Method for in silico calculating perfusion metrics including calculating of arterial input function based on a parallel or serial distribution model

Abstract

The present invention relates to a method for calculating in silico an arterial input function (AIF), wherein the method comprises selecting a class (CM, CMC) and an order (n) of the pharmacokinetic model. A pharmacokinetic model class is selected from a parallel distribution (CM) model from a central compartment to one or more peripheral compartments or a serial distribution (CMC) model from a central compartment in series through one or more intermediate compartments to one or more peripheral compartments. The order (n) of the pharmacokinetic model is the number of compartments in the selected pharmacokinetic model. In particular, the invention provides a computation of the arterial input function (AIF) at the inlet to the target circulatory area (VOI). The computed arterial input function (AIF) is then used to calculate perfusion and in particular perfusion metrics. In silico computed arterial input functions (AIF) were compared with results obtained in vivo. Consistency was observed between in silico and in vivo results at a level allowing for medical application of the invention. In particular, allowing the determination of perfusion metrics.

Description

[0001] METHOD FOR IN SILICO CALCULATING PERFUSION METRICS INCLUDING CALCULATING OF ARTERIAL INPUT FUNCTION BASED ON A PARALLEL OR SERIAL DISTRIBUTION MODEL

[0002] TECHNICAL FIELD

[0003] The invention relates to the determination of perfusion, in particular perfusion metrics for human subjects. Determination of perfusion is carried out in silico, and in a patient-specific manner.

[0004] BACKGROUND ART

[0005] Coronary artery disease is the leading cause of death among adults. Approximately 610.000 people die from this disease annually in the United States, and 17.8 million worldwide. In Europe, 1.7 million people die from cardiovascular disease every year (32.7% of all deaths). These values significantly exceed the percentage of deaths caused by cancer (22.5%) . It is estimated that the average cost of health care for patients with coronary artery disease in the United States exceeds $200 billion annually (Brown JC, Gerhardt TE, Kwon E, Risk factors for coronary artery disease StatPearls. StatPearls Publishing, Treasure Island (FL), 2022; Eurostat database Cardiovascular diseases statistics, accessed: November 2023).

[0006] Coronary artery disease is a consequence of persistent blood supply deficiency. A blood supply deficiency is an inadequate provisioning of the myocardium to meet physiological needs. Perfusion anomalies directly characterize the blood supply deficit. Perfusion is a quantity describing the transport of blood in a volume of tissue per unit time. Perfusion can be expressed as a unit flow of MBF [ml / 100g-min] (Petralia G, Bonello L, Viotti S, Preda L, d'Andrea G, Bellomi M (2010) CT perfusion in oncology: how to do it. Cancer imaging: the official publication of the International Cancer Imaging Society, 10(1), 8-19). Diagnostic methods determine the diagnostic data (imaging information) used to determine perfusion. Perfusion determination is also called perfusion imaging. Diagnostic methods include, for example, CT, MRI, and nuclear medicine (Villemain O, Baranger J, Jalal Z, Lam C, Calais J, Pemot M, Cifra B, Friedberg M K, Mertens L (2020) Non-invasive imaging techniques to assess myocardial perfusion. Expert review of medical devices, 17(11), 1133-1144). All these methods use a common scheme of the procedure as an examination protocol. This is due to their common genesis as methods derived from tracers techniques.

[0007] The scheme of the procedure (examination protocol) includes, for a stabilized and prepared to determine the perfusion human subject, the administration of a contrast agent into the peripheral vein in a specific regimen (including the moment of administration, the time of administration and the amount of contrast agent administered). After administration, the contrast agent undergoes passive transport with the flow of blood to the target circulatory area (VOI, volume of interest, also as an area of interest). The target circulatory area is the area of the human body in which the perfusion value is determined. The transport of contrast agent (also referred to as tracer, contrast substance) within VOI is recorded non-invasively most often in the form of a series of images obtained using low-dose X-rays. The series of images are obtained using two measurement strategies: static and dynamic. The static strategy is earlier and is now being replaced by a dynamic strategy. The static strategy involves acquiring a series of images in one time layer at maximum saturation. The dynamic strategy involves the acquisition of a series of images with a time interval. The entire acquisition is synchronized with the ECG of a human subject performed simultaneously. This synchronization is to ensure compliance with the phase of the cardiac cycle. Tracer methods have different tracer media. Different tracers are used in tomography, resonance imaging, and nuclear imaging.

[0008] Positron Emission Tomography (PET) is a molecular imaging technique that allows noninvasive and quantitative evaluation of biological processes. Biological processes include glucose consumption and amino acid uptake. The PET technique is based on the detection of emitted photons from radiotracers. Radiotracers are divided due to the nuclide contained. For example, for brain imaging, mainly fluorine- 18, carbon-11, gal-68 as well as other radiotracers are used (Smeraldo A, Ponsiglione AM, Soricelli A, Netti PA, Torino E (2022) Update on the Use of PET / MRI Contrast Agents and tracers in Brain Oncology: A Systematic Review. International Journal of Nanomedicine, 17, 3343-3359). Radiotracers containing atoms such as fluorine-18, copper-64, carbon-11, gal-68, rubid-82, oxygen-15, nitrogen-13 can also be used in PET imaging, and examples of radiotracers are acetate- 11C, palmitate- 11C, fluorodeoxyglucose- 18F, ammonia- 13N and others (Davidson CQ, Phenix CP, Tai TC, Khaper N, Lees SJ (2018) Searching for novel PET radiotracers: imaging cardiac perfusion, metabolism and inflammation. American Journal of Nuclear Medicine and Molecular Imaging, 8(3), 200-227).

[0009] Another similar method used for perfusion imaging is single photon computed emission tomography (SPECT). Instead of positron emitting radiotracers, SPECT directly uses isotopes emitting gamma radiation and this radiation is subject to direct registration. The movement of radiotracers attached to a biologically active ligand specific to the VOI area is recorded using a gamma-camera. The most popular radiotracers are iodine-123 and technetium-99m. It is also used to a slightly lesser extent tal-201 (Yandrapalli S, Puckett Y (2022) SPECT Imaging. In StatPearls . StatPearls Publishing).

[0010] For magnetic resonance imaging, contrast agents are used to better distinguish between normal tissue and pathologically altered tissue. A better distinction is made by increasing the tonal differences of the recorded images. This is due to the following features of the contrasting substance: magnetic properties, chemical composition, presence or absence of specific element atoms, route of administration and biodistribution. Most contrasting substances are superparamagnetic magnetite particles (for example, iron oxide) and paramagnetic gadolinium ion complexes. Paramagnetic contrast compounds are usually made of Dy3+ dysprosium, Gd3+ gadolinium metal lanthanide, or Mn2+ manganese transition metal, and are soluble in water (Xiao Y D, Paudel R, Liu J, Ma C, Zhang ZS, Zhou SK (2016) MRI contrast agents: Classification and application. International journal of molecular medicine, 38(5), 1319-1326).

[0011] In computed tomography perfusion (CTP) imaging, a contrasting effect is achieved by using iodinated substances containing the tri-atomic iodine molecule L. Such substances include, for example, the compounds iohexol and iopromide and are offered under various trade names (such as Omnipaque or Ultravist-300, for example).

[0012] If the purpose of perfusion imaging is to evaluate the blood supply deficit, it is necessary to use A2A receptor agonists to induce hyperemia. More specifically, pharmacological hyperemia. In this way, a reliable and objective (regardless of the method used) assessment of the blood supply deficit is possible. The A2A receptor agonist may be a specific A2A receptor agonist. Exemplary agonists are those offered as adanosine, regadenoson, and binodenoson, under the trade names Adenocor, Rapiscan, and CorVue respectively.

[0013] The contrast agent is excreted completely and effectively from the body. For health reasons, contrast agents that accumulate in the human body are not used.

[0014] Descriptions of studies on the safety of contrast agents are known (for example: Olsson B, Aulie A, Sveen K, Andrew E (1983) Human pharmacokinetics of iohexol. A new nonionic contrast medium. Invest Radiol, 18(2): 177-182). In a clinical study, a group of volunteers were given a contrast agent in the form of iohexol at doses of 125, 250, 375, 500 mg I / kg. However, regardless of dose and individual characteristics, the volume of distribution was in the range of 19.6-22.1, and the purification factor (clearance) was 118-128 ml / min for the kidneys, 116-128 ml / min for the whole body (values for the 95% probability level). Similarly, there will be little variation in the kinetics of the radiotracer itself in the volume of the vascular placenta represented in the central compartment model. Descriptions of the pharmacokinetics of tracer substances for blood plasma are also known (Jensen LI, Dean PB, Nyman U, Golman K (1985) Contrast media for CT. An analysis of the early pharmacokinetics. Invest Radiol., 20(8):867-870).

