Determination of cerebral autoregulation state

Abstract

The present invention relates to a method to determine cerebral autoregulation (CA) state in a subject. The method of the invention comprises the provision of high frequency measures of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP) and their characterization using an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state. The invention further relates to a device for monitoring a subject's CA state configured for the implementation of the method of the invention and to a computer-readable storage medium for CA state monitoring device, comprising an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state.

Description

[0001] DETERMINATION OF CEREBRAL AUTOREGULATION STATE

[0002] FIELD OF THE INVENTION

[0003] The present invention relates to a method to determine cerebral autoregulation (CA) state in a subject. The invention further relates to a device for monitoring a subject’s CA state and to a computer-readable storage medium for a CA state monitoring device.

[0004] BACKGROUND OF THE INVENTION

[0005] Cerebrovascular autoregulation (CA) is a homeostatic physiological mechanism that ensures an adequate cerebral blood flow (CBF) over a varying range of cerebral perfusion pressures (CPP) to provide nutrients and oxygen to neurons. CPP reflects the pressure gradient between arterial blood pressure (ABP) and intracranial pressure (ICP) (CPP = ABP - ICP). The crucial mechanism driving CA is myogenic: Changes in intraluminal pressure are reflected in changes to arteriolar vessel tone, and hence, in cerebrovascular resistance (CVR). Arterioles vasodilate to increase CBF when CPP decreases or actively enforce vasoconstriction to reduce CBF when CPP increases. However, the capacity of CA to adjust arteriolar vessel diameters in response to CPP decreases or increases is limited.

[0006] In 1959, Lassen was the first to produce a CA curve based on averaged human data from 11 studies by plotting CBF (y-axis) against mean ABP (x-axis). A plateau, parallel with the x - axis, of constant CBF emerged over a wide range of ABP values, edged to the left by the lower limit of autoregulation (LLA). Later, the seminal triphasic CA curve was introduced, also including an upper limit of autoregulation (ULA). Below LLA and above ULA the CBF trended down - and upwards respectively due to the CA mechanism becoming inactive, and hence, a pressure passive relationship between CBF and CPP. In recent work, it was found in a porcine cranial window model that the CA curve was quadriphasic with two ULAs instead. A near-plateau to the left side was observed, that protects against arterial hypotension until LLA, and a gently increasing upward bend to the right side of baseline, representing gradual exhaustion of CA between ULA1 and ULA2. Beyond ULA2, a positive linear relationship was observed between CPP and CBF. In the same study, significant variability of limits between piglets was found. While the static representation of CA remains useful to study the CA mechanism, its clinical utility is severely limited due to: 1) intra -and inter-individual LLA and ULA(s) variation which reflects the dynamic and gradual nature of CA impairment, and 2) the lack of a reliable direct CBF monitor.

[0007] In traumatic brain injury (TBI), CA can be dynamically impaired. Knowledge of CA capacity would be very useful to steer blood pressure out of hypo -and hyperperfusion ranges. To indirectly detect dynamic impairment of CA, numerous correlation - based indices have been developed that compute moving Pearson correlation coefficients between a CBF surrogate measure and ABP. Positive or negative correlations are then interpreted as inactive or active CA, respectively. Pressure - reactivity index (PRx) uses ICP as CBF surrogate and is computed as the moving correlation coefficient between 30 consecutive 10 second averages of ICP and ABP (Ref. 6). PRx attemps to grasp slow wave arterial transmission to the brain. Slow ABP and ICP waves (< 0.05 Hz) were deemed the most relevant signal features to model CA reflecting myogenic CVR changes. Numerous drawbacks exist to utilizing a simple correlation coefficient to model a complex, multifaceted biological mechanism.

[0008] The question that arises from the above, is whether the joint slow ABP and ICP waves information in concurrent ABP and ICP signals is sufficient to assess CA capacity. Higher - frequency information present in the ABP and ICP signals and their potential interactions are neglected in slow-wave based correlation coefficients such as PRx. Focusing on ICP slow waves excludes Mayer waves (0.1 Hz) and cardiac cycle (1 - 1.3 Hz) information, among other CA related signal components. For example, Mayer waves correlate with haemodynamic oscillations and likely encompass myogenic, neurogenic and metabolic information of CA. ICP pulse morphology comprises markers (i.e. Pl, P2, P3) that reflect both cerebrovascular haemodynamic and cerebrospinal pressure-volume compensation, which are otherwise lost looking solely at mean ICP. It remain to be elucidated if modeling the full complexity of the ABP and ICP signal could aid in delineating active from inactive CA and whether such a model utilizes the aforementioned information in the signal(s). Adoption of advanced machine learning methods to directly model the multivariate interactions between physiological time series, too complex to grasp with correlation based indices, is lacking. A feasibility study exists in which the authors used an unsupervised, data-driven, machine learning approach to enhance the discriminative power of transfer function analysis (TFA) features between healthy subjects and symptomatic patients with severe intracranial stenosis (Ref. 1). However, the latter relied on measure of cerebral blood flow velocity (CBFV) as CBF surrogate, not reflective of cerebrovascular reactivity. Moreover, the model input were TFA derivatives (e.g. gain, phase,. . .) for which dynamic CA is assumed to be a linear time-invariant system which does not stroke with reality (e.g. hysteresis in CA). In addition, down sampling to 1 Hz excludes potentially relevant CA information. Machine learning models have been developed to detect and predict intracranial hypertension with good performance (Ref. 2 to 5). However, the latter models solely focused on the ICP signal and hence do not allow to determine CA states because of their focus on a partial facet of the CA curve.

[0009] Advances in machine learning and computing power allow to apply deep learning to complex multivariate time series data. Of particular interest are sequentially connected encoder -and decoder neural network architectures. The encoder network learns to project the input data to an optimal latent representation while the decoder network learns to reconstruct the original input data from the latter latent representation. Unsupervised encoder - decoder anomaly detection methods were for instance successfully used to model multivariate sensor data in industrial equipment for fault detection, and arrhythmia detection from electrocardiography, among others.

[0010] SUMMARY

[0011] It is an object of embodiments of the present invention to provide methods and devices to determine CA states directly from the full ABP and ICP signal.

[0012] Such method could model the full complexity of the multivariate nonlinear signals and their interactions, partially unknown, that potentially characterize the underlying (in)active CA processes. The inventors have developed a method to determine CA states and a device and a model for the implementation thereof. The method uses a deep learning model that was trained on concurrent ABP and ICP high frequency data segments and as such does not rely on unreliable CBF measurements, while outperforming PRx in reliably detecting CA states. The use of such a model furthermore enhances the ability to discriminate between the quadriphasic CA states when compared to PRx.

