellular matrix maintenance, and the catabolic molecules, for the matrix breakdown. A detrimental tilt in this balance, due to the disturbance of the extracellular environment, may cause a cascade of biological reactions and result in the ruination of the matrix integrity and the failure in the tissue-level structure and function, thereby leading to tissue degeneration. Put simply, a lack of balance in the mechano-electrochemical environment in which such disc cells live may detrimentally affect the geometry of the intervertebral disc, and thereby lead to the degeneration of said intervertebral disc.

However, for a plurality of reasons, such as the asymptomatic nature of intervertebral disc degenerations, the understanding of the degeneration of intervertebral discs remains deficient. For instance, one such reason stems from a lack of understanding of the causes of such mechano-electrochemical imbalances. Specifically, as technology has progressed, the traditional thinking of such causes has shifted from the traditional views of environmental exposures, such as smoking, and occupation, to more contemporary views, such as mechanical, nutritional, and genetic factors.

Similarly, the current experimental methods and systems through which degeneration of intervertebral discs are studied compound such deficient understanding. Specifically, due to the difficulty of obtaining human spinal tissue, and particularly ‘normal’ human spinal tissue, the viability of conducting in vivo experiments is extremely limited. Accordingly, experimental model systems designed to study intervertebral disc degeneration normally consist of in vitro cell culture, in vitro explant culture of whole discs, and in vivo animal models.

Although these systems previously led to a significant amount of in-depth knowledge on the degenerative disc cascade, it may be understood these model systems are insufficient to infer the pathophysiology of human intervertebral discs and effective treatment strategies therefor. For instance, because in vitro experiments require highly specific conditions to induce the naturally observed behaviors of cells, and because different experiments on different cell cultures are often necessary to obtain different levels of understanding, it is challenging to systematically compile and analyze such experimental findings at multi-scale levels. Likewise, because in vitro experiments may only maintain near in vivo conditions for a short duration of time, it is challenging to investigate the chronic nature of the degeneration process, which may take decades, in such models. Finally, as may be understood, it is difficult to assess the efficacy of treatment strategies targeting the halting and reversal of the progression of intervertebral disc degeneration in animal models at least because the causes of disc degeneration are different. For instance, disc degeneration in animals is typically generated through surgery or chemical treatment, whereas disc degeneration in humans typically may occur from genetic factors and/or insufficient nutrient supply.

In view of the above challenges, there remains a need in the art for an improved model system designed to study the pathophysiology of human intervertebral discs. Given the complexity of the mechano-electrochemical environment in which intervertebral disc cells operate, computational model systems have proven particularly useful in the modeling thereof. Moreover, any such computational model system should be particularly disposed to study, through computational simulations, such intervertebral discs as a part of an in vivo human model, in addition to the in vitro cell, in vitro explant, and in vivo animal models present in prior art models. Further, such a computational model system should have the capacity to: (1) systematically synthesize existing experimental results and findings to illustrate intervertebral disc pathophysiology; (2) provide quantitative information on complicated interactions among the bioinformatics (e.g., biological, chemical, and mechanical) within the human intervertebral discs in various pathophysiological conditions; and (3) predict the evolution of disc pathophysiology caused by external stimuli, including factors causing disc diseases and interventions treating same, in an accurate and efficient manner.

SUMMARY OF THE INVENTION

The present invention is directed to a computer-implemented method and system for simulating the pathophysiology of intervertebral discs. At least one embodiment of the present invention includes an initial data input from any number of sources. Generally speaking, and after the input of such anatomic data, a simulation program may be implemented to utilize said anatomical data to solve sets of equations disposed within a biophysical model. Such sets of equations may include various combinations of governing equations, constitutive equations, boundary conditions, initial conditions, and parameter values. The equations disposed within such biophysical model may be solved by the simulation program according to a plurality of numerical methods, wherein the solutions to same may be displayed as a plurality of pathophysiological metrics.

Further, in at least one embodiment, such pathophysiological metrics may then be stored within the simulation program as historical data, for use as comparison values in subsequently enacted simulations. Moreover, as may be understood, such a biophysical model may be altered prior to running the simulation program, thereby allowing a user to obtain a variety of physiological metrics in accordance with a given intervertebral disc under a variety of different conditions. Accordingly, a user of such a computer-implemented method and system may not only obtain at least one of a plurality of physiological metrics in which he or she is interested in, but also may compare such physiological metric(s) with previously determined data, whether from the same intervertebral disc or data representing a sample population, thereby allowing for the effective use of such data for a variety of different purposes, including, without limitation, research, education, drug and medical device development, clinical trials, diagnoses, and treatment strategies.