[0015] Iodinated contrast media are eliminated almost exclusively by glomerular filtration. During glomerular filtration, blood is filtered by tiny capillaries in the kidneys (glomeruli). The contrast molecules are small enough to pass through the glomeruli and enter the filtrate, a fluid similar in composition to urine. The filtrate then flows through the renal tubules, where part of the contrast medium is reabsorbed into the bloodstream. The remainder of the contrast material is excreted in the urine. With normal renal function, the elimination half-life is approximately 90 minutes, and almost all of the applied dose of contrast material is excreted within 24 hours.

[0016] Gadolinium-based contrast agents are excreted almost exclusively by the kidneys or by the dual route of elimination by the kidneys and the hepatobiliary system together with the bile. Bile is produced by liver cells - hepatocytes, and then stored in the gallbladder. From the gallbladder, it is released into the small intestine.

[0017] The diagnostic method used does not affect the value of diagnostic indicators used to determine perfusion. The reason is that diagnostic methods for in vivo perfusion imaging provide only imaging information illustrating changes in radiodensity in VOL The values of the diagnostic indicators used to determine perfusion are obtained by post-processing of the said imaging information.

[0018] Post-processing of imaging information is independent of the imaging method used. Post-processing is carried out on the basis of an analysis of the mutual relationship of changes in radiodensity within each ROI (region of interest) belonging to the VOL ROI can be a voxel. This relationship analysis provides TAC (tissue attenuation curve) for ROI, and AIF (arterial input function) at blood supply to VOL There is a dependence of the TAC, among others, on the AIF. In the case of qualitative methods (for example SPECT), post-processing is greatly simplified. Post-processing for the qualitative method usually involves determining the percentage change between the rest phase (rest) and the pharmacological hyperemia phase (hyperemia). Nowadays, however, following the expectations of clinicians, device manufacturers and accompanying software try to provide quantitative information. This makes post- processing more complex, although it does not necessarily determine the resting phase and the pharmacological hyperemia phase.

[0019] An elementary and easiest way to determine perfusion refers to the parameters of the TAC curve. The parameters of the TAC curve include TTP (time to peak), i.e. the time elapsed in the case of a given ROI (e.g. voxel), when the contrast saturation at the TAC reaches its maximum. Sometimes, the BAT (bolus arrival time) is given, i.e. the time after which the contrast reaches a specific ROI. The basic metric for determining contrast flow dynamics is the expected value of flow times (MTT, mean transit time) MTT = Jo°° t ■ h(t)dt, wherein h(t) = TAC(t) / J0C° TAC(t)dt, that is MTT is determined using the probability density function (h(t)). In some implementations, a cumulative distribution function (H(t)) or a residual function (R(t)) is also introduced for this purpose. As a result, there is MTT = J0°°(l — Htftydt = J00R(t)dt. The basic metric and quantitative indicator of perfusion assessment is the aforementioned MBF [ml / 100g min], MBF is the flow of the incoming blood volume relative to the unit of muscle mass (or volume) and time interval. We estimate MBF by arranging the mass balance of the tracer between inlet and outlet, the dynamics of which are determined by AIF(t) and TAC(t) by neglecting the venous outlet. We obtain MBF = l / pt• max(d TXC(t) / dt) / rnax(AIF(t)), wherein is the tissue density and max (•) determines the maximum value of the function-argument (•) . This MBF estimation analyses only the course of the accumulation phase. The accumulation phase is the time interval - at most - between BAT and TTP when d TAC(t) / dt » 0. Hence, the said estimation is called maximum-slope . This is how MBF is calculated in a given ROI (voxel) based on the local value max(d TAC(t) / dt) . This MBF estimation is the first of the post-processing methods of perfusion imaging that has been used in routine medical diagnostics. The reason may be simplicity and huge computational efficiency. A significant weakness and limitation of this method is the fact that the accumulation phase covers at most several points on TAC(t) (for example, only three). A small number of points on the TAC(t) does not give high precision and high accuracy. Convolutional methods have a high precision and high accuracy. These methods extend the tracer substance balance from several points to a time interval (from 0 to t). As a result, there is TAC(t) = ptMBF • — T)C / T. AS it can be observed, the local contrast concentration determined by the recorded value TAC(t) expresses the convolutional product AIF(t) and the impulse response function IRF(t), that is TAC(t) = AIF(t) ® IRF(t). Given that the residual function R(t) e< 0,1 >, a unit flow is MBF = l / ptmax (IRF(tJ). There are also other methods of post-processing perfusion imaging, for example: BTX (blood-tissue exchange) (Xue H, Brown LAE, Nielles-Vallespin S, Plein S, Kellman P (2020) Automatic in-line quantitative myocardial perfusion mapping: Processing algorithm and implementation. Magnetic resonance in medicine, 83(2), 712-730; Bassingthwaighte JB, Wang CY, Chan IS (1989) Blood-tissue exchange via transport and transformation by capillary endothelial cells. Circulation research, 65(4), 997-1020). These methods, although very promising, find mainly research applications. This is due to the degree of complexity or the number of empirical parameters they require for reconciliation.

[0020] The acquisition quality of the radiodensity curve at the inlet side (AIF(t)) is of primary importance for the precision and accuracy of the post-processing product. Apart from the TAC(t) parameters, AIF(t) is what affects the computation values in each voxel and each ROI. AIF(t) is highly exposed to artifacts for VOI perfusion imaging, which includes an organ subject to continuous motility, such as the heart (due to a systolic -diastolic cycle and / or respiratory activity). These artifacts mean that post -processing does not use registered AIF(t), but approximations of AIF(t) based on measured points are used. The approximation of AIF(t) is a significant problem hindering the process of quantification of the perfusion phenomenon.

[0021] One of the first works attempting to address the problem of approximation of AIF(t) is Thompson HK Jr., Starmer CF, Whalen RE, Mcintosh HD (1964) Indicator transit time considered as a gamma variate. Circulation research, 14, 502-515. While in the early 1960s purely theoretical attempts were made to analyze the course of radio-density curves AIF(t), their actual effectiveness turned out to be very limited. Hence, Thompson et al. adopted an ad hoc proposal for approximation based on the principle put forward in Evans RL (1959) Two comments on the estimation of blood flow and central volume from dye-dilution curves. Journal of Applied Physiology, 14(3), 457, the contrast concentration AIF(t) t-AT was presented as AIF(t) = C(f) = K(t — AT)ae P , where t - determines the time from the moment of injection, K- was the constant of the scaling coefficient, AT- is the moment of observing the contrast in the reference cross-section, and a, f are arbitrary empirical parameters. A validation attempt C(t) on the example of 114 in vivo results showed strikingly good effectiveness of Evans' equation. A very similar way of describing AIF(t) is presented in the paper Madsen MT (1992) A simplified formulation of the gamma variate function. Physics in Medicine & Biology, 37(7), 1597-1600. Similarly to less than thirty years earlier in Evans' work, we observe in Madsen an approximation of the relationship formally similar to the gamma probability density function known from statistics. Based on the experiences of the time, a modified form of Thomson's equation was introduced, including new parameters. This modified form reduced practical problems related to undesirable mathematical properties (such as, for example, the impact of changes in parameters a and ft on the time of descent and rise of the function, as well as the change in the location and maximum value of the function). However, this new form of the equation forced the use of an additional scaling step due to the difficulty in predicting changes in functions after changing the aforementioned new parameters. The final form of Thomson's equation was established as y(t') = ymaxt'aexp(a(l — t')), where: f=(t-to) / (tmax-to), where to is the delay time from t=0 to the time of the start of the tracer accumulation phase, / ma\ is the time when y(t) reached its maximum, and a is an empirical parameter. Bindschadler M, Modgil D, Branch KR, La Riviere PJ, Alessio AM (2014) Comparison of blood flow models and acquisitions for quantitative myocardial perfusion estimation from dynamic CT. Physics in medicine and biology, 59(7), 1533-1556 describes fine-tuning the selection of acquisition protocols and MBF models derived from CTP. One of the described examples of the selection of the acquisition protocol and computation models of the MBF indicator includes a procedure for adjusting the radio density curves. The authors emphasize that in order to estimate MBF using the maximum-slope method, it is first required to calculate (i) the maximum input value of the TAC of the left ventricle subtracted from the background and (ii) the slope of the increasing part of the TAC of the myocardium subtracted from the background. Citing the work of Mischi M, den Boer JA, Korsten HH (2008) On the physical and stochastic representation of an indicator dilution curve as a gamma variate. Physiological measurement, 29(f>), 281-294 as well as Bindschadler M et al., the single-pass bolus shape in the vascular system is usually well represented by the gamma probability density distribution function. On the other hand, in the topic of artifact reduction and limited sampling AIF(t), Bindschadler M et al. determine the maximum value of AIF(t) by matching the gamma probability density distribution function and selecting the peak value of the matched gamma probability density distribution function. In this example, the measured maximum value AIF(t) is not used. To determine AIF(t) the equation according to (Madsen, 1992), y(t) = Ymax(f / feak)a exP (a(f ~ t / tpeak) )> wherein: tpeak - the moment of time marked as a single value, in which y(t) reached its maximum value, t - an independent time parameter, / mas - the maximum value of the variable y, a - the empirical parameter of the model . The above equation was used to match the TAC input from the starting point to the point when the function value decreased to 50% of the maximum value. Matching was carried out only to this point, because from this point there is a significant deviation of the TAC from the shape of the matched gamma probability density distribution function due to contrast recirculation. A similar fit occurs in the case AIF(t). A good summary and recommendation in this regard can be found in Peerlings D et al. (2021) Variation in arterial input function in a large multicenter computed tomography perfusion study, European Radiology, 31(11), 8317-8325. This paper analyzed the variability of the intravenous contrast injection (IV bolus) AIF curve based on the results of a multicenter clinical trial involving 14 clinical units (1422 patients). With the help of statistical analysis, the following were assessed: differences in amplitudes, area under the curve (AUC), bolus arrival time (BAT) and time to peak (TTP). Perfusion parameters were automatically determined from AIF matched gamma distribution. This work clearly confirmed the effectiveness and practical usefulness of the method involving matching the gamma probability density function to the AIF.