[0013] The present invention relates to a method to determine cerebral autoregulation (CA) state in a subject comprising the steps of : a. providing concurrent measurements, previously obtained from said subject, of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP), with a sampling frequency of at least 0.1 Hz and a sampling duration of at least 20 seconds; b. providing an artificial neural network previously trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state of a control subject or population thereof, and deriving, using the artificial neural network, reconstructed ABP values from the concurrent measurement of ICP previously obtained from the subject in step a, and / or reconstructed ICP values from the concurrent measurements of ABP previously obtained from the subject in step a; and / or a latent feature from said concurrent measurements of ABP and of ICP previously obtained from the subject in step a; c. comparing, the reconstructed ABP value obtained at step b to the concurrent measurement of ABP previously obtained from the subject in step a and / or the reconstructed ICP value obtained at step b to the concurrent measurement of ICP previously obtained from the subject in step a and / or the latent feature derived at step b to a reference latent feature corresponding to a reference CA state; and, d. assigning, based on the results of step c, the concurrent measurements of ABP and ICP to a CA state, thereby determining the CA state of said subject. The present invention further relates to a device for monitoring a subject’s CA state, comprising:

[0014] (i) means for measuring, and / or for receiving, concurrent measurements of ABP and ICP;

[0015] (ii) a computer-readable storage medium comprising an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state;

[0016] (iii) a computer configured for performing step b, c and d of the method of the invention using said artificial neural network; and,

[0017] (iv) means for transmitting information on the subj ect’ s C A state generated by the computer to a user and / or to another device.

[0018] The present invention also relates to a computer-readable storage medium for CA state monitoring device, comprising an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state. Such medium is configured so that when connected to a computer, it causes the computer to carry out the method of the present invention, at least the step of deriving reconstructed APB values from the concurrent measurement of ICP, and / or reconstructed ICP values from the concurrent measurements of ABP (the measurements being obtained in a previous step), and / or a latent feature from said concurrent measurements of ABP and ICP obtained in a previous step.

[0019] In one embodiment, the artificial neural network is configured to model temporal variation.

[0020] In one embodiment, the artificial neural network comprises an encoder- and a decoder- neural network.

[0021] In one embodiment, the encoder neural network is configured to learn multiple intraperiod- and interperiod-variations

[0022] In one embodiment, the encoder neural network comprises TimesBlocks. In one embodiment, the reference CA state is active CA. Thus, the artificial neural network is trained on reference concurrent measurements of active CA.

[0023] In one embodiment, the sampling frequency of said concurrent measurements of ABP and ICP is at least 0.2, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 or 20 Hz.

[0024] In one embodiment, the sampling duration of said concurrent consecutives measurements of ABP and ICP is at least 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, or 99 seconds, preferably at least 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124,

[0025] 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142,

[0026] 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160,

[0027] 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178,

[0028] 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196,

[0029] 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214,

[0030] 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232,

[0031] 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250,

[0032] 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268,

[0033] 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286,

[0034] 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298 or 299 seconds, more preferably at least 300 seconds.

[0035] In one embodiment, said means for measuring concurrently ABP and ICP is configured to measure ABP and ICP with a sampling frequency of at least 0.1 Hz, preferably with a sampling frequency of at least 0.2, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 or 20 Hz.

[0036] In one embodiment, said means for transmitting information on the subject’s CA state generated by the computer to a user, is a user interface, preferably is a user interface selected from the group consisting of display and speaker.

[0037] DEFINITIONS In the present invention, the following terms have the following meaning.

[0038] The term “artificial neural network” is used herein in reference to a trainable or adaptive algorithm comprising a plurality of nodes, each node defining a function to generate an output based on an input and each node being connected to one or more node via edges, such that the input of a given node is based on the output of another node. The functions and / or edges include parameters that may be determined or adjusted using a training set of input and desired output, for example in the context of the invention using reference concurrent measurements of ABP and ICP corresponding to reference CA state(s). Nodes are typically aggregated into layers and signals travel from the first layer (the input layer) to the last layer (the output layer), passing through multiple intermediate layers (hidden layers). Hidden layers define a so-called latent space.

[0039] “Cerebral autoregulation” or “CA” are used herein interchangeably in reference to the homeostatic physiological mechanism that ensures an adequate cerebral blood flow (CBF) over a varying range of cerebral perfusion pressures (CPP). The phenomenon is apparent as, for example and without being limited to, a plateau observed when plotting CBF over a varying range of CPP, or over a varying range of arterial blood pressure (ABP), such plot being referred to in the art as the CA curve. Such a curve also illustrates, in the form of difference in the CA curve behavior, differences in the status of cerebral autoregulation. “Cerebral Autoregulation State” or “CA state” are used herein interchangeably in reference to the status, or degree, of CA in a subject. CA states may be defined ad hoc, depending, for example and without being limited to, on whether a distinction is made between active and partially active CA and / or on whether distinction is made between hypotensive inactive CA and hypertensive inactive CA.

[0040] The term “latent feature” is used herein in reference to any input representation within the latent space of an artificial neural network. It is within the reach of the skilled artisan to select appropriate latent feature representation. Examples of such representation include, without being limited to, power spectral density (PSD) and cross-spectrum.

[0041] DETAILED DESCRIPTION

[0042] The present invention hence relates to a method to determine cerebral autoregulation (CA) state in a subject. In one embodiment, the subject is a mammal. In one embodiment, the subject is human.

[0043] In one embodiment, the method of the invention comprises a step of providing concurrent measurement of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP).

[0044] In one embodiment, the concurrent measurement of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP) were previously obtained from the subject. In this embodiment the method of the invention does not comprise a step of measuring ABP and ICP in the subject and / or the method of the invention is performed ex-vivo and / or the method of the invention is computer-implemented.

[0045] In one embodiment, the method of the invention is for monitoring cerebral autoregulation (CA) state in a subject. In one embodiment of the method of the invention for monitoring cerebral autoregulation (CA) state in a subject, the method comprises a step of obtaining concurrent measurement of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP) in the subject.

[0046] The term “ABP measurement”, as used herein, includes, without being limited to, raw signals obtained from any ABP measurement device as well as any ABP signal obtained after signal processing. Similarly, the term “ICP measurement”, as used herein, includes, without being limited, to raw signals obtained from any ICP measurement device as well as any ICP signal obtained after signal processing. Example of signal processing that may be considered in the context of the invention include, without being limited to, filtering, upsampling, downsampling, amplifying, averaging, compressing, and the like.

[0047] In one embodiment, the concurrent measurements of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP) have a sampling frequency of at least 0.1 Hz, preferably at least 0.2, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, or 9 Hz, more preferably a sampling frequency of at least 10, 11, 12, 13, 14, 15, 16, 17, 18, or 19 Hz, even more preferably a sampling frequency of at least 20 Hz.