In at least one embodiment of the present invention, the simulation of an intervertebral disc in the computer model envisioned herein begins with the aforementioned initial data input. As previously stated, such initial data input of an anatomic dataset may come from any number of sources, whether input manually by a user, or automatically from an interconnected medical imaging device or like apparatus. For instance, such an anatomic dataset may be manually input by a user in accordance with the results ascertained from a diagnostic test performed on a patient. Such a diagnostic test may comprise, for instance, the medical history of patient, a physical exam, and other more invasive procedures, such as a provocative discogram. Alternatively, the anatomic dataset may comprise information ascertained through various interconnected diagnostic imaging devices, such as X-rays, computed tomography scans, and magnetic resonance imaging scans, wherein such data may automatically be transmitted into, and received by, a memory disposed to receive the anatomic dataset. As may be understood, such an anatomic dataset may be stored by at least one memory device, for the later retrieval and use thereof. Moreover, as may be understood, such an anatomic dataset may be modified manually by a user for the tailoring towards any specific simulation of an intervertebral disc.

Moreover, in order to both provide greater flexibility in such a computer-implemented model, and to further provide greater efficiency in executing the simulation program disposed therein, such an anatomic dataset may comprise, at least, the geographic information of a given intervertebral disc. As may be understood, such geographic information may comprise, for instance, the disparate portions of an intervertebral disc, such as the annulus fibrosus, the central nucleus pulposus, and the two cartilaginous endplates, and the solid, fluid, and solute phases associated therewith.

In addition to such anatomic dataset, the memory may also store a biophysical model. Said biophysical model may comprise a system of mathematical equations expressing the complicated mechano-electrochemical environment in which the intervertebral disc operates. By way of a non-limiting example, a subsystem of the biophysical model may include governing equations, generally expressed through a plurality of differential equations, wherein said governing equations describe, for example, the spatiotemporal variations of variables representing the pathophysiological features of the intervertebral disc. Likewise, an additional subsystem, such as the constitutive equations, may describe the observed, theoretical, and/or assumed relationships between biophysical quantities, thereby characterizing specific features of the intervertebral disc. Additional subsystems may comprise initial conditions, parameter values, and boundary conditions, which may operate to constrain the simulation program to only those solutions which are the most efficient and reasonable. Further, as will be discussed later, such boundary conditions may further be disposed to define the type of simulation to be performed, whether an in vivo human model or otherwise. Moreover, it is envisioned each individual subsystem of said biophysical model may be situationally adjusted or modified, thereby providing greater flexibility to the simulation program.

In other words, and as will be discussed in greater detail hereafter, the biophysical model may be understood as a representation of the active and passive interaction between the various phases of an intervertebral disc, wherein at least a portion of the model comprises a mathematical description of the interactions between cells and all other constituents. Specifically, the biophysical model may be disposed to model intervertebral disc tissues as multiphasic materials, including, without limitation: (1) a solid phase, which is composed of multiple solid constituents including, without limitation, non-charged macromolecules, negatively charged glycosaminoglycans, and cells; (2) a fluid phase, including, without limitation, interstitial fluid; and (3) a solute phase comprising a plurality of species, such as, sodium ions, chloride anions, oxygen, glucose, lactate, etc.

Accordingly, such biophysical phases, and the biophysical activities occurring both therein and therewith, may be represented through the biophysical model using a plurality of theorems and principles, such as, without limitation, the continuum-mixture theory. For instance, constitutive equations comprising mass balance and linear momentum equations may be written for each phase, or any mixture thereof. Likewise, thermodynamics laws may be applied to constrain such constitutive equations.

Moreover, a plurality of assumptions may be made to further constrain the system, thereby simplifying same and increasing output efficiency. For instance, such assumptions may comprise, for instance: (1) the domain is fully saturated; (2) each phase is intrinsic incompressible; (3) the volume fraction of the solute phase is negligible; and (4) the changes in mass and volume of each phase due to biological activities is negligible.

With further reference to at least one embodiment of the present invention, a processor may be disposed in connection with the memory, wherein the processor is disposed to run a simulation program upon the input of the anatomical dataset and the biophysical model. Such a simulation program may comprise a plurality of algorithms, through which the solutions to said biophysical model may be ascertained. As may be understood, such algorithms may comprise, for instance, at least one of a plurality of applicable numerical methods including, without limitation, finite difference, finite volume, finite element, spectral, lattice Boltzmann, particle-based, level-set methods, and other past, present, or hereafter discover equivalents and/or combinations thereof. Accordingly, when a biophysical model over a specific anatomic dataset is solved, the simulation program may return the results as a series of pathophysiological datums in the form of discrete, numerical metrics.