[0022] In addition to a purely experimental approach to the study of in vivo perfusion, attempts were also made to evaluate perfusion using appropriate phenomenological models of flow and numerical solutions, i.e. in silico. An early example of a work presenting the method in silico is the paper of Schmidt R, Graafen D, Weber S, Schreiber LM (2013) Computational fluid dynamics simulations of contrast agent bolus dispersion in a coronary bifurcation: impact on MRI-based quantification of myocardial perfusion. Comput Math Methods Med. 5131870. This paper revealed a combination of a well-known numerical model of blood flow in the coronary arteries, based on the classical system of mass and momentum balance equations (Euler and Navier-Stokes) and - interestingly - a multi-path, multi-indicator, four- region MMID4 model derived from the blood-tissue exchange BTX concept (Bassingthwaighte JB, Wang CY, Chan IS (1989) Blood-tissue exchange via transport and transformation by capillary endothelial cells. Circ Res.65 (4): 997- 1020). All types of individual variable data were obtained directly on the basis of in vivo measurement using magnetic resonance imaging (MRI) method. In this way, the boundary conditions as well as the course of AIF variability at the inlet side were determined, and the curve itself was approximated in accordance with the distribution of the gamma probability density function. A completely different concept is presented in the work of LeeJ, Nordsletten D, Cookson A, Rivolo S, Smith N (2016) In silico coronary wave intensity analysis: application of an integrated one- dimensional and poromechanical model of cardiac perfusion. Biomechanics and modeling in mechanohiology, 15(6), 1535-1555. In the field of perfusion modeling, it already refers directly to phenomenological models of porous media, in particular to the Darcy equation, combining, however, the full ventricular-aortic -coronary coupling. This was finally achieved by integrating one-dimensional vascular flow modeling supplemented with Windkessel-type boundary conditions and poroelastic perfusion through a specific myocardial framework (as the authors define it). The work of Zingaro A et al. (2023) operates with an even greater degree of generalization of the concept of the phenomenological model. A comprehensive mathematical model for cardiac perfusion. Scientific Reports, 13(1), 14220. This model includes cardiac electrophysiology, active and passive mechanisms, hemodynamics, cardiac valves modelling, and a multi -compartmental perfusion model derived from Darcy's equations. The researchers emphasize that their integrated model does not require the selection of assumptions about boundary conditions at the inlet sections of large coronary arteries. For the description of solid structures (analysis of mechanical structures, so-called structural analysis), the researchers chose the model of elastodynamics in the formalism of the Piol -Kirchhoff tensor and the energy density of Green's deformation. The authors describe the model by comparing coronary flow rates in silico and mean MBF with literature values of clinically established ranges. In addition, the effect of aortic regurgitation on myocardial perfusion was examined. This effect included a decrease in myocardial perfusion due to the blood flow received by the left ventricle during diastole. From a practical point of view, combining the flow model in the lumen of vessels and muscle tissue into a single structure creates a considerable challenge for computational expenditures. Another interesting example is Papamanolis L, Kim HJ, Jaquet C, Sinclair M, Schaap M, Danad I, van Diemen P, Knaapen P, Najman L, Talbot H, Taylor CA, Vignon-Clementel I (2021) Myocardial Perfusion Simulation for Coronary Artery Disease: A Coupled Patient-Specific Multiscale Model. Annals of Biomedical Engineering, 49(5), 1432-1447. This example contains a model of a porous medium used in relation to the myocardium in the form of the classical Darcy equation, so as a result there is u + KVp = 0, wherein K represents the permeability of the medium. On the other hand, the flow in the vessels responsible for the provisioning of the myocardium was modelled using a simplified one -dimensional mass balance model ( dQ / dt) and momentum d / dz(aQ2 / .4) + A / tody / dz + 8TTVQ / .4 = 0). In order to quantify the phenomenon of perfusion, the authors of the publication introduced a conventional metric for a unit coronary flow, while in the original, marked as MBF, it - in fact - has little to do with a parameter with an identical name used in clinical practice.

[0023] To sum up, the determination of perfusion parameters is carried out according to two strategies: in vivo and in silico. Each of them involves three steps. The first step in the in vivo method, the only one used in routine clinical diagnosis, includes measuring in vivo the effects of the flow of contrasting substances with blood within the selected VOI to determine blood flow. In the in silico method, blood flow is reproduced in silico thanks to the solutions of appropriate phenomenological models of transport. In the case of both strategies, the final effect of this step is information on the dynamics of the contrasting substance in the form of TAC curves in each VOI voxel. TAC curves are a response to controllable AIF forcing at the inlet cross-section from which the selected VOI is supplied. The third step includes, based on combining of AIF dynamics and TAC responses, the computation of the perfusion metric in the form of unit MBF, MBV and TTP, MTT times, as well as other perfusion parameters. The concentration of the contrast agent, and thus the AIF values, may be disturbed by (1) renal dysfunction (which applies in particular to iodine- and gadolinium-based agents), (2) hydration (if its level provides the kidneys with a sufficient amount of fluid to filter and excrete the contrast agent), (3) individual factors (age, sex and associated medical conditions), as described in Kaller MO, An J. Contrast Agent Toxicity. In: StatPearls. StatPearls Publishing, Treasure Island (FL); 2022.

[0024] The above description indicates the importance of AIF in precise and accurate determination of perfusion. Many attempts to determine AIF were also shown. The present invention provides a method for determining an AIF in a precise and accurate manner, thus determining in silico perfusion parameters in a precise and accurate manner.

[0025] BRIEF DESCRIPTION OF THE INVENTION

[0026] The present invention provides the identification and analytical description of an arterial input function (AIF). This makes it possible to obtain reliable perfusion parameters that properly describe the condition of the human subject. In embodiments, the invention provides a patient-specific AIF. The patient- specific AIF should be understood as AIF specific to a given human individual. In particular, this is not an AIF curve describing the averaged state of the system of a group of human subjects. A method of the embodiments can be implemented as a computer-implemented invention. The implementation may be local or involve the use of an internet network, including the internet.

[0027] For medical purposes, any perfusion model must provide parameters describing in silico the transport phenomena of the tracer substance in muscle tissue comparable to those obtained from in vivo methods. Only comparable parameters to those obtained in vivo can be used to correctly assess the health status of a human subject. According to the Inventors, in order for the model to be able to provide parameters comparable to in vivo measurement, it requires a predetermined a priori patient-specific AIF curve, i.e. the dependence of the contrast substance concentration on time in a given area of interest (target circulatory area, VOI).

[0028] The central compartment may indicate plasma and highly vascularized tissues. Highly vascularized tissues include the kidneys and liver. Poorly vascularized tissues include a layer of fat. This definition is consistent with the definition used in the art. A person of ordinary skill in the art will have no trouble determining which tissues are highly vascularized and which are not.

[0029] The present invention provides a model to relate changes in the concentration in the central compartment (cx(t)) to changes in the concentration in the circulatory (peripheral) area (Cj(t)) for which perfusion is to be determined. In particular, the pharmacokinetic model allows to determine the concentration in the circulatory area i, which allows to use the pharmacokinetic model to determine the AIF curve and consequently to determine the perfusion for the circulatory area i. The above can be illustrated as

[0030] In a most general aspect, the present invention provides a computation of an arterial input function (AIF).

[0031] The computation of arterial input function (AIF) includes the selection of a pharmacokinetic model, which includes the selection of a class (CM, CMC) and order (n) of the pharmacokinetic model. The pharmacokinetic model class is selected from a parallel distribution (CM) model or a serial distribution (CMC) model.