[0048] In one embodiment, the concurrent measurements of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP) have a sampling duration of at least 20, 21, 22, 23, 24, 25, 26,

[0049] 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,

[0050] 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,

[0051] 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, or 99 seconds, preferably a sampling duration of at least 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123,

[0052] 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141,

[0053] 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159,

[0054] 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177,

[0055] 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195,

[0056] 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213,

[0057] 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231,

[0058] 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249,

[0059] 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267,

[0060] 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285,

[0061] 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298 or 299 seconds, more preferably a sampling duration of at least 300 seconds.

[0062] In one embodiment, the method of the invention comprises a step of deriving, using an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state, reconstructed ABP values from said concurrent measurement of ICP and / or reconstructed ICP values from said concurrent measurements of ABP; and / or a latent feature from said concurrent measurements of ABP and / or of ICP, in particular of ABP and of ICP.

[0063] In one embodiment, the artificial neural network is configured to model temporal variation.

[0064] In one embodiment, the artificial neural network comprises an encoder- and a decoder- neural network.

[0065] In one embodiment, the artificial neural network is configured to learn multiple intraperiod- and interperiod-variations.

[0066] In one embodiment, the encoder- neural network is configured to learn multiple intraperiod- and interperiod-variations.

[0067] In one embodiment the encoder- neural network comprises, or uses, TimeBlocks. The term “TimeBlocks” is used herein in reference to the modular multiperiodicity discovery and representation algorithm described in Wu et al. (TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. arXiv:2210.02186v3; doi: 10.48550 / arXiv.2210.02186), in particular in section 3.2 therein, that is incorporated herein by reference.

[0068] The term “reference concurrent measurements of ABP and ICP” refers to the measurement the ABP and ICP in a given control subject or, preferably, in a population of control subjects of known CA state. Said known CA state being referred to herein as a “reference CA state”. It is within the reach of the skilled artisan to select the measurements and control subjects appropriate for comparison purpose, accounting for example and without being limited to, for the sampling frequency and sampling duration. Any embodiment, or combination thereof, relating to the concurrent measurement of ABP and ICP obtained from the subject may apply to the reference concurrent measurements of ABP and ICP mutatis mutandis. These reference concurrent measurements, obtained from a reference subject, are used to train the artificial neural network. They are different from the concurrent measurements of the ABP and ICP of the subject whose CA is being studied. First the artificial neural network is trained with reference concurrent measurements, then a set of concurrent measurements of ABP and ICP are obtained. Then the set of concurrent measurements are used with the trained artificial neural network.

[0069] In one embodiment, the reference concurrent measurements of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP) have a sampling frequency of at least 0.1 Hz, preferably at least 0.2, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, or 9 Hz, more preferably a sampling frequency of at least 10, 11, 12, 13, 14, 15, 16, 17, 18, or 19 Hz, even more preferably a sampling frequency of at least 20 Hz.

[0070] In one embodiment, the reference concurrent measurements of Arterial Blood Pressure (ABP) and Intracranial Pressure (ICP) have a sampling duration of at least 20, 21, 22, 23,

[0071] 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,

[0072] 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,

[0073] 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95,

[0074] 96, 97, 98, or 99 seconds, preferably a sampling duration of at least 100, 101, 102, 103,

[0075] 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121,

[0076] 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157,

[0077] 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175,

[0078] 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193,

[0079] 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211,

[0080] 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229,

[0081] 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247,

[0082] 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265,

[0083] 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283,

[0084] 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298 or 299 seconds, more preferably a sampling duration of at least 300 seconds.

[0085] In one embodiment, the reference CA state is active CA and / or partially active CA. In other words, in one embodiment, the reference concurrent measurements of ABP and ICP were obtained from control subject(s) wherein CA is active and / or partially active.

[0086] In one embodiment, the method of the invention comprises a step of comparing, the reconstructed ABP values obtained during the deriving step to the concurrent measurement of ABP (previously) obtained from the subject, and / or the reconstructed ICP values obtained during the deriving step to the concurrent measurement of ICP (previously) obtained from the subject and / or the latent feature obtained during the deriving step to a reference latent features corresponding to a reference CA state. It is to be understood that in the method of the invention, the comparison step is adapted to the deriving step so that the information (i.e. reconstructed ABP values, reconstructed ICP value and / or latent feature derived from said concurrent measurements of ABP and / or of ICP) derived during the deriving step and that compared during the comparing step are the same. The term “reference latent feature” is used herein with respect to a latent feature derived, using an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state, from reference concurrent measurements of ABP and ICP as defined hereinabove. A reference latent feature is hence associated with, or characteristic of, a reference CA state.

[0087] In one embodiment, the method of the invention comprises a step of assigning, based on the results of the comparing step, the concurrent measurements of ABP and ICP to a CA state, thereby determining the CA state of said subject. The present invention further relates to a device for monitoring a subject’s CA state.

[0088] In one embodiment, the device of the invention comprises means for measuring concurrently ABP and ICP. Example of means for measuring ABP that may be used in the context of the invention include without being limited to arterial line and non-invasive continuous arterial pressure monitoring system (such as for example blood pressure cuff, oscillometric blood pressure monitoring devices). Examples of means for measuring ICP that may be used in the context of the invention include, without being limited to, ICP monitoring probes (such as for example parenchymal miniature pressure gauze based ICP probe or parenchymal fiberoptics based ICP probe), Brain external ventricular drain line and non-invasive continuous intracranial pressure monitoring systems.

[0089] In one embodiment, said means for measuring concurrently ABP and ICP is configured to measure ABP and ICP with a sampling frequency and / or with a sampling duration as described hereinabove in embodiments of the method of the invention pertaining to sampling duration and sampling frequency of the concurrent measurements of ABP and ICP. Any embodiments, or combination thereof, pertaining to the sampling frequency and / or sampling duration of the concurrent measurements of ABP and ICP, may thus apply herein mutatis mutandis.

[0090] In one embodiment, the device of the invention comprises means for receiving concurrent measurement of ABP and ICP.

[0091] In one embodiment, the device of the invention comprises a computer-readable storage medium comprising an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state. Any embodiments, or combination thereof, pertaining to the artificial neural network and / or to the reference concurrent measurements of ABP and ICP, described hereinabove in relation to the method of the invention, may apply herein mutatis mutandis.

[0092] In one embodiment, the computer-readable storage media is non-transitory.

[0093] Example of (non-transitory) computer-readable storage media that may considered in the context of the invention include, without being limited to, RAM, ROM, programmable ROM (PROM), erasable programmable ROM (EPROM), electronically erasable programmable ROM (EEPROM), flash memory, a hard disk, a compact disc ROM (CD- ROM), a floppy disk, a cassette, magnetic media, optical media, and any other computer readable storage devices.