As may be understood, such pathophysiological metrics may, in at least one embodiment of the present invention, be displayed in accordance with any number of visualization techniques through an interconnected graphical user interface, which may be disposed in input-output relation with the memory and the processor. Accordingly, such an interconnected graphical user interface may not only change the way in which such pathophysiological information is presented, but may also be disposed to modify any data disposed in the anatomical dataset, and any subsystems disposed in the biophysical model, upon user interaction, to specifically tailor the simulation program to any specific pathophysiological metric associated with a given intervertebral disc.

Further, in at least one embodiment of the present invention, the simulation obtained pathophysiological metrics may then be stored in a database to be compared with historical data obtained from alternative simulations, anatomic datasets, and/or biophysical models. The computer-implemented method may also include methods for manual or automatic analysis of the solutions to the biophysical model over the domain defined with the anatomic dataset. Comparison of the instant solutions with previously acquired solutions may subsequently be used to empirically create trends between different biophysical events and conditions, or to draw inferences about any level of disc health for diagnostic or prognostic analysis of intervertebral disc pathophysiology in relation to any external or internal factors.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention is directed towards a computer-implemented method and system for simulating the pathophysiology of intervertebral discs. Generally speaking, the present invention is directed towards at least one memory, which is disposed to store an anatomic database, a biophysical model, and a simulation program. The at least one memory may further be disposed in connection with at least one processor which may, upon user input, apply the simulation program to the anatomic database and the biophysical model to solve series of equations using at least one of a plurality of numerical methods to determine certain pathophysiological metrics associated with the given anatomic database. As may be understood, in at least one embodiment, the anatomic database and the biophysical model may be altered by a user to dispose the simulation thereof in various experimental models, such as in vivo human conditions, or to change other biophysical conditions, such as constitutive equations or initial conditions associated with the simulation model, to solve for pathophysiological metrics associated with an intervertebral disc disposed in varying degeneration conditions.

As previously stated, the present invention may utilize at least one memory disposed in connection with at least one processor, for effectuating the simulation of the pathophysiology of intervertebral discs. As may be understood, the at least memory may have computer-readable instructions stored thereon, and may comprise, for instance, solid state drives, RAM, hard disk drives, removable disk drives, network storage, data farms, cloud storage, and any other type of data storage reasonably suited for storing such computer-readable instructions, while taking into account the scale at which the simulation program of the present invention is disposed to operate. Such storage may be achieved entirely, or in part, by a sole computing device, which may be locally situated or otherwise. As may be further understood, in at least one embodiment of the present invention, the at least one memory and at least one processor may be further disposed in input/output connection with at least one graphic user interface, which may be disposed for user input directed towards the operation of the simulation program of the present invention.

Depicted inFIG.1is a schematic representation of a computer-implemented method and system for simulating the pathophysiology of intervertebral discs100in accordance with at least one embodiment of the present invention. As may be seen, disposed in connection with a simulation program20, may be an anatomic dataset10and a biophysical model30, which may comprise a plurality of subsystems, such as governing equations31, constitutive equations32, boundary conditions33, initial conditions34, and parameter values35. As may be seen, the simulation program20may be disposed to determine the pathophysiological metrics40from the anatomic dataset10and the biophysical model30.

With continued reference toFIG.1, and with further reference toFIG.2, it may be seen the anatomic dataset10may serve to represent a two-dimensional and/or three-dimensional intervertebral disc60. For instance, the anatomic dataset10may comprise geometric information, such as the nucleus pulposus61, the annulus fibrosis62, and the cartilaginous endplates63. Moreover, the anatomic dataset10may further comprise certain anatomic information about the intervertebral disc60, such as the anatomic information pertaining to the solid phase65, the fluid phase66, and the solute phase67of the any particular geometric area of the anatomic dataset. For instance, the anatomic dataset10may further comprise a defined geometry64, represented by the mesh disposed on the intervertebral disc60, which may serve to specifically identify the geometric and anatomic information to which a given simulation pertains.

As may be understood, the anatomic dataset10may be generated from a variety of sources such as, for example, medical images of an intervertebral disc60, as depicted inFIG.2. Such medical images may be automatically disposed to be input into the computer-implemented method and system100of the present invention. For example, a medical imaging device or like apparatus, such as X-rays. computed topography scans, and magnetic resonance imaging scans, may be interconnected to the memory of the computer-implemented method and system100of the present invention, for the automatic upload of such anatomic information10. Alternatively, users may elect to manually input the anatomic dataset10in accordance with any alternative medical or diagnostic tests performed on a patient. Such a diagnostic test may comprise, for instance, the medical history of the patient, a physical exam, and other more invasive procedures, such as a provocative discogram. Moreover, as may be understood, in at least one embodiment of the present invention, the anatomic dataset10may be manually modified by the user after the input into the memory thereof, for the tailoring towards any specific simulation of an intervertebral disc60. For instance, the anatomic dataset10may be altered in subsequent simulations to obtain different sets of pathophysiological metrics from a given anatomic dataset10.