[0032] The parallel distribution (CM) model assumes distribution from a central compartment to one or more peripheral compartments. The serial distribution model (CMC) assumes distribution from a central compartment in series through one or more intermediate compartments to one or more peripheral compartments. The order (n) of the pharmacokinetic model is the number of compartments in the selected pharmacokinetic model. These models may include more assumptions. For example, the CMC model may include the assumption of short time scales, which results in the lack of return transport. Return transport should be understood as transport in the opposite direction to the transport of a tracer substance following the administration of the tracer substance. For example, after administration, a concentration in a central compartment increases, from which the transport of the tracer substance takes place to a selected peripheral compartment. In this example, the return transport is the transport from a peripheral compartment to a central compartment.

[0033] In a further step, the computation includes selection of kinetic parameters and initial concentration of the tracer substance for the selected pharmacokinetic model.

[0034] The next step is to calculate an arterial input function (AIF) at the inlet to the target circulatory area (VOI) using the solution of the selected pharmacokinetic model.

[0035] The calculated arterial input function (AIF) is essential to determine perfusion. The correctness of the computation of the arterial input function (AIF) has an impact on the correctness of the perfusion determination, in particular on the correctness of the determination of perfusion metrics.

[0036] The next step is to calculate the perfusion metrics, where the perfusion metrics are calculated using the concentration of the tracer substance and the arterial input function (AIF). Computation of perfusion metrics includes determination of blood flow for the target circulatory area (VOI) and computation of arterial input function (AIF) for the target circulatory area (VOI). The target circulatory area (VOI) includes the peripheral compartment. It then includes determining the changes in the tissue attenuation curve (TAC) for the target circulatory area (VOI) using the arterial input function (AIF), and calculating the perfusion metrics based on the specific tissue attenuation curves (TAC) for the target circulatory area (VOI) using the calculated arterial input function (AIF).

[0037] In embodiments, determining the concentration of the tracer substance in compartment (z) may be described by the equation wherein: VLis the value of the volume of distribution available for the tracer substance in the compartment (z), cLis the transient value of the concentration of the tracer substance in the compartment (z), and qin, qout, cin, coutdescribes the size of the volumetric flow rate (q) with a given concentration (c) at the inflow (in) to and outflow (out) from the compartment (z).

[0038] In embodiments, the kinetic model class may be a parallel distribution (CM) model, wherein the tracer substance concentration at the central compartment may be in the form of and for peripheral compartments

[0039] In embodiments, the concentration of the tracer substance in the compartment (z) may be described by the equation wherein the change in concentration in the compartment (z) is dcL / dt. the flow arriving from the compartment preceding is (kj-i t c^), and from the subsequent one (ki+1 tci+1), and the flows backflowing from each of them — (kL + kL (+1) cL. and c is the concentration, k is the reaction rate constants, t is the time, and the indices z-1, z, z+1 are the preceding, current, and next compartments, respectively.

[0040] In embodiments, the equation describing the concentration of the tracer substance may include excretion of the tracer substance from the body. In particular, by the following form wherein (kL 0) cLis a fraction of the tracer substance is excreted from the body. In embodiments, the tracer substance may be excreted from the body exclusively from the central compartment.

[0041] In embodiments, the excretion of the tracer substance from the body may be described by the Michaelis- Menten formalism or may be captured by using the Hill -Langmuir equation. In particular, the Hill- Langmuir equation may be in the form of where vmaxdetermines the maximum elimination rate of the tracer substance, and z, KDare the empirical constants.

[0042] In embodiments, the parallel distribution (CM) model may be a two -compartment (2CM) or three- compartment (3CM) model, wherein the two -compartment (2CM) model comprises a central compartment and a single peripheral compartment, and wherein the tracer substance concentration for the central compartment may be in the form and for the peripheral compartment may be in the form of and where k21it is the rate constant between the peripheral compartment and the central compartment, k12is the rate constant between the central compartment and the peripheral compartment, k10is the rate constant of elimination of the tracer substance from the central compartment. Here, k10it is also the rate constant of excretion of the tracer substance from the human body.

[0043] In embodiments, the kinetic model class may be a serial distribution model (CMC), and the concentration in the given compartment (z) is shaped based on the cascade of compartments preceding the given compartment, the return transport of the tracer substance is negligible and there is no excretion of the tracer substance from the body. Determination of kinetic parameters for any compartment (z) may be in the form of wherein i is in the range of 1 to n. For example, n = 3, 4, 5, 6, 7, 8 or 9. In embodiments, the selection of kinetic parameters may comprise the use of experimentally determined tracer substance kinetics, research on the safety of clinical use of the tracer substance, approximation of kinetic parameters, use of analytical models, and / or use of a regression model.

[0044] In embodiments, the selection of kinetic parameters can be performed using a regression model, in which each in the set of parameters Y = { / c12, ■■■ } is defined as a function of Y = / (X, lb) + e X predictors describing the general medical and hemodynamic features of the patient, and parameters lb with a certain random error e, wherein the set of X predictors is determined by the general medical data, as well as empirical indicators associated with the general medical data. In particular, the set of X predictors can be complemented by hemodynamic indicators and parameters. Hemodynamic indicators and parameters can be selected from a group comprising: HR pulse (1 / min), IBI cardiac cycle duration (sec), characteristic blood pressure levels in the form of systolic SYS (mm Hg), diastolic DIA (mm Hg), and / or PP= SYS-DIA pulse (mm Hg), and / or MAP=DIA+PP / 3 mean arterial pressure, a continuously recorded peripheral or central arterial pressure wave. Empirical indicators may be associated with cardiac output or result from the Liljestran-Zander model. Empirical indicators associated with cardiac output can be selected from the group comprising: SV ejection volume, CO cardiac output, flow parameters, coronary flow, coronary unit flow, cerebral flow, cerebral unit flow, cardiac index, cerebral index. In embodiments, the general medical data may consist of or include the following elements: sex, age Y, weight W, height H, and the empirical indicators may consist of or include the following elements: body mass index BMI = W / H2, body surface area BSA, and basal metabolic rate BMR.

[0045] In embodiments, the concentration of the substance may be expressed in conventional units, radiodensity, or relative X-ray attenuation capacity. They can be expressed in Hounsfield Units (HU) scale in detailed embodiments.

[0046] The computation of an arterial input function (AIF) in embodiments may include, as a final step, approximation by an analytical model or a gamma probability density distribution function.

[0047] In embodiments, the concentration of the indicator substance may include the influence of patient- specific variable hemodynamic features and / or factors selected from the group consisting of or comprising: (1) renal impairment, (2) hydration, and (3) individual factors including age, sex, and associated medical conditions.

[0048] A detailed description includes a number of exemplary embodiments and the benefits thereof. These examples may be combined in any order and number, and matching elements of the embodiments may be combined to provide new embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] A detailed description is provided with reference to the accompanying drawings. The accompanying drawings are for illustrative purposes only and illustrate only examples of embodiments of the invention. The drawings are intended to facilitate the understanding of the operation of the invention and are not to be considered as limiting the area, scope or application of the invention. In drawings, the first left digit (s) of the numeric reference identifies the drawing in which the numeric reference first appears. The use of the same numerical references indicates similar but not necessarily the same or identical elements. Various numerical references can also be used to identify similar elements. Various embodiments may use elements or components other than those shown in the drawings, and some elements and / or components may not be present in various embodiments. The use of a single terminology to describe a component or element may, depending on the context, include the plural of such components or elements, and vice versa.

[0050] FIG.01. An embodiment of perfusion metrics calculation;

[0051] FIG.02. Kinetic diagram of the active substance: (A) a general mass balance diagram, (B) in supplying parallel peripheral compartments, and (C) for a serial arrangement of peripheral compartments;

[0052] FIG.03. Reconstruction of the AIF curve in a parallel distribution system to peripheral compartments using stochastic selection of individually variable parameters: comparison of the course of the obtained curves with in vivo clinical data for the two -compartment pharmacokinetic model of 2CM (A) and three- compartment model of 3CM (B) and deviations of the area under the AUC curve for both models of 2CM (C) and 3CM (D);

[0053] FIG.04. The effect of the order of the serial (cascade) pharmacokinetic model on the ability to reproduce clinical results in vivo for the system of 3, 4, 5, 6, 7, 8 and 9 compartments, as regards the Perason correlation coefficient (A) and the deviation of the area under the curve (B);

[0054] FIG.05. Reconstruction of the AIF curve in the cascade of compartments using a model of stochastic selection of individually variable parameters of the pharmacokinetic model.

[0055] DETAILED DESCRIPTION

[0056] The embodiments described below include a method of determining an AIF curve for calculating perfusion metrics. These examples should not be used to limit the invention but only to illustrate aspects thereof.

[0057] In embodiments, the method for calculating perfusion metrics for the in silico method is shown in steps in FIG.01, as discussed below. In this method, the blood flow is reproduced in silico thanks to the solutions of the respective transport models. In an embodiment, the method comprises determining the perfusion parameters and performing the analysis thereof. Perfusion parameters include MBF unit flow.