[0094] In one embodiment, the device of the invention comprises a computer configured for performing the deriving step, the comparing step and the assigning step of the method of the invention using the artificial neural network described above. Any embodiment, or combination thereof, relating to these steps of the method of the invention described hereinabove may therefore apply to the configuration of said computer mutatis mutandis.

[0095] In one embodiment, said computer is configured for receiving, and, optionally, for processing, the signal obtained using the means for receiving concurrent measurement of ABP and ICP and / or the means for measuring concurrently ABP and ICP. Said computer may include the trained artificial neural network, for example in a computer-readable storage medium of embodiments of the present invention.

[0096] In one embodiment, the device of the invention comprise means for transmitting information on the subject’s CA state generated by the computer to a user and / or to another device.

[0097] Any user interface may be used for transmitting information on the subject’s CA state generated by the computer to a user. Example of user interface include, without being limited to, display, speakers.

[0098] The invention further relates to a computer-readable storage medium for CA state monitoring device, comprising an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state. Any embodiment, or combination thereof, pertaining to the computer-readable storage medium described hereinabove in relation to the device of the invention may apply herein mutatis mutandis. The computer-readable storage medium may comprise instructions which, when executed in a computer, causes the computer to carry out at least the step of deriving, using the artificial neural network, reconstructed ABP values from the concurrent measurement of ICP previously obtained from the subject in step a and / or reconstructed ICP values from the concurrent measurements of ABP previously obtained from the subject, and / or a latent feature from said concurrent measurements of ABP and ICP, optionally to carry out more steps, such as steps c and / or step d of the method of embodiments of the present invention.

[0099] BRIEF DESCRIPTION OF THE DRAWINGS

[0100] Figure 1 is an example of quadriphasic curve constructed from a hypo -and hypertension piglet experiment data set. Cerebral perfusion pressure (CPP) was plotted against the percentage change of laser doppler flowmetry (LDF) from baseline values prior to arterial blood pressure (ABP) manipulation. Lower limit of autoregulation (LLA) and upper limits of autoregulation (ULA1 and ULA2) were computed using segmented regression with 1 and 2 breakpoints, respectively.

[0101] Figure 2 illustrates percentage change of ABP and ICP mean squared reconstruction error (MSE) and PRx over cerebral perfusion pressure (CPP). Panel A show ABP (dashed line) and ICP (dotted line) MSE percentage difference from active CA. Panel B shows PRx (dashed line) plotted against corresponding CPP values. Both graphics were visualized with laser Doppler flow (LDF - solid line) percentage difference from baseline depicted on the right y-axis. Data points were smoothed using a locally weighted non parametric regression with an a of 0.75 and visualized with their 95% confidence intervals.

[0102] Figure 3 illustrates TimesNet test prediction error and PRx distribution along quadriphasic cerebrovascular autoregulation (CA) states. LiCA, Active CA, HPaCA, and HiCA correspond to the hypotensive inactive CA, active CA, hypertensive partially active CA, and hypertensive inactive CA states, respectively. Panel A: TimesNet test log mean squared reconstruction error (LogMSE) per quadriphasic CA state. LogMSE was computed per reconstructed concurrent ABP (unfilled box-plot, left) and ICP (filled boxplot, right) segment of 300 seconds. A lower LogMSE reflects better reconstruction performance. Active CA ABP reconstruction LogMSE was significantly lower than ABP LiCA, HPaCA and HiCA reconstruction LogMSE. Active CA ICP reconstruction LogMSE was significantly lower than LiCA and HiCA reconstruction LogMSE but not HPaCA reconstruction LogMSE. Panel B: PRx distribution along CA state. Active CA state PRx distribution was significantly lower than the HiCA CA state. ABP and ICP data was modeled with a linear mixed effects model (LMM) with a main effect of variable, CA state and their interaction as fixed effect. PRx data was modeled with a LMM with CA state as fixed effect. The fixed effect CA states were subsequently contrasted and corrected for multiple comparisons with Holm-Bonferroni correction. Note, that for the ABP - ICP model, the CA states constrasts were conditioned on Variable. **** p < 0.0001; *** p < 0.001; ** p < 0.01; * p < 0.05; ns = not significant.

[0103] Figure 4 illustrates TimesNet test data set latent space output smoothed power spectral density (PSD) per quadriphasic cerebrovascular autoregulation state (CA). LiCA, Active CA, HPaCA, and HiCA correspond to the hypotensive inactive CA, active CA, hypertensive partially active CA, and hypertensive inactive CA states, respectively. PSD was retrieved from each available test data segment after which the mean was computed per unique combination of latent dimension, frequency value, unique piglet, and CA label. PSD’s were smoothed over all eight latent space dimensions and piglets in the test data set utilizing a locally weighted non parametric regression with an a of 0.15 and visualized with their 95% confidence intervals.

[0104] Figure 5 illustrates basic precision-recall curves for threshold-based classification. Fully inactive cerebrovascular autoregulation (CA) was considered the positive sample, and inactive CA the negative sample. Pressure Reactivity Index (PRx) were assessed from -1 to 1. ABP log mean squared error (LogMSE) or ICP LogMSE were evaluated from low to high. AUC: Area Under Curve. ABP LogMSE AUC: 0.413; AUC ICP LogMSE: 0.485 and AUC Prx: 0.254.

[0105] EXAMPLES

[0106] The present invention is further illustrated by the following examples.

[0107] Example 1

[0108] Materials and Methods

[0109] Data set

[0110] The data utilized for the present study derives from a porcine closed cranial window model developed at KU Leuven and gathered as part of other work (Ref. 7). Briefly, twenty 6-week-old male piglets (domestic swine; Zootechnical Center, KU Leuven University) were non-pharmacologically induced with hypotension or hypertension by gradually inflating a balloon catheter in the inferior vena cava or abdominal aorta, respectively. In addition, physiological data was sampled at relatively high - frequencies and subsequently stored using ICM+ software (Cambridge University, Cambridge, UK), including ABP and ICP at 100 Hz, and laser Doppler flow (LDF) at 500 Hz. LDF served as a direct measurement of CBF, validated utilizing direct CBF measurements from pial arterioles in the original study.

[0111] The quadriphasic CA definition served as CA state ground truth. Baseline values of LDF were determined per piglet as the average monitored value prior to inflation of the balloon catheter. Ten second summarized CPP (= mABP - mICP) were plotted against the respective LDF difference from baseline values expressed as percentage difference. A systematic LDF de -or increase emerged in the hypotension -or hypertension experiments, respectively. Thereafter, a segmented regression was computed per piglet to derive the CPP transition point(s) reflecting a change in CA state. Piglets in the hypotension experiments solely had one breakpoint (i.e. LLA), while piglets from the hypertension experiments had two breakpoints (i.e. ULA1 and ULA2). No qualitative breakpoints could be computed for 4 out of 20 piglets, resulting in a final data set of 16 piglets (n_hypotensive=7). Henceforth, the quadriphasic CA states will be defined as: Active CA (between LLA and ULA1), hypotensive Low inactive CA = LiCA (below LLA), hypertensive High Partially active CA = HPaCA (between ULA1 and ULA2, hypertensive High inactive CA = HiCA (above ULA2).