As previously mentioned, and with further reference toFIG.1, the memory may store a biophysical model30, disposed to comprise a plurality of subsystems, which may comprise a system of mathematical equations expressing the complicated mechano-electrochemical environment in which the intervertebral disc operates. For example, as shown inFIGS.1and2, an intervertebral disc60may be modeled as a mixture of multiple components, classified as the solid phase65, fluid phase66, and solute phase67. The solid phase65may represent all the components, such as collagen, proteoglycan, and the cell, forming the solid matrix of an intervertebral disc60. Likewise, the fluid phase66may represent interstitial fluid, whereas the solute phase67may represent all the solutes disposed in an intervertebral disc60, such as sodium ions, chloride anions, oxygen, glucose, lactic acids, and growth factors. Accordingly, it may be assumed at any instant in time, all such phases of an intervertebral disc60are present at every material point. As may be understood, all such phases may be represented through the plurality of subsystems comprising the biophysical model30, all of which will be discussed in greater detail hereafter.

One such subsystem of the biophysical model30comprises the governing equations31. The governing equations31may describe the spatiotemporal variation of variables representing the pathophysiological features of the system and may be constructed for each component of an intervertebral disc60based on the biophysical principles inherent therein. For instance, the governing equations31may include, without limitation, equations detailing various conservation laws, such as the conservation of mass, the conservation of linear momentum, the conservation of angular momentum, and the conservation of energy, and laws pertaining to entropy inequality. Likewise, an electroneutrality condition may be applied through such governing equations31.

As may be understood, the governing equations31may be typically expressed in the form of partial and/or ordinary differential equations, wherein combinations of such governing equations31may be used to model a particular biophysical model. For example, dependent upon the specified defined geometry64from the anatomic dataset10, particular governing equations31may be applied to more accurately represent same. For instance, an electroneutrality condition may be used to accurately model various electrochemical effects, such as the differences between an area of interest and an environment. Likewise, because an imbalance of ions resulting between an electrochemical effect may drive water from one area of an intervertebral disc60to another, which may subsequently cause the swelling of tissues in the porous solid phase65, additional governing equations31may be required to describe the space and temporal flow of such an intervertebral disc60. Accordingly, combinations of governing equations31pertaining to such plurality of conservation laws may be necessary to provide a physical model of an intervertebral disc60compliant with the continuum-mixture theory. As may be understood, solutions to such governing equations31may be available for any given time or location of an intervertebral disc60, despite such an intervertebral disc60having a variety of phases simultaneously present therein.

For example, for a domain consisting of a solid phase (s)65with multiple components (β), fluid phase (w)66, and solute phase67with multiple species (α), one may write governing equations31comprising the conservation equation of mass, conservation equation of linear momentum, and electroneutrality condition, all based on the continuum mixture theory, as follows:

As may be understood, the aforementioned governing equations31may be derived according to a plurality of assumptions, namely: (1) the domain is saturated; (2) each phase is intrinsic incompressible; (3) the volume fraction of the solute phase67is negligible; (4) the changes in mass and volume of the solute phase67and the fluid phase66due to biological activities are negligible; and (5) the effect of inertial forces on linear momentum in each phase is negligible (i.e., the system is at a quasi-static state).

With continued reference toFIGS.1and2, it may be seen the biophysical model30may further include a subsystem comprising constitutive equations32. Such constitutive equations32may comprise a plurality of equations disposed to quantitatively describe the relations between two or more biophysical quantities, thereby characterizing specific features on an intervertebral disc60. As may be understood, such constitutive equations32may be derived from theory, observation, and assumption. For example, a constitutive equation32describing the glucose-concentration-level-dependent-cell-viability may be developed based on experimental observation and assumptions. Likewise, a constitutive equation32representing an external osmolarity-mechanical function may be developed in accordance with same. As may be understood, because constitutive equations32describing the relationships between two or more biophysical factors may be very complex and difficult to express for all solutions as an exact equation, such relationships may be approximated as models created according to historical empirical statistics for specific constraints.

For instance, and with the aforementioned governing equations31in mind, certain constitutive equations32may be written in accordance with the following examples. For example, where fluid is driven by the gradients of the modified fluid chemical potential (εw) and modified solute electro-chemical potential (εα), a constitutive equations32directed thereto may be written as follows:

jw=-R⁢T⁢k⁡(∇ɛw+∑α⁢cαɛα⁢∇ɛα⁢Hα)
where R is the universal gas constant, T is the absolute temperature, k is permeability, and Hαis the hindrance coefficient of solute species α for convection. Further, where solute is advected by fluid as well as driven by its electro-chemical potential gradient, the solute flux can be written as:

jα=Hα⁢cα⁢jw-ϕw⁢cα⁢dαɛα⁢∇ɛα
where dαis solute diffusivity. Here, the transport properties k, dα, and Hαcan be constants or functions of other primary variables.