[0058] The determination of perfusion can be performed in an embodiment according to Mirota K (2022) Assessment of myocardial perfusion using non-invasive measurements and poromechanics, WO2023166333A1. The entirety of this application, including all aspects and embodiments thereof, is incorporated into the scope of this application by reference in such a way that the elements of this application are to be treated as the elements described in this application. This ensures, on the one hand, the provision of many essential elements for the present application without the need to rewrite the entire description of WO2023166333A1 to the present description. The purpose of this inclusion is also to combine the embodiments described in the present application providing the computation of the AIF functions with the embodiments of WO2023166333A1 in which the calculated AIF function is used to calculate the perfusion and its metrics.

[0059] In embodiments, the invention comprises determining an AIF curve for calculating perfusion metrics, wherein the particular AIF is comparable or identical for the waveform of the AIF recorded under clinical conditions (in vivo) as a function of time, wherein recording the waveform of the AIF comprises administering a contrast medium at a distal site, followed by non-invasive imaging of the transport of the contrast medium through the body of the human subject. The transport takes place to the destination VOL The invention provides a determination of an AIF that is comparable or identical to a registered AIF for a VOI, which may be a myocardium, a brain, or both. The invention provides a determination of an AIF that is comparable or identical to a registered AIF, the VOI may be other organs for which a perfusion may be determined.

[0060] The invention provides in silico results comparable or identical to in vivo also when the contrast agent is administered orally, rectally, intravenously, or by injection into the body cavity. Also, when the route of administration of the contrast agent for most perfusion imaging techniques is an intravenous infusion (also referred to as an infusion, IV bolus). To simplify, this administration involves rapid intravenous injection of the substance (American College of Radiology Manual on contrast media, ACR Committee on Drugs and Contrast Media, 2023).

[0061] It is known that, depending on the technical details of in vivo imaging, appropriate tracer substances are used. Including PET, SPECT, CTP, and MR. The invention provides results comparable or identical to the recorded course of the AIF with the use of any tracer substances. In particular, tracer substances such as radiotracers containing isotopes such as fluorine- 18, copper-64, carbon-11, gal-68, rubidium - 82, oxygen- 15, nitrogen- 13, or combinations thereof, and also containing the triatomic iodine molecule L - radiotracers being iohexol or iopromide compounds. Embodiments provide compliance with the registration of AIFs in which the tracer substance is administered by intravenous infusion (IV bolus) at a distal location. The term distal location is known in the art. According to embodiments, it is assumed that in the central compartment, in a negligible short time At -> 0 from the moment of administration (t=0), the concentration of the active tracer is cr(0) .

[0062] In embodiments, the tracer substance is transported with the flowing blood in concentration c1(t). During transport, the tracer substance is rapidly distributed not only in the vascular bed but also in the extravascular space, without a pharmacodynamic effect. In other words, the tracer substance does not act on the body of the human subject as an active substance, it is not metabolized and it is only transported in the body of the human subject. If the volume of the vascular bed is on average on the order of several liters, the conventional volume of distribution for a typical contrast agent is much larger.

[0063] According to embodiments in FIG.01, the AIF is determined in three or four steps.

[0064] The first step is to select a pharmacokinetic model and this includes the selection of the class and order of the radiotracer pharmacokinetic model. According to embodiments, it is possible to select two different classes of reconstruction of AIF curves (radiodensity): the first, based on a model of parallel distribution from a central compartment (representing, for example, blood plasma) to peripheral compartments, and the second, based on a cascade system of serial distribution of short time scales. Short time scales should be understood as short periods. In this specification, these models are denoted as nCM and nCMC, respectively, where n specifies the number of compartments used to build the model. The number of compartments here is also called the model order. Among the embodiments discussed, the preferred example comprises a serial (cascade) model of 4CMC. In embodiments of higher complexity and post-processing using convolution / deconvolution methods, higher-order models (5CMC, up to 8CMC) are used. Second-order 2CM parallel distribution models are also preferred.

[0065] In the second step, the kinetic parameters (k or ky, according to the model class) and the initial concentration ci(0) are selected. The parameters ky and k, of the models can be determined on the basis of the results of clinical trials of the kinetics of a given contrast substance from the available papers of the test results (if they are available in extenso) or from own results (if there are no appropriate sources). For nCM class models, ky parameters can also be determined on the basis of their approximation and analytical models available in the papers, for example for the central compartment. Ultimately, the kinetic parameters of the model - and this is the preferred embodiment - may be determined on the basis of a regression model, which determines them as predictors describing the general medical and hemodynamic characteristics of patient. The initial concentration may be expressed in a customary manner as the amount of substance in a unit of mass or volume, or units on a conventional scale (e.g., the Hounsfield scale). Initial concentration ci(0) can be calculated in the usual way, referring the dose of contrast agent (selected according to the guidelines of the clinical trial protocol by a given method) to the volume of distribution (according to the type of contrast agent). If an analytical kinetic model for the central compartment in the form of a linear combination is available for a given tracer substance, the initial concentration can be calculated directly as the sum of the coefficients of the linear combination. An alternative and preferred embodiment will be to use a stochastic model as for the kinetic constants, and the set of predictors will be identical.

[0066] Step three is to reconstruct the AIF curve (radio density) in the agreed VOI supply area. Regardless of the assumed class of the pharmacokinetic model and its order, the reconstruction of the curve will be based on the solution of the system of differential equations of the model. Two equivalent strategies may be used. In the first and most direct solution can be obtained using numerical methods with the initial condition in the form of a non-zero concentration in the first (central) compartment calculated as in the second step and zero for each subsequent one (c,(0)=0 for z>l). Since the system itself, in the most unfavorable case, involves no more than a few equations, this does not pose a serious challenge in a numerical sense. Naturally, the numerical solution will provide only approximate values, hence the second strategy providing accurate solutions and involving the use of analytical solutions. Precise solutions can be obtained, for example, using integral transformation methods, such as the Laplace transformation.

[0067] An optional and a finishing fourth step to complete the reconstruction of the AIF curve model may be to approximate its course with the selected model. The selection of the model is carried out advantageously by taking into account the complexity of the computations, and the preferred models offer less complex computations. The approximation can be according to the analytical model, or according to the gamma probability density distribution function. However, this is not an obligatory step and is desirable only in the case of reconstructions based on first-class models, i.e. parallel distribution (nCM). In the case of second-class models, i.e. serial distribution in a cascade system, this is an unnecessary step.

[0068] In embodiments, the tracer substance is assumed to produce a tracer substance concentration of c1(0) in the central compartment within a negligible amount of time At -> 0 from the moment of administration (t=0). The tracer substance, according to an embodiment, is transported with the flowing blood in a concentration cx(t) . In embodiments, the tracer substance reaches further circulatory areas ( / ) and thus another compartment in pharmacokinetic senses (Rescigno A (2010) Compartmental analysis and its manifold applications to pharmacokinetics. The AAPS journal, 12(1), 61-72), where, due to the differentiation of perfusion in the tissue, local changes in transient concentration values c((t) are observed in accordance with the general mass balance equation (FIG.02, (A)) wherein: VLis the value of the volume of distribution available for the tracer substance in the circulatory area / , c(is the transient value of the concentration of the tracer substance in the circulatory area / , and qm, (lout>cin>cout describes the value of the volumetric flow rate (q) with a given average concentration (c) at the inflow (in) to and outflow (out) from the circulatory area i. In embodiments, the inlet may be a designated injection site and the outlet may be kidneys.

[0069] In these embodiments, the tracer substance is subject to distribution and accumulation upon administration, from the central compartment to one or more circulatory areas i - in the sense of pharmacokinetics - peripheral compartments. The course of distribution and accumulation, in accordance with embodiments, is shaped mainly under the influence of individually variable hemodynamic features. As individually variable features of hemodynamics, they can be characterized in particular by: (1) time parameters of cardiac contraction as cycle length (IBI, sec) or frequency (HR, 1 / min), (2) course of changes in cycle pressure values, including systolic (SYS, mm Hg) and diastolic (DIA, mm Hg), (3) cardiac output parameters as ejection volume (SV, ml), cardiac output (CO, 1 / min), (4) coronary arteries flow parameters (CBF, ml / s). There are also other parameters characterizing patient- specific features of hemodynamics. Taking into account the above-mentioned features may be implemented by taking into account the tracer substance concentration in the computation. Taking into account the patient-specific characteristics of hemodynamics improves the consistency between the calculated parameters (including AIF, perfusion parameters) and the parameters obtained from in vivo studies.

[0070] In an embodiment, the kinetic model for a single compartment i is in accordance with the diagram in FIG.02 (parts A and B), and therefore change in concentration in the compartment i calculated as dcL / dt is the effect of the superposition of the flow arriving from the preceding and subsequent compartment (ki+1 tci+1) and the flows backflowing from each of them — ( / q + kL L+1) cL. and optionally also in the part of the flow excreted from the organism — (kt 0) c^. As before, the symbol c denotes the concentration, k the reaction rate constants, and t the time, while the indices i-1, i, i+1 denote selected in the sense of pharmacokinetics the circulatory areas (preceding, current and subsequent).