[0112] Data Preprocessing

[0113] Physiological time series monitored during the gradual blood pressure manipulation were extracted from the ICM+ ,hdf5 data format. For the present study, solely the ABP and ICP traces were utilized each sampled at 100 Hz. Firstly, extreme values were filtered out (ABP > 300 mmHg; ABP < 10 mmHg; ICP < -5 mmHg) after which a simple filter for extreme values was applied per piglet for each signal (p_Signal±3*o_Signal). No data imputation was performed to fill the introduced missing values. Secondly, the a priori determined CA transition points per piglet (Figure 1) were utilized to project the CA state onto the extracted ABP and ICP time series data. Thirdly, a 10 Hz low-pass Butterworth filter of the 5th order was applied after which ABP and ICP signal were downsampled to 20 Hz, adhering to the Nyquist - Shannon sampling theorem to prevent aliasing. The highest frequency component present in the ABP and ICP signal time series derives from the cardiac cycle. At 10 Hz the heart rate was generously capped at 600 beats per minute, ensuring that no essential signal information was lost while significantly reducing high - frequency noise.

[0114] Model Architecture

[0115] The utilized deep learning model architecture concerns the recently published TimesNet, a temporal 2D - variation modeling technique for general time series analysis which achieved stellar performance on unsupervised multivariate time series anomaly detection benchmarks, among other tasks (Ref. 8). A key innovation of the TimesNet architecture with respect to classical deep learning architectures is that it allows the model to learn multiple intraperiod -and interperiod-variations. To do so, TimesNet projects the ID time series to 2D tensors based on multiple periods to unravel present complex temporal variations by utilizing a specialized 2D kernel, the so called TimesBlock. TimesNet allows us to learn a deep representation of the complex multivariate time series that can be exploited to perform reconstruction error based anomaly detection due to its encoder - decoder formulation.

[0116] Model Training

[0117] TimesNet model was trained to reconstruct 300 second segments of concurrent ABP and ICP time series, i.e. 6000 data points per variable at 20 Hz, that were labeled as active CA. ABP and ICP training segments were generated with a 99 % sliding window. Given the limited amount of piglets present in our data set, 4-fold cross-validation was performed with two repeats, resulting in eight trained models. Piglets were randomly assigned to the train (n=12), validation (n=2) and test (n=2) data set stratified on ABP manipulation (i.e. hypo - or hypertension experiment) using a quasi-random number generator. The ABP and ICP signal data in the training data set corresponding to the active CA state were used to standardize the train, validation and test data sets. Note that the latter models were trained and evaluated on distinct train, validation and test subsets of the total data set. Models were trained on a single NVIDIA VI 00 GPU for 100 epochs with a batch size of 32 to minimize the mean squared error (MSE) utilizing the adaptive moment estimation (Adam) optimizer with a starting learning rate of 0.0001 (Ref. 9). Model training was halted when the validation loss did not decrease for 5 consecutive epochs. Model training was performed utilizing Python 3.9.16, and Pytorch 2.0.0.

[0118] Model Performance

[0119] To assess TimesNet model performance, ABP and ICP reconstruction error was assessed of non-overlapping test data set segments. Firstly, a qualitative assessment was performed by visualizing randomly selected concurrent test data set ABP and ICP segments and their reconstructions. Secondly, per second averaged ABP and ICP error trends were assessed over time and over CPP. To do so, percentage change of ABP and ICP reconstruction error (MSE) was computed for which the piglet-specific average ABP and ICP MSE governed by active CA served as baseline. The latter visualizations are accompanied by percentage change in LDF with respect to the initial experimental LDF baseline prior to blood pressure manipulation. Finally, to assess TimesNet’ s potential discriminative ability between CA states based on ABP and ICP per segment reconstruction error, MSE was log transformed (LogMSE). Analyses on ABP and ICP LogMSE were performed utilizing linear mixed effects models (LMM). LMMs were employed given the repeated nature of observations present between and within each CA state, piglet and over model folds. Afterwards, pairwise comparison revealed (non)significant differences between the four CA states, adjusted for multiple comparisons utilizing the Holm-Bonferroni method. Given the large amount of test data points, pairwise comparisons were computed from asymptotic results (z-test). In addition, PRx computed from the equivalent test segments was extracted from ICM+ (Cambridge University, Cambridge, UK) 10 - second summarized time series and subsequently analyzed.

[0120] Model Behavior: Power spectral density (PSD)

[0121] To study model behavior, the input time series and their respective latent space outputs and reconstructed inputs were studied. To do so, PSDs were computed for each possible combination of input variable, latent space, and reconstructed output and their interdependence was studied using distance correlations (DCs). The respective PSDs were estimated using Welch’s method outlined in the SciPy Python library with default hyperparameters (version 1.11.3). PSD allows for easy comparison between signals from different sources since each power value within a PSD is divided by the total power across all frequencies. DCs quantify a measure of dependence for both linear and nonlinear associations present between two vectors, here PSDs, ranging from 0 (independent) to 1 (dependent). Such DCs were computed for all input - latent - reconstruction output combination possible, in sum, between ABP and ICP input (i.e. DC(PSDABPinPut, PSDicpinput)), ABP and ICP reconstruction output (i.e. DC(PSDABPoutPut, PSDicpoutput)), input - reconstruction output (e.g. DC(PSDABPinPut, PSDABPoutput )), input - latent or latent - reconstruction output (e.g. DC(PSDicpinPut, PSDosoutput) or DC(PSDD4outPut, PSDABPoutput)).

[0122] Model Performance: Classification

[0123] TimesNet outputs two types of so-called features that could be utilized to classify 20 Hz ABP and ICP input segments, namely ABP and ICP reconstruction error and the latent space output. Simple classification models were subsequently trained and tested following TimesNet initial cross - validation paradigm. Firstly, ABP and ICP LogMSE served as input for logistic regression (LR) and K - nearest neighbor (KNN; K = 7) models to classify the CA state as active or inactive. Secondly, to utilize the latent space as feature input, the power spectral density (PSD) function was computed from each latent dimension. A selection of latent dimension PSDs served subsequently as feature input for a small convolutional neural network (CNN). In addition, the median and mean PSD per segment were computed from the eight latent dimensions and served as input for logistic regression and KNN (K = 14) models. Baseline classification performance was determined by binary classification performed utilizing PRx 0.0 and 0.3 thresholds (PRx < threshold = active CA; PRx > threshold = inactive CA) derived from the matching ICM+ 10 second summarized time series. Consequently, TimesNet feature model classification was limited to binary classification where HPaCA was considered to belong to active CA, while LiCA and HiCA both were classified as inactive CA. Given the imbalanced data set, performance metrics concerned binary and weighted precision (P), recall (R), and Fl. Binary metrics reflect the classification performance on the positive class (i.e. inactive CA), while weighted metrics concerned the weighted average by number of true instances for each label (i.e. active CA vs. inactive CA).