Further, the consumption/production rates, ĉαand {circumflex over (ρ)}β, may be derived from biology principle, observation, and assumption. For example, based on biology principles, the rate of net mass change of glycosaminoglycan equals to the difference of synthesis rate and breakdown rate, and thus, such a constitutive equation32may comprise:
{circumflex over (ρ)}β=λsynρcell−λdegrρβ, β=glycosaminoglycan
where λsysis the glycosaminoglycan synthesis rate per unit cell, and λdegris the glycosaminoglycan degradation rate per unit of glycosaminoglycan mass. As another example, a relationship between cell viability and extracellular glucose concentration (cg) can be developed based on experimental observations as follows,

With further reference toFIG.1, it may be seen boundary conditions33comprise another such subsystem of the biophysical model30and comprise constraints imposed thereon for the solution of such governing equations31. As may be understood, such boundary conditions33may be adjusted according to the specific situation at hand, whether such situation pertains to the defined geometry64or otherwise. As may be understood, because the governing equations31typically comprise a plurality of partial and/or ordinary differential equations, and because solutions to such partial and/or ordinary differential equations typically comprise a plurality of solutions, of which only one may be reasonable, such boundary conditions33may be imposed upon the biophysical model30to eliminate such unreasonable solutions, thereby simplifying the model100and increasing the efficiency of the simulation thereof.

As may be understood, a plurality of boundary conditions33may be applied in accordance with the numerical methods in which the biophysical model30may be solved by the simulation program20. As previously mentioned, such numerical methods may include, without limitation, finite difference, finite volume, finite element, spectral, lattice Boltzmann, particle-based, level-set methods, and other past, present, or hereafter discovered equivalents and/or combinations thereof. Accordingly, it may be understood such boundary conditions33may comprise any boundary condition suitable for the applicable numerical method used, and for constraining the biophysical model30in accordance with the disclosure herein.

However, in at least one embodiment of the present invention, such boundary conditions33may specifically comprise a first boundary condition51, which may comprise a Neumann boundary condition, and a second boundary condition52, which may comprise a Dirichlet boundary condition. As may be understood, such first boundary condition51and second boundary condition52may likewise comprise alternative boundary conditions which suitably constrain the biophysical model30in accordance with same.

As previously stated, the first boundary condition51may comprise a Neumann boundary condition. As may be understood, such a first boundary condition51may thus operate to specify the values in which the derivative of a solution may be applied within the boundary of the anatomic dataset10. Likewise, the second boundary condition52, which may comprise a Dirichlet boundary condition, may operate to specify the values a solution must take along the boundary of the anatomic dataset10. The application of such first boundary condition51and such second boundary condition52will be discussed in greater detail hereafter.

Returning toFIG.1, it may be seen a further subsystem of the biophysical model30may comprise the initial conditions34. As may be understood, such initial conditions34may comprise the values of independent variables at some point in time, which may be designated as the initial time. Such initial conditions34may be constants and/or functions of other variables, such as, for instance, space. As may be understood, such initial conditions34may be adjusted in accordance with the simulation of a specified set of conditions of an intervertebral disc60.

One final subsystem of the biophysical model30, in accordance with at least one embodiment of the present invention, may comprise parameter values35. Parameter values35may comprise numerical characteristics used to help define the remaining subsystems of the biophysical model30, such as the constitutive equations32, the boundary conditions33, and the initial conditions34. As may be understood, the values of such parameter values35may be obtained and/or estimated through experimental measurements.

With further reference toFIG.1, at least one embodiment of the present invention may comprise a simulation program20, disposed in connection with the anatomic dataset10and the biophysical model30. Such a simulation program20may comprise, for instance, a numerical algorithm disposed to solve the biophysical model30over the domain defined by the anatomic dataset10. As previously stated, such a numerical algorithm may comprise at least one of a plurality of numerical methods disposed to solve same, such as, for instance, finite difference, finite volume, finite element, spectral, lattice Boltzmann, particle-based, level-set methods, and other past, present, or hereafter discovered equivalents and/or combinations thereof. Accordingly, as may be understood, the application of certain numerical methods may be specifically applied to solve for specified pathophysiological metrics40, in accordance with the biophysical model30and the domain defined by the anatomic dataset10.