[0071] Diagrams B and C in FIG.02 show two different methods for describing the distribution of the tracer substance between compartments according to two alternative embodiments. These methods differ in the way of mapping the exchange of the tracer substance between individual compartments. Compartments can be defined as circulatory areas differing in perfusion parameters to the selected substance. Differences between perfusion parameters should be statistically significant. In embodiments, the selected substance may be contrast. In FIG.02 B, the distribution of the tracer substance can take place directly, where the circulatory area (for example, peripheral) is supplied directly from the central compartment (area), where the central area has been supplied in the same manner as if it were an IV bolus. In this method, the aim is to determine perfusion parameters for the peripheral compartment (area). This method of describing the distribution, and thus a method of reconstruction of AIF, allows for the correct determination of perfusion parameters for the peripheral compartment. This method may have a discrepancy with the registration results to the extent that it describes an accumulation step. This stage is represented by the initial fragment of the AIF curve. This method corresponds to the parallel distribution (CM) model.

[0072] Alternatively and as shown in FIG.02 C, the peripheral circulatory area (peripheral compartment within the meaning of pharmacokinetics for which perfusion parameters are determined) is separated by other compartments (intermediate) from the central compartment. This method of description provides greater compliance of the obtained results than the method of FIG.02 B. This method describes the accumulation stage much better, i.e. the initial fragment of the AIF curve. This method corresponds to a serial distribution model (CMC).

[0073] In both alternative embodiments, the assumed mechanism of transporting the tracer substance with a flow from the moment of its administration (in particular, in an intravenous infusion) leads to a progressive distribution and accumulation of the contrast substance in subsequent circulatory areas. At the same time, however, as shown in the diagram (FIG.02 parts B and C) and kinetic equation (2), it is assumed that return transport is possible - indirectly or directly - to the central compartment.

[0074] The second and parallel and opposite process to distribution and accumulation, as captured by the kinetic equation (2) and diagrams B and C in FIG.02, is the removal of the tracer substance from the human system. Such removal can take place mainly through the kidneys. Removal can occur from any compartment, as described by equation (2). Removal from each compartment may give better quantitative results for selected tissues for which perfusion can be determined, and for which removal constitutes an important contribution to perfusion parameters.

[0075] In the preferred embodiment, the tracer substance can only be removed from the central compartment. The use of such a method of perfusion computation allows to obtain correct results of perfusion parameters with simultaneous acceleration of computations, and thus with easier availability of this embodiment.

[0076] According to embodiments, the rate at which the tracer substance will be removed is directly proportional to the current concentration that will be formed within the transient equilibrium in the central compartment.

[0077] In embodiments, the concentration values may be expressed in a customary manner, i.e. as the amount of substance per unit volume or weight. Concentration values can also be expressed in conventional units, radiodensity, or using measures of the relative X-ray attenuation capacity - for example: represented on the Hounsfield units (HU) scale. In such embodiments, for each voxel HU = 1000 (p — (iwaterJ / CPwater—Pair), which corresponds to a concentration value c = a + b(kVp) • HU at a « 0. This relationship is consistent with Bae KT. Intravenous contrast medium administration and scan timing at CT: considerations and approaches. Radiology. 2010;256(l): 32-61, Chuo CC, Pan HB. CT value reliability measurement and correlation between CT enhancement and contrast medium concentration on a 16 cm wide-detector CT scanner: a phantom study. Congress ECR 2017 / C-2848, DOI: 10.1594 / ecr2017 / C-2848. The linear relationship between relative units and concentration has no impact on post-processing and thus on the obtained perfusion parameters. For comparison, the existence of a non-linear relationship in place of the above-mentioned linear relationship would cause changes in the obtained perfusion parameters. Establishing and incorporating such dependencies in the embodiments allows the interchangeable use of conventionally sensed concentrations with concentrations expressed by HU.

[0078] The expression of concentration in customary or conventional units has no impact on the methods and formulated models for determining AIF curves presented here. Embodiments include both methods of expressing concentrations. Embodiments include known methods for post-processing perfusion imaging results, and the methods and models themselves are not dependent on the chosen post-processing method.

[0079] In embodiments, the concentration of the tracer substance may be subject to change under the influence of the following factors: (1) impaired renal function (which applies in particular to iodine and gadolinium-based agents), (2) hydration (if its level provides the kidneys with a sufficient amount of fluid for filtering and excretion of contrast medium), (3) individual factors (age, sex, and associated medical conditions). Depending on the human subject, consideration of these factors can play a key role in obtaining reliable results of perfusion parameters. Taking into account these factors results in more reliable results, i.e. results defined as better.

[0080] Taking into account these factors can be achieved through the non-linear nature of the elimination of the tracer substance in the Michaelis-Menten formalism (Stein AM, Peletier LA. Predicting the Onset of Nonlinear Pharmacokinetics. CPT Pharmacometrics Syst Pharmacol. 2018;7(10):670-677), Hill- Langmuir (Zhang J, Jiang J, WuX. Mathematical Solution of a Pharmacokinetic Model with Simultaneous First-Order and Hill-Type Elimination. Journal of Applied Analysis & Computation. 2023; 13(2): 623-643) or the Black-Leff formalism (Kenakin T. The mass action equation in pharmacology. British Journal of Clinical Pharmacology. 2016;81(l): 41-51). In a more preferred embodiment, consideration of these factors is made through a nonlinear tracer substance elimination model using the Hill-Langmuir equation. In this example, the kinetic equation (2) is replaced by the equation where vmaxit determines the maximum elimination rate of the tracer substance and m, KDare the empirical constants of this equation.

[0081] The effect of patient-specific variability in accordance with embodiments increases for circulatory areas distant from the distal location where the tracer substance was administered, and to account for this effect requires a greater complexity of the pharmacokinetic model. In embodiments, individual variability is considered using experimentally determined tracer substance kinetics. The experimentally determined kinetics may be in the form of parameters inserted into the kinetic equation (for example, equation (2) or equation (2) generalized) or may be determined on the basis of another equation or model, especially a regression model, the purpose of which is to describe the stochastic relationship. The source of parameters for a given tracer substance may be described clinical trials for a given tracer substance. For example, studies on the safety of clinical use for a given tracer substance. Exemplary values for use in embodiments are included in Edelson J, Shaw D, Palace G. Pharmacokinetics of iohexol, a new nonionic radiocontrast agent, in humans. JPharm Sci. 1984;73(7):993-995 or Jensen LI, Dean PB, Nyman U, Golman K. Contrast media for CT. An analysis of the early pharmacokinetics. Invest Radiol. 1985;20(8):867-870. The use of data from safety trials provides better results for distal areas. Another source may be clinical trials performed specifically to determine these parameters. Examples of test results to be used in embodiments are included in Salmon-Gandonniere C, Benz-de Bretagne I, Mercier E, et al. Iohexol clearance in unstable critically ill patients: a tool to assess glomerular filtration rate. Clin ChemLab Med. 2016;54(l 1): 1777-1786). In particular embodiments, the method comprises conducting clinical trials for a novel tracer substance or tracer substance without literature data regarding the kinetics required in the embodiments.

[0082] In an embodiment with parallel distribution (diagram B in FIG.02) to peripheral areas from the central compartment, introducing a two-compartment model formalism (2CM) comprising a central compartment and a single peripheral compartment (as a second compartment), the kinetic equation in 2CM for the central compartment may be in the form and for the peripheral circulatory area (second compartment) according to the general model given by equation (2). From the above, using the Laplace transform (marked by overline) we can obtain (assuming that C2(0)=0) which leads to operator relations towards the central compartment: where for the sake of simplicity, (k12+ k21+ ke) = (a + b) and (ke / c21) = (a • b) have been used. Now, by performing the partial fraction decomposition, we can obtain for the central compartment which leads to the original (in the formal sense of the theory of operator methods and integral transformations) for the concentration in this compartment c^t) = A ■ e~a t+ B ■ e~b t. (7)

[0083] In this example, using equation (5), we describe the concentration changes in the second compartment. Given that c2= ki2c1 / (s + k21) the concentration described in (7) may obtain the form wherein parameter C is defined by the equation rot 1 }

[0084] At the same time, having the values of empirical parameters A, B, a, b from an embodiment, we can calculate appropriate values of empirical constants of the kinetic model:

[0085] For obvious reasons, not always and not in every case papers reporting the results of studies on the pharmacokinetics of the tracer substance make an effort to build a theoretical model. Often, such works are limited only to the transmission of the results in extenso, adding only collective non-compartmental metrics. While the lack of an analytical description of variability c1(t) explicitly constitutes an initial impediment, there is no limitation for embodiments, because for experimental data it is possible to introduce approximation of any degree (in particular, the degree specific to a given complexity of the pharmacokinetic model). The function cr(t) matching in the case of the 2CM kinetic model will take place according to equation (7), and can be implemented as an optimization (minimization) task. In a preferred embodiment, this is a non-linear Levenberg-Marquardt mean squares method (Vetterhng WT, Flannery BP, Press WH, Teukolsky S. Numerical Recipes in C. 2nd Edition, Cambridge University Press, 1992).