[0124] Secondary analyses and visualizations were performed in R 4.3.1 (R Proj ect for Statistical Computing) utilizing the Tidyverse ecosystem and lme4 package. Results and conclusions

[0125] TimesNet model evaluation was performed by combining the results derived from cross- validation test data sets. Reconstructed ABP and ICP segments were gathered from each independent test data set utilizing their optimized TimesNet model. Altogether, 16 piglets were evaluated of which 12 (number of hypotensive piglets, nhypottention = 6) were unique between the 8 folds’ test data sets. To evaluate PRx performance, the latter 12 unique piglets were utilized. Test segment distribution per CA state was as follows: (1) PRx: Active CA = 86.57%; LiCA = 2.43%; HPaCA = 6.09%; HiCA = 4.91%, (2) TimesNet: Active CA = 87.74%; LiCA = 1.92%; HPaCA = 4.09%; HiCA = 6.25%.

[0126] To initially assess reconstruction performance of the optimized TimesNet models, a qualitative ABP and ICP signal reconstruction inspection was warranted. Original signal inputs and reconstructions of 300 seconds were randomly sampled from their CA state subgroup. Notably, an optimized TimesNet reconstructed ABP and ICP traces governed by active CA more closely to their respective original input signals than under HPaCA, LiCA, and HiCA. Slow waves seemed to be reasonably well reconstructed over all CA states.

[0127] ABP and ICP reconstruction error generally increased over time for piglets in both the initial hypo -and hypertension experimental condition when approaching the inactive CA state. Centering the onset of inactive CA (hypotension experiments = LiCA; hypertension experiments = HPaCA), based on the quadriphasic labeling, at time point 0 allowed to visualize piglet’s error trends grouped over time. To do so, the average MSE per unique piglet within a cross-validation test data set fold was computed under active CA and used to derive percentage in / decrease in MSE over the complete ABP and ICP time series. In the hypotension experimental condition, ICP reconstruction error increased concurrently with a decrease in LDF with respect to baseline, however, the latter occurs approximately 1000 seconds prior to the determined onset of LiCA using breakpoints. ABP reconstruction error increases match the decrease in CBF as measured by LDF with respect to baseline, albeit to a lesser extent as the ICP error increase. Conversely, in the hypertension experiments, ABP reconstruction error increased concurrently with LDF increases with respect to baseline which occurred prior to HPaCA. ICP percentage reconstruction error increase started manifesting after the CA mechanism was completely inactive (HiCA). Figure 2 displays LDF percentage change from baseline, ABP and ICP MSE percentage error change with respect to average active CA MSE (figure 2A) and PRx (figure 2B) over CPP. TimesNet ICP reconstruction error increased more on the low CPP side, while ABP reconstruction error increased more on the high CPP side with respect to their average active CA reconstruction error. Changes in ABP and ICP percentage increase of reconstruction MSE did follow LDF percentage de / increase more closely than PRx on both the low -and high CPP side. Notably, ICP reconstruction error increase seemed particularly indicative of the LLA. Reconstruction error of ABP and / or ICP seemed to reflect the transition point of changing LDF more precisely than PRx and the originally denoted breakpoints.

[0128] Indeed, a quantitative assessment of TimesNet’ s ABP and ICP log MSE (LogMSE) and PRx over the quadriphasic CA states favored ABP and ICP LogMSE. Statistical analyses were performed for ABP and ICP LogMSE (figure 3A) and PRx (figure 3B) separately utilizing a LMM followed - up by pairwise comparisons between CA states. Final LMMs were constructed from the first maximal random effects structure justified by the experimental design. More specific, final TimesNet LMM was simplified to a fixed main effect for variable (i.e. ABP and ICP), CA state and their interaction, and a by - piglet, cross-validation fold random intercepts and slopes for variable with an uncorrelated random effects structure. A significant main effect of CA state (p < IO'04), variable (p < 1 O'04) and their interaction (p = 1 O'04) emerged.

[0129] To assess the fixed effect of CA state on each of the variable’s reconstruction LogMSE the pairwise comparisons were conditioned on the variable fixed effect. Utilizing asymptotic z-test with Holm - Bonferroni corrections revealed that: (1) ABP reconstruction LogMSE governed by active CA was on average significantly lower than ABP LogMSE governed by HPaCA Est.ActiveCA-HPaCA= -0.5193 ± 0.1975, p = 0.0343), LiCA (Est.LiCA-ActiveCA= 0.9968 ± 0.2605, p = OxlO’04), and HiCA (Est.ActiveCA-HiCA= -1.3614 ± 0.1594, p < IO'04), and (2) ICP reconstruction LogMSE governed by active CA was on average significantly lower than ICP LogMSE governed by fully inactive CA (Est.LiCA-ActiveCA= 2.4006 ± 0.2605, p < IO’04; Est.ActiveCA-HiCA= -0.9601 ± 0.1594, p < IO’04), but not by HPaCA (Est.ActiveCA-HPaCA= -0.0288 ± 0.1975, p = 0.8839) (figure 3A). As a consequence of the significant CA state and variable interaction, ICP LogMSE increased more than ABP LogMSE in LiCA with respect to active CA while the opposite holds true in HPaCA and HiCA.

[0130] PRx LMM consisted of a fixed main effect for CA state, and a by - piglet random intercepts and slopes for CA state with an uncorrelated random effects structure. CA state was a significant predictor of PRx value (p = 0.0122). Pairwise comparisons of the fixed CA state effect of the PRx LMM model utilizing asymptotic z-test with Holm - Bonferroni corrections revealed that PRx governed by active CA was on average significantly lower than PRx governed by HiCA (Est.ActiveCA-HiCA= -0.4183 ± 0.1382, p = 0.0148), but not LiCA nor HPaCA (figure 3B).

[0131] A set of features was derived from TimesNet test data set outputs to classify CA state. LogMSE was computed for each reconstructed ABP and ICP segment and served as features as is. A PSD was computed for each latent dimension output present in the model which served as input for a CNN, or after taking the mean / median over the eight dimensions for a LR and KNN model. In general, HPaCA PSD’s approached the active CA PSD’s, while LiCA and HiCA PSD’s were more distinct from active CA. Distance correlations (de) were computed between the distinct CA states after taking the median PSD’s per CA class for every dimension and piglet. Note, distance correlation bounds range from 0 (low) to 1 (high). Formally, active CA PSD profiles differed from inactive CA profiles, i.e. DC(PSDActive CA, PSDJJCA)=0.07 ± 0.04 and DC(PSDActive CA, PSDHICA) = 0.26 ± 0.21.. HPaCA PSD’s were more similar to active CA, DC(PSDActive CA, PSDHPacA) = 0.47 ± 0.29, than HiCA, DC(PSDHpacA, PSDHicA) = 0.13 ± 0.15.