For example, a lattice Boltzmann method may be used to simulate fluid collision processes and viscous flow behavior of the fluid phase in the biophysical model. Likewise, finite difference methods may be used to solve simpler sets of linear equations, dependent upon the simplicity of the biophysical model30. Level-set methods may be used to calculate interface interactions between two different fluids. For example, use of such level-set methods may be particularly useful in calculating the interactions between water-imbibed collagen in the solid phase and the interstitial fluid phase, because such fluid interfaces often have complicated tension and/or interaction effects due to the non-zero net force on the molecules at such fluid interface.

Accordingly, it is envisioned, in at least one embodiment of the present invention, any combination of such numerical methods may be tailored and applied to efficiently solve for any specific biophysical model30. Thus, the method and system100in accordance with at least one embodiment of the present invention may be able to solve for, store, and analyze nearly any desired relationship between the biological, electrical, chemical, and mechanical events and/or interactions within an intervertebral disc60with just one anatomic dataset10.

With further reference toFIG.1, following the application of the simulation program20, and the obtainment of solutions to the biophysical model30, it may be understood pathophysiological metrics40may be extracted therefrom. Such pathophysiological metrics40may subsequently be displayed in accordance with any number of visualization techniques through a graphic user interface, as previously mentioned. For example, such pathophysiological metrics40may be used to illustrate the simulation of disc degeneration caused by the reduction of permeability of the cartilaginous endplates, as depicted inFIG.3, wherein the glycosaminoglycan content is represented by the concentration of charged groups attached thereto. Likewise, such pathophysiological metrics40may be used to illustrate the spatial distribution of cell viability in an engineered intervertebral disc tissue, as depicted inFIG.4, wherein the black line represents the pathophysiological metrics40and the gray line represents experimental measurements.

Such pathophysiological metrics40may have a variety of uses. For instance, such pathophysiological metrics40may be used as data collection for the systematic synthetization and creation of a more accurate illustration of intervertebral disc pathophysiology. Moreover, in at least one embodiment, such pathophysiological metrics40may be stored in the memory as historical data, for the subsequent comparison with pathophysiological metrics40derived from subsequent simulations. As may be understood, such comparison may be accomplished in any number of ways, whether through direct eye-test comparisons, or through further statistical models and/or analysis, such as the provision of normal distribution ranges and comparison of percentile ranges. Accordingly, the pathophysiological metrics40may be used to draw inferences in accordance with such historical data or may simply be incorporated as another data point in a trend analysis. Thus, comparison with such historical data may provide for the determination of any differences and/or similarities between intervertebral discs, anatomic dataset, and/or simulations, which may accordingly be used in the prediction of the evolution of the pathophysiology of an intervertebral disc, and for prognostic and diagnostic information thereto.

With reference toFIG.5, depicted therein is a method200for applying the aforementioned components in the simulation of the pathophysiology of an intervertebral disc. As may be seen, such method200may first comprise the step of an input210of the anatomic dataset10and the biophysical model30, to be stored on at least one memory. As previously stated, the anatomic dataset10may be input either automatically, through an interconnected device, such as a diagnostic imaging device, or manually through a user. Conversely, the biophysical model30may be already stored on the memory for use in accordance with the anatomic dataset10. Further, as previously stated, such anatomic dataset10and biophysical model30may be disposed in connection with a simulation program20, which may also be stored on the memory, all of which may be disposed to be operated on by at least one processor, for the simulation thereof.

The following steps of a method200in accordance with at least one embodiment of the invention comprises the selection220of a defined geometry64. As previously stated, the defined geometry64may comprise, for instance, a particular geometric area of an intervertebral disc60for which a particular simulation may be processed. Accordingly, such a defined geometry64may pertain, for illustrative purposes, to an entire intervertebral disc or, alternatively, to a cross-sectional layer of an entire intervertebral disc60, as depicted by the mesh inFIG.2. Conversely, such defined geometry may comprise only a portion of an intervertebral disc, such as a region pertaining solely to the annulus fibrosis62, the nucleus pulposus61, or the cartilaginous endplates63. Thus, the selection220of the defined geometry64may serve to specify the type of simulation to be run in accordance with the method200.

In accordance therewith, the method200may subsequently discretize230the biophysical model30over such defined geometry64. As may be understood, such discretization step230serves to improve the efficiency of the method200by transferring the continuous functions of which the biophysical model30is comprised into discrete counterparts, thereby simplifying such functions and constraining the biophysical model30only to those functions appropriate for representing the defined geometry64.

The next step of the method200, in accordance with at least one embodiment of the present invention comprises defining240the plurality of subsystems of the biophysical model30. As previously stated, such subsystems comprise the governing equations31, the constitutive equations32, the boundary conditions33, the initial conditions34, and the parameter values35. Moreover, as previously stated, such subsystems may be altered by a user in a further attempt to constrain the simulation to a specified application, as will be discussed in greater detail hereafter.