[0086] In another preferred embodiment, the selection of empirical parameters of kinetics can be implemented on the basis of a previously prepared regression model, in which each in the set of parameters Y = { / c12, ... } is defined as a function Y = f(X, lb) + e of X predictors (describing the general medical and hemodynamic features of the patient) and parameters lb with a certain random error e. The set of X predictors is determined by general medical data (such as: sex, age Y, weight W, height H), as well as associated empirical indicators such as body mass index (BMI = W / H2), body surface area (BSA), and basal metabolic rate (BMR). This model is particularly useful when empirical data on excretion of a given tracer substance from the organism are not available.

[0087] In one embodiment, the BSA can be estimated, for example, according to the BSA = 0.007184 • H0 725• W0,425Du Bois&Du Bois or Schlich formula BSA = 0.000975482 • H1 08• W046for women and for men BSA = 0.000579479 • H1 28• W0 38. BMR is estimated according to Mifflin St Jeor BMR = 10 • W + 625 - H + 5 - Y. Other similar anatomical and physiological indicators can also be included and estimated in a similar manner (Reed, R. M., Netzer, G., Hunsicker, L., Mitchell, B. D., Rajagopal, K., Scharf, S., & Eberlein, M. (2014). Cardiac size and sex-matching in heart transplantation : size matters in matters of sex and the heart. JACC. Heart failure, 2(1), 73-83; Kawut, S. M., Lima, J. A., Barr, R. G., Chahal, H., Jain, A., Tandri, H., Praestgaard, A., Bagiella, E., Kizer, J. R., Johnson, W. C., Kronmal, R. A., & Bluemke, D. A. (2011). Sex and race differences in right ventricular structure and function: the multi-ethnic study of atherosclerosis-right ventricle study. Circulation, 123(22), 2542-2551).

[0088] In embodiments, the set of X predictors can be complemented by hemodynamic indicators and parameters, thus relating to the heart action and the resulting blood flow parameters. This allows to take into account that the transport of the tracer substance is carried out with flowing blood. In detailed embodiments, hemodynamic indicators and parameters are selected from: HR pulse (1 / min) or IBI cardiac cycle duration (sec), characteristic blood pressure levels in the form of systolic SYS (mm Hg) and diastolic DIA (mm Hg) or PP= SYS-DIA pulse (mm Hg), mean arterial pressure (MAP) MAP=DIA+PP / 3, continuously recorded peripheral (such as radial) or central arterial pressure wave. Said indicators and parameters are readily available, which is important for the availability of embodiments. The determination of these indicators and parameters can be carried out invasively or, more preferably, non-invasively.

[0089] In a further embodiment, parameters associated with cardiac output can be used to determine empirical indicators. Parameters associated with cardiac output may include: SV stroke volume (ml) and associated cardiac output (CO = SV • HR, l / min) and flow parameters or flow indices characteristic of the target VOI (for example: coronary or cerebral unit flow or flow and cardiac CI = CA / BSA cerebral CCRI = CBF / CO index, respectively). In particular embodiments, empirical models of the values of descriptive variables can be used to construct a stochastic model. An example of an empirical model is the Liljestran-Zander model known in the art. This model binds the cardiac output to the parameters of the contractile activity of the heart. The model dates back to 1928 and has been modified several times, for example CO = PP / (SYS + DIA) • HR (Koenig J, Hill LK, Williams DP, Thayer JF (2015) Estimating cardiac output from blood pressure and heart rate: The Lilj estrand & Zander formula. Biomedical sciences instrumentation, 51, 85-90). These modifications as well as the original form of the model are used in embodiments.

[0090] In a further embodiment, the stroke volume (SV) may be used instead of the cardiac output (CO). This is possible because the cardiac output CO - as stated earlier - remains in a linear relationship with the heart rate (HR) and the stroke volume (SV). In a more detailed embodiment, the stroke volume can be estimated empirically using SV = k • MAP and SV = k • PP. In another example, the Liljestrander- Zander relationship can be used more advantageously when implicit SV = k ■ PP / (SYS + DIA). Other embodiments may use the empirical formula from Starr I, Schnabel TG Jr, Askovitz SI, Schild A( 1954). Studies made by simulating systole at necropsy. IV. On the relation between pulse pressure and cardiac stroke volume, leading to a clinical method of estimating cardiac output from blood pressure and age. Circulation. 9(5):648-663. In more favorable examples, it is used SV = 91 + 0.54 • PP — 0.57 • DIA — 0.61 • Y (now called the Starr equation). Other embodiments use dependencies from Bridwell T, Greene DG, Jenss RM (1956) An evaluation of Starr’s equation for the prediction of stroke volume. Circulation.14(2):250-253 in SV = 66.0 + 0.34 • PP — 0.11 • DIA — 0.36 • Y relation to in vivo data. In the work on embodiments, it was found that correctly taking into account the influence of the patient's age provides better results compared to taking into account pressure-related parameters. Yet another and much more refined form of this type of formula can be found in the work of Lee J, Sohn J, Park J, Yang S, Lee S, Kim HC (2018) Novel blood pressure and pulse pressure estimation based on pulse transit time and stroke volume approximation. Biomed Eng Online. 17(1): 81 .

[0091] Modem methods of monitoring cardiac function, in addition to the possibility of easily measuring characteristic values such as HR, SYS and DIA, also offer the possibility of recording full pressure variability in the unfolding cycle as a pressure wave and flow volume (invasively or fully non- invasively). In particular, SV estimates are used on the basis of estimating the energy flow carried by a pressure wave of the type SV = k • J f / g / (p(t) — MAP)2dt or limited to the contraction phase SV = k • (1 — Tsyvs / Tdia) f p(t)dt - as a rule, they strive to achieve a dimensional reduction of the pressure *sys wave measurement result in such a way that it is possible to use classic formulas such as Liljestrander- Zander or Starr. The most preferred embodiment uses Windkessel models described in Kosior A, Mirota K, Tamawski J (2018) Patient-specific modeling of hemodynamic parameters in coronary arteries (U.S. Patent No. 11,871,995). This description is incorporated in its entirety into the description of the present application. In particular, by reference. In these embodiments, the whole circulatory system is described by a set of interconnected functional blocks of a model with lumped parameters, described by a system of equations balancing the change in volumetric flow rate and pressure between the conventional input and output as wherein the in and out indices denote the parameters of the flow state at the side of the conventional inlet and outlet, and the symbols R, L, C determine the total resistance, inertance and compliance, respectively.

[0092] In even more preferred embodiments, it is possible to derive a model of the form (11) for three pulmonary circulatory compartments (i.e. right blood circulation, for: elastic pulmonary arteries, separately smaller caliber arteries containing less of the collagen component in the walls and the venous reservoir) and five main circulatory compartments (successively for: the main artery / aorta and - further - proximal to its ducts of susceptible arteries, distal muscle arteries, the arterial reservoir in the main circulation and performing return transport to the heart - veins). In other less preferred embodiments, the main circulation is mapped via two compartments and the pulmonary circulation is mapped as one compartment.

[0093] In embodiments, the totality of the pharmacokinetic model may complement the atrioventricular cardiac model, separately for the pulmonary circulation and separately for the main circulation providing an analytical description of the pressure-volume coupling loop. In a more preferred embodiment, a variable elastance model is used E(t) = dpv / dV, according to which the transient pressure within the heart cavity pv= E(t) ■ (Fv—k0). and thus the blood volume flow flowing through any cardial cavity, is

[0094] E dV dpvpydE

[0095] (12) dt dt E dt '

[0096] The presented method of selecting empirical parameters of the AIF curve pharmacokinetic model can be used both for the previously given two -compartment model (2CM), as well as - striving to improve the quality of AIF reconstruction - of any higher order, both in the parallel and serial distribution system. In a further preferred embodiment, an n-compartmental (nCM) distribution system parallel to peripheral areas may be used. In this example, the generalized form of the central compartment kinetic equation may take the form assuming the removal of contrast from this compartment outside the human organism. For peripheral, so each subsequent z=2... w, it may be wherein, similarly to the remainder of the description and according to FIG.02 B, c, and kf!represent the concentrations and rate constants, respectively. The Laplace transform can lead here to a system of operator equations: for the central compartment (assuming according to the real conditions of physiology Q(0) = 0, dla i > 1)

[0097] (s + k12+ k13+ — I- km + kio)di d- sc2+ sc3+ — I- scn= cx(0), (15) and peripheral (z=2...«)

[0098] (s + ki^ct = klic1. (16)

[0099] As a result, as in the case of the 2CM considered early, the concentration for z>l can be determined by the operator equation wherein

[0100] Accordingly, we can obtain in the form of a linear combination regardless of which compartment is currently under consideration. The above equation is applicable to embodiments where higher order pharmacokinetic models are employed. In a further embodiment, a comparison of the method using the model of parallel distribution of contrast medium to peripheral compartments from the central one was made with the results obtained in a clinical trial carried out as part of the POIR.01.01.01-00-393 19 research project (in particular for the third stage of this project). The clinical trial included a group of human subjects (also referred to as patients) with a diagnostic indication of chronic coronary syndrome, in whom at least one stenosis of not less than 50% was found in coronary artery angiography by computed tomography. The group included a total of 71 people (men 43 / women 28) aged 40... 84 (67.70±6.52 including men 66.30±6.52 / women 69.80± 4.82) years with BMI= 19.20... 34.72 (26.89±3.20 including men 27.08±3.42 / women 26.0414.14), estimated BSA=1.51...2.49 m2(1.8910.20 including men 2.0110.18 / women 1.7810.15). In all these patients, a quantitative assessment of myocardial perfusion was made, obtaining MBF= 94.28... 333.58 ml / lOOml-min for unit coronary flow (165.31131.58 including men 183.01140.54 / women 155.05130.45). For each of the above-mentioned parameters, the range of variability was given, and in parentheses - due to the asymmetry of distributions - the value of the second quartile Q2 (medians) the median absolute deviation MAD (i.e. as the median of the absolute value of deviations from the median).