[0132] TimesNet model features and respective classification performance was contrasted with PRx threshold based classification. Given that the PRx solely allowed binary classification, the quadriphasic labeling was simplified to binary labels. Namely, LiCA and HiCA were considered as inactive CA whereas HPaCA was considered as active CA given its similarity in latent representation to active CA and generally lower ABP and ICP LogMSE. Firstly, the PRx was utilized as threshold based classifier for which PRx > 0.0 and PRx > 0.3 thresholds were employed to classify a segment dynamically as inactive CA. PRx > 0.3 attained higher Fl scores with respect to PRx > 0 threshold for both binary as weighted scoring (Table I). Table I: Precision, recall and Fl of PRx and TimesNet features based classifiers. Precision, Recall, and Fl of inactive CA (binary) or average weighted (weighted) by support for both active and inactive CA. PRx : pressure-reactivity index; LogMSE: Log mean squared error; LR: logistic regression; KNN; K-nearest neighbor; PSD: Power spectral density; ConvNet: Convolutional neural network. The standard deviation of performance between model cross-validation folds is indicated between brackets.

[0133] ABP and ICP LogMSE were utilized as features in a LR and KNN (K = 7) model. All LogMSE based models showed improved overall performance (Fl) with respect to PRx in classifying ABP and ICP LogMSE as either active -or inactive CA, with the KNN being the best performer (Table I). Finally, PSD as features derived from the eight latent TimesNet dimensions seemed relevant features that are indicative of CA states (figure 4). A small CNN matched the performance of LogMSE based classification by utilizing eight PSDs (Table I). Similarly, when taking the average or median per frequency bin over computed PSD latent dimensions to utilize as KNN (K = 14) input, an overall improved or matching performance (Fl) was observed with respect to LogMSE KNN.

[0134] Note that the precision is higher for KNN LogMSE while recall was higher for PSD ConvNet and PSD (mean / median) KNN. In sum, TimesNet feature based classification overall outperformed PRx in classifying segments as (in)active CA.

[0135] Example 2

[0136] Additionally, model behavior and feature based classifiers were evaluated, focusing on:

[0137] 1) input time series (ABPinput and ICPinput),

[0138] 2) latent space output given the input time series derived from the eight latent dimensions of the model (i.e. DI - D8), and

[0139] 3) reconstructed inputs (ABPoutput and ICPoutput)

[0140] Material and Methods dataset

[0141] The data sets from example 1 (train, validation, test), were extracted per cross - validation trained model fold from the original train, validation and test data with a 25 % sliding window (equivalent to 75 seconds).

[0142] Model performance: classification

[0143] First, the basic precision - recall curve was computed to classify inactive CA vs active CA from a range of thresholds for PRx, ABP LogMSE, and ICP LogMSE individually. Simple classification models were subsequently trained and tested following the model’s initial cross-validation paradigm using random sampling, resulting in eight folds.

[0144] Second, feature type 1 (LogMSE) served as input for logistic regression (LR) and K - nearest neighbor models (KNN; K = 7) to classify the xCA state as active or as inactive.

[0145] Third, the eight latent PSDs, or a permutation thereof, served subsequently as feature input for a small convolutional neural network (CNN) which was optimized with a weighted cross-entropy loss.

[0146] To determine the contribution of each latent dimension that served as input for the CNN to the precision, recall and Fl score of that CNN, a Bayesian hierarchical model was used. The latent dimension contributions to classification performance were assessed to derive the most informative latent dimensions for the developed CNN classifier. Precision, recall or Fl served as dependent variable and the presence of DI - D8 as independent categorical predictor, with a random intercept for model fold. Models were fit with uniform priors, estimated using Markov chain Monte Carlo (MCMC) sampling with 8 chains, each for 5000 iterations after an initial warmup of 2500 iterations. To achieve adequate convergence and reliable estimates the potential scale reduction factor ( R) should be below 1.01, and the effective sample size (ESS) above 1000.

[0147] The mean or median PSD over the eight latent dimensions was used as feature input for a KNN (K = 14) or LR. To assess classification performance in an imbalanced dataset, Binary and Macro precision, recall, and Fl were chosen as evaluation metrics. Binary metrics reflect the classification performance on the positive class (i.e. inactive CA), while Macro metrics reflect the average precision, recall, and Fl on each class (i.e. active CA and inactive CA).

[0148] Results

[0149] Classification of ABP and ICP reconstruction errors (LogMSE) or latent PSD features were contrasted with classification based on PRx. Results in figure 5 indicate that threshold - based classification using single - variable ABP or ICP LogMSE outperforms PRx.

[0150] The following results in Table II focus on the so-called binary classification performance, in other words, how good can the classification models detect inactive CA state when it occurs. However, the macro average precision, recall and Fl across active - and inactive CA states is also shown. Overall, PRx threshold-based classification yielded the lowest Fl score, while PSD-based (using D2, D3, D4, D6, and D8) CNN classification achieved the best Fl score (Table II)

[0151] Table II: Precision, recall and Fl of inactive CA (Binary) or the average of active and inactive CA (Macro). Interquartile range are indicated between brackets. CNN: Convolutional neural network; KNN K-nearest neighbor; LogMSE: LOG Mean Squared Error; LR: Logistic regression; PRx: pressure-reactivity index; PSD: Power Spectral Density.

[0152] PRx

[0153] Precision of PRx was especially low, for both 0.0 (Preci si onPRx>0 = 0.14) and 0.3 (PrecisionPRx>0.3 = 0.19) thresholds. A trade-off was observed between precision and recall for ABP and ICP LogMSE-based classification using a LR or KNN, with LR emphasizing recall and KNN precision. Latent PSD-based classification, using LR, KNN, or a CNN further outperformed the ABP and ICP LogMSE -and PRx-based classification

[0154] (Table II)

[0155] The choice of latent dimensions for the CNN-based classifier derived from assessing all permutations of latent PSDs as input for binary precision, recall and FL Classification performance of the CNN classifier was affected in both directions by the inclusion of specific latent dimensions used for model input (Table III).

[0156] Table III: Bayesian Hierachical fixed effect parameter to determine latent dimension contributions to convolutional neural network (CNN) classifier. Fl, precision and recall were determined by the classification performance on the positive class (i.e. inactive CA), for intercept and 8 latent dimensions (DI to D8). EST: model predictor estimate (categorical); SE: standard error; CE 95% confidence interval.