For example, although the solid phase65, the fluid phase66, and the solute phase67may be adopted to represent intervertebral disc tissues in the biophysical model30, any such phases may be disabled in the biophysical model30if the biophysical activities or biophysical fields associated therewith are not relevant to the user in performing a specific application of the method200. One way to effectuate such disablement is to selectively exclude the governing equations31pertaining to the irrelevant phase. For example, because the cell viability in an engineered intervertebral disc may be predicted by solving the governing equations related to the solute phase67and the cells in the solid phase65, such governing equations31may be selectively used and disposed within the defined geometry64. Alternatively, a phase may also be disabled indirectly by adjusting certain parameter values35to make the contribution of such phase to the overall biophysical model30negligible. For example, the mechanical responses, or disc height, of an intervertebral disc60at the static state may be simulated by setting the parameter values35pertaining to fluid permeability and solute diffusivities to values much higher than their physiologically reasonable levels, thereby negating their impact on the biophysical model30as a whole. Accordingly, the computational time may be significantly reduced without affecting the computed mechanical responses of an intervertebral disc60at the static state.

One such manner in which the plurality of subsystems may be defined240particularly comprises the simulation of an intervertebral disc60at in vivo human conditions. Specifically, in vivo human conditions may be prescribed to an intervertebral disc60by defining240the plurality of subsystems to comprise specific boundary conditions33disposed to closely represent such in vivo human conditions. While alternative boundary conditions33are contemplated herein, at least one embodiment of the present invention may dispose the method200to simulate such in vivo human conditions by prescribing the boundary conditions33in the following manner.

First, where the first boundary condition51comprises a Neumann boundary condition and the second boundary condition52comprises a Dirichlet boundary condition, it may be understood the boundary conditions33for each phase may be selectively divided into such first boundary condition51and such second boundary condition52, to be applied to the biophysical model30as a whole. Moreover, such boundary conditions33may be prescribed in accordance with the type of intervertebral disc at issue, whether native or engineered. Accordingly, for a native intervertebral disc, such first boundary condition51and second boundary condition52may be defined by the outer surface of the annulus fibrosis, and the interface between the cartilaginous endplates and the vertebra. Likewise, for an engineered intervertebral disc, the first boundary condition51and the second boundary condition52may be defined according to the culture conditions of such engineered intervertebral disc. Accordingly, the boundary conditions33for the solid phase65, the fluid phase66, and the solute phase67may be defined as follows, wherein n represents the outward unit normal to the boundary and * represents the prescribed values:

Accordingly, with such boundary conditions33in mind, the defining240of the boundary conditions33subsystem in relation to the remaining biophysical model30may comprise the appropriate application of certain boundary conditions33, pertaining to specified portions of the biophysical model30. Specifically, such boundary conditions33may comprise a first designated boundary condition53, and second designated boundary condition54, and a third boundary condition55, each of which will be discussed in greater detail hereafter, with reference toFIG.6.

The first designated boundary condition53may comprise the application of a first boundary condition51, representing an equivalent spring boundary condition, to the outer surface of the annulus fibrosis, thereby representing the mechanical interaction between an intervertebral disc60and its surrounding tissues. If the mechanical interaction is not to be considered, it may be understood the parameter value35representing the equivalent spring stiffness for such first boundary condition51may be set to zero.

The second designated boundary condition54may comprise a selective application of either the first boundary condition51and the second boundary condition52, dependent upon the type of mechanical loading at issue on the superior and/or inferior surface of an intervertebral disc60. Specifically, the application of either the first boundary condition51or the second boundary condition52depends upon whether such mechanical loading on the superior and/or inferior surface of an intervertebral disc60is prescribed by displacements on the interface of the cartilaginous endplates63and the vertebra, or whether such mechanical loading may be described by mechanical force and/or stress. In the event such mechanical loading comprises displacements, then the second boundary condition52may be applied to such interfaces of the cartilaginous endplates63and the vertebra. Conversely, where such mechanical loading comprises mechanical force or stress, the full or partial superior and/or inferior vertebrae may be included within the biophysical model30and the first boundary condition51may be applied on the vertebra surfaces.

The third designated boundary condition55may comprise the selective application of the first boundary condition51and the second boundary condition52for the values of chemical potential and electro-chemical potential of an intervertebral disc60for the fluid phase66and the solute phase67, respectively.

As may be understood, when defining240the plurality of subsystems, any deformed state may be chosen as a reference configuration for strain. However, the swelling pressure at such reference configuration should be subtracted from the total stress in the simulation. Likewise, one must note the computed mechanical stress is not an absolute value, but rather, is a relative value to such reference configuration.

With continued reference toFIG.5, it may be seen the method200in accordance with at least one embodiment of the present invention may further comprise the step of computing250at least one solution to the biophysical model using the simulation program. As previously stated, such computation250may comprise the application of at least one of a plurality of numerical methods to determine the solutions to the biophysical model. In the event boundary conditions33have been applied in accordance with the aforementioned step for defining240the plurality of subsystems, it may be understood such at least one solution may be constrained to only those solutions which represent the simulation of an intervertebral disc60at in vivo human conditions. Finally, once such at least one solution has been determined, the pathophysiological metrics40may be extracted260therefrom, and subsequently displayed270using a graphic user interface.

With additional reference toFIG.7, at least one embodiment of the present invention may further comprise a method200disposed to store280such extracted pathophysiological metrics40as historical data, thereby allowing for the subsequent comparison and display of pathophysiological metrics40obtained from subsequent simulations therewith.

Moreover, as may be seen with continued reference toFIG.7, one additional step may be contemplated in at least one embodiment of the present invention, namely, a step for selectively redefining240athe plurality of subsystems. As may be understood, such selective redefining240aof the plurality of subsystems of the biophysical model30may allow a user to research a plurality of specified pathophysiological metrics40from a single anatomic dataset10. Likewise, such selective redefining240amay alternatively allow a user to generate specific degeneration scenarios of an intervertebral disc60stemming from a single anatomic dataset10.

For instance, one such way the plurality of subsystems may be selectively redefined240ais to simulate the disc degeneration of an intervertebral disc60at in vivo human conditions. More specifically, a user may selectively redefine240acertain subsystems of the biophysical model30to generate specified conditions in which the degeneration of an intervertebral disc60at in vivo human conditions may occur, thereby allowing a user to model an intervertebral disc60at in vivo human conditions for an extended length of time, thus allowing for the realistic modeling thereof.

For example, while alternative methods and techniques for selectively redefining240athe plurality of subsystems to represent the disc degeneration of an intervertebral disc60at in vivo human conditions are contemplated herein, at least one embodiment of the present invention may employ three alternative ways in which in vivo disc degeneration may be simulated through such selective redefinement240a.

For instance, one such technique comprises changing the boundary conditions33to generate disc degeneration cascades in the simulated domain. For example, a user may progressively alter the boundary conditions33to reduce the solute electro-chemical potential at a boundary of an intervertebral disc60, thereby simulating the effects of same over a period of time.

Likewise, an alternative technique comprises changing the constitutive equations32to change the material properties of certain aspects of an intervertebral disc60. For instance, a user may reduce the permeability of an intervertebral disc60to obtain pathophysiological metrics40in accordance withFIG.3. Further, a user may instead alter the spatial distribution of glycosaminoglycan content in a degenerated disc to obtain pathophysiological metrics40in accordance withFIG.4.

Moreover, one further technique comprises changing the constitutive equations32to adjust the cell metabolic activities or viability thereof. For instance, a user may reduce the glycosaminoglycan synthesis rate to simulate the loss of glycosaminoglycan content in the degeneration process.

Of course, all pathophysiological metrics40obtained through such selective redefinement240aof the plurality of subsystems may be stored280as historical data, for later comparison. In this manner, the degeneration of an intervertebral disc60at in vivo human conditions may be modeled for an extended length of time and at multi-scale levels, thereby allowing for a more accurate modeling thereof.

Accordingly, it may be understood the present invention provides a computer-implemented system for modeling the pathophysiology of human intervertebral discs. Moreover, in addition to providing the ability to model such intervertebral discs as a part of in vitro cell and in vitro explant models, at least one embodiment of the present invention further enables a user to model an intervertebral disc at in vivo human conditions, while minimizing and/or eliminating the typical limitations encountered when attempting to model an intervertebral disc under such conditions. For example, the ability of at least one embodiment of the present invention to both impose in vivo human conditions, and likewise simulate the degeneration of a single intervertebral disc over changing conditions may allow a user to model a human intervertebral disc at multi-scale levels while simultaneously investigating the chronic degradation process an intervertebral disc may experience. Finally, yet additional embodiments of the present invention may likewise allow a user to systematically synthesize existing experimental results to illustrate the pathophysiology of an intervertebral disc, obtain quantitative information on complicated bioinformatics interactions, and predict the evolution of intervertebral disc pathophysiology as caused by a plurality of external stimuli.

Since many modifications, variations, and changes in detail may be made to the described preferred embodiment of the present invention, it is intended that all matters in the foregoing description and shown in the accompanying drawings be interpreted as illustrative and not in a limiting sense. Thus, the scope of the invention should be determined by the appended claims and their legal equivalents.