[0157] The modeling of independent model coefficients (i.e. po or intercept, DI - D8) to estimate Fl, precision, and recall successfully converged ( R < 1.01) and the estimated indices were reliable (ESS > 1000). The inclusion of D2, D3, D4, D6, and D8 had a positive effect on the classification of inactive CA in the test dataset as shown in Table III. Fl is a summary measure for precision and recall, as such a slight trade-off exists for D2 and

[0158] D8 due to which a strong increase in precision caused a slight decrease in recall. The opposite holds true for D6.

[0159] In summary, the results show that the present invention allows an accurate identification of the CA state from the concurrent measurements of ABP and ICP, using a trained neural network with reference concurrent measurements of the same parameters.

[0160] References 1- Wu M, Zhang W, Guo Z, et al. Separation of normal and impaired dynamic cerebral autoregulation using deep embedded clustering: A proof-of-concept study. Physiological Measurement 2021;42(7):074002.

[0161] 2- Scalzo F, Hamilton R, Asgari S, et al. Intracranial hypertension prediction using extremely randomized decision trees. Medical Engineering & Physics 2012;34(8): 1058- 1065.

[0162] 3- Giiiza F, Depreitere B, Piper I, et al. Novel methods to predict increased intracranial pressure during intensive care and long-term neurologic outcome after traumatic brain injury: Development and validation in a multicenter dataset. Critical Care Medicine 2013;41(2):554-564.

[0163] 4- Quachtran B, Hamilton R, Scalzo F. Detection of Intracranial Hypertension Using Deep Learning. In: 2016 23rd International Conference on Pattern Recognition (ICPR) 2016; pp. 2491-2496.

[0164] 5- Ye G, Balasubramanian V, Li JK-J, et al. Machine Learning-Based Continuous Intracranial Pressure Prediction for Traumatic Injury Patients. IEEE journal of translational engineering in health and medicine 2022; 10:4901008.

[0165] 6- Czosnyka M, Smi elewski P, Kirkpatrick P, et al. Continuous Assessment of the Cerebral Vasomotor Reactivity in Head Injury. Neurosurgery 1997;41 ( 1 ): 11-19.

[0166] 7- Klein SP, De Sloovere V, Meyfroidt G, et al. Differential Hemodynamic Response of Pial Arterioles Contributes to a Quadriphasic Cerebral Autoregulation Physiology. Journal of the American Heart Association 2022; 1 l(l):e022943.

[0167] 8 - Wu et al., TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis. arXiv:2210.02186v3; doi: 10.48550 / arXiv.2210.02186.

[0168] 9- Kingma and Adam: A Method for Stochastic Optimization. 2017; doi: 10.48550 / arXiv.1412.6980.

Claims

CLAIMS1. A method to determine cerebral autoregulation CA state in a subject comprising the steps of : a. providing concurrent measurements, previously obtained from said subject, of Arterial Blood Pressure ABP and Intracranial Pressure ICP, with a sampling frequency of at least 0.1 Hz and a sampling duration of at least 20 seconds; b. providing an artificial neural network previously trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state of a control subject or population thereof, and deriving, using the artificial neural network, reconstructed ABP values from the concurrent measurement of ICP previously obtained from the subject in step a and / or reconstructed ICP values from the concurrent measurements of ABP previously obtained from the subject in step a; and / or a latent feature from the concurrent measurements of ABP and of ICP previously obtained from the subject in step a; c. comparing, the reconstructed ABP value obtained at step b to the concurrent measurement of ABP previously obtained from the subject in step a and / or the reconstructed ICP value obtained at step b to the concurrent measurement of ICP previously obtained from the subject in step a and / or the latent feature derived at step b to a reference latent feature corresponding to a reference CA state; and, d. assigning, based on the results of step c, the concurrent measurements of ABP and ICP to a CA state, thereby determining the CA state of said subject.

2. The method according to claim 1, wherein said artificial neural network is configured to model temporal variation.

3. The method according to any one of claims 1 or 2, wherein providing said artificial neural network comprises providing an encoder- and a decoder- neural network.

4. The method according to claim 3, wherein providing said neural network comprises providing a neural network configured to learn multiple intraperiod- and interperiod-variations.

5. The method according to any one of claims 1 to 4, wherein providing an artificial neural network trained on reference concurrent measurements of a reference CA state comprises providing said artificial neural network trained on said reference concurrent measurements of active CA.

6. The method according to any one of claims 1 to 5, wherein the sampling frequency of said concurrent measurements of ABP and ICP is at least 0.2, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 or 20 Hz.

7. The method according to any one of claims 1 to 6, wherein the sampling duration of said concurrent consecutives measurements of ABP and ICP is at least 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75,76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97,98, or 99 seconds, preferably at least 100, 101, 102, 103, 104, 105, 106, 107, 108,109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124,125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140,141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156,157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172,173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188,189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204,205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220,221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236,237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252,253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268,269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284,285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298 or 299 seconds, more preferably at least 300 seconds.

8. A device for monitoring a subject’s CA state, comprising:(i) means for measuring, and / or for receiving, concurrent measurements of ABP and ICP;(ii) a computer-readable storage medium comprising an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state;(iii) a computer configured for performing step b, c and d of the method according to any one of claims 1 to 7, using said artificial neural network; and,(iv) means for transmitting information on the subj ect’ s C A state generated by the computer to a user and / or to another device.

9. The device according to claim 8, , wherein said artificial neural network is configured to model temporal variation.

10. The device according to claim 8 or 9, wherein said artificial neural network comprises an encoder- and a decoder- neural network.

11. The device according to claim 10 , wherein said encoder neural network is configured to learn multiple intraperiod- and interperiod-variations.

12. The device according to any one of claims 8 to 11, wherein said reference CA state is active CA.

13. The device according to any one of claims 8 to 12, wherein said means for measuring concurrently ABP and ICP is configured to measure ABP and ICP with a sampling frequency of at least 0.1 Hz, preferably with a sampling frequency of at least 0.2, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 or 20 Hz.

14. The device according to any one of claims 8 to 13, wherein said means for transmitting information on the subject’s CA state generated by the computer to auser is a user interface, preferably a user interface selected from the group consisting of display and speaker.

15. A computer-readable storage medium for CA state monitoring, comprising an artificial neural network trained on reference concurrent measurements of ABP and ICP corresponding to a reference CA state, which when connected to a computer, causes the computer to carry out at least the step of deriving, using the artificial neural network, reconstructed ABP values from the concurrent measurement of ICP previously obtained from the subject in step a of the method of any one of claims 1 to 7 and / or reconstructed ICP values from the concurrent measurements of ABP previously obtained from the subject in step a of the method of any one of claims 1 to 7; and / or a latent feature from said concurrent measurements of ABP and of ICP previously obtained from the subject in step a of the method of any one of claims 1 to 7.

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