[0101] FIG.03 (curve T) shows the results of the reconstruction of the AIF curve based on the previously formulated pharmacokinetic models describing the parallel distribution to the peripheral compartments, in combination with the return transport, and the elimination of the contrast material is carried out from the central compartment. The upper part of FIG.03 (A) and (B) shows exemplary results of reconstruction of AIF curves for a single case using a 2CM model (as A) and a 3CM model (as B). On the graphs, concentrations are represented by Hounsfield scale units, i.e. as recorded by the device during the test. The values recorded by the device during the test were marked with points, and their approximation through the empirical curve of the gamma probability density distribution of the form

[0102] 3946.594 / t - 5.9O8388\3 000 / t - 5.908388\

[0103] ~ 1.835762 ^(4.000) \ 1.835762 J6XP\ 1.835762 J’ which was ultimately used for post-processing of image data. The values of the parameters (K, a, P) of this distribution were obtained using the non-linear Levenberg -Marquardt mean square minimization algorithm. In this way, results that can be compared to those obtained in other studies were obtained. This function allows to effectively eliminate motion-type artifacts, and even more so the consequences of recirculation of the tracer substance, which are a natural and inevitable consequence of the large volume of distribution (clearly visible in the in vivo recorded series of measurements in FIG.03). Both variants of the 2CM and 3 CM pharmacokinetic model in the parallel distribution system reproduce the overall course of the AIF curve in vivo in a similar manner. As for the absolute value of the field differences limited by the AIF curve, when the concentrations were expressed on the Hounsfield units scale (described in the figure as AUC), it is 96.44±172.46 for 2CM and 187.39±160.65 for 3CM (as Q2±MAD), with a slight dominant of lower values, because with a skewness of 0.36 and 0.35, respectively. When calculating the relative error as a deviation AAUC = (AUG — AUC0) / AUC0(where AUCo is the area under the in vivo curve, and AUC is the area under the AIF curve for the obtained approximation), we have on average deviations of 2.97% and 4.98% for 2CM and 3CM. In general, if we take into account the mapping of average values, the 2CM model reflects slightly better than the 3CM model. At the same time, the former shows a tendency to some overestimation of peak values. However, the differences are very subtle, and both models correctly reproduce clinical trial results. In particular, after taking into account the size and distribution of the characteristics of the research group. The only fragment of the course of the AIF curve, where deviations between the in vivo curve and its reconstruction are more pronounced, is a short fragment (up to 5 seconds) corresponding to the initial phase of contrast accumulation. This result is consistent with the expectation and previous description, since, as described above, parallel distribution models may not fully describe the initial concentration in the central compartment.

[0104] In a further preferred embodiment, a serial compartment model is used. This example uses a model built as follows: (1) in a system of serially connected compartments, (2) in each of them the concentration is shaped under the influence of a cascade of preceding compartments, but (3) only under the assumption of short time scales. In this type of time scales, there is no return transport from a given compartment to the preceding compartment. For longer time scales, which can thus be distinguished from short time scales, transport can be reversible. In this preferred embodiment, the AIF curve reconstruction model assumes that the transient concentration value in the peripheral compartment, i.e. the course of the AIF curve: (1) is solely a consequence of accumulation and transport in the cascade of preceding compartments, and (2) the short-scale effects of return transport are treated as negligibly small, and (3) the inability to discharge the tracer substance outside the organism is assumed. As part of the model of this example, the local concentration evolution is described by the following equation det

[0105] — = k^c^ - kiCi, (20) at wherein - as in the previous part of the description, kl-1, cl-1represent the concentration and rate constant in the preceding and / q , c, in the current compartments (for the clarity of the description, double indexing was omitted). Thus, in the first compartment, we have a model of the kinetics in the form of and in the following compartments: until the last one

[0106] If - again - determine the Laplace transforms of the above equations assuming - according to the actual physiological conditions - the initial concentration in the first compartment cx(0) #= 0, and each subsequent one in the cascade c, (0) = 0 for z> 1, we obtain: (s + k^cr= c^

[0107] (s + k2)c2= kxcx: (25) kn-ljCi-l=^n-2^n-2 + kn)cnkn-iCn-i

[0108] Concentrations in subsequent compartments may determine transforms - starting from the central

[0109] _ Q(Q)

[0110] C1(26) s + k-t ’ and each subsequent, including and key to this embodiment, compartment thereby providing a reconstruction of the AIF curve

[0111] Thus, the operational transform of the AIF curve - in the class of the adopted cascade model of short time scale and thus, also

[0112] In the conditions of short-scale kinetics, it may be justified to assume that the rate constants will be similar, i.e. iq « k2~ k3« ••• « kn= k, (30) consequently, the operational transform of the AIF

[0113] Accordingly, the inverse transform can have the form where the proportionality constant is c1(0) • kn-1 / (n — 1)!, and the approximation of the AIF function is

[0114] Equations (33) may be used for models of any order. For example, for n = 4 in the 4CMC model or n = 8 in the 8CMC model.

[0115] An AIF curve reconstruction was performed using this embodiment, i.e. for a cascade distribution model to compare with the results of the previously described clinical trial. FIG.04 compares the values of the Persona correlation coefficient and the relative error A AUG expressed as a percentage depending on the adopted order w=3...9 of the cascade distribution model. As the order of the model increases (i.e. the number of compartments connected in series), the order of approximation increases, and the correlation coefficient of the AIF curve with respect to in vivo results increases gradually. It amounted to [%] respectively: 97.7±1.09, 98.59±0.66, 98.9I±0.6I, 99.16±0.51, 99.28±0.47, 99.39±0.41, 99.46±0.39 (calculating as before, as Q2±MAD). The opposite trend is observed in relation to the relative error of the calculated area under the AIF curve - for n=3...9 we have [%]: 3. 17±2.71, 1.99±1.44, 1 ,9±1.49, 1.51±1.26, 1 ,36±1. 14, 1 ,34±1. 16, 1.26±1.08. The minimum order of approximation of the model was assumed in this casen > 4, because the case n=3 clearly stands out in terms of approximation agreement from the others, and additionally n = 3 is characterized by poor adaptability (approximately in 1...2 out of 10 analyzed cases, the model n = 3 showed poor numerical stability and very slow convergence).

[0116] FIG.05 shows the result of an AIF curve reconstruction for an exemplary result of an in vivo perfusion imaging (dotted points on the graph). The result was smoothed according to the routinely used approximation with the gamma distribution function (dashed line), in part: (A) using a 4-compartment cascade model (4CMC), i.e. in the minimum variant, and (B) an 8-compartment cascade model (8CMC). The dash-dot bold line shows the result for the case when the condition (30) is met and so when the kinetic constants are close to a certain constant, and the result for the generalized model is marked with the bold-solid line. The lower part of FIG.05 (C, D) shows the error (absolute) in the approximation of the area under the AIF curves (calculated in relation to the reconstruction carried out for in vivo data). The presented results indicate a very high effectiveness of the cascade model, starting from n=4. At the same time, excellent accuracy of mapping the course of the AIF in the range of maximum values is observed, significantly exceeding in this respect not only the previously discussed 2CM and 3CM for the parallel distribution system, but also the standard approximation by the gamma probability density function (curve drawn with a dashed line in FIG.04, part (A) and (B)). This is of vital importance to the quality of post-processing of results using the max-slope type method. Further increasing the order of the model does not cause significant changes except for a very short fragment of the curve in the initial phase of contrast accumulation, which may make it more useful in the case of post -processing using convolutional / deconvolutional type methods. The total absolute error calculated regarding the obtained AUC for the median is -252.57±169.98, and doubling the order of the model is -196. 19±137.73, which can be clearly seen in FIG.05 (C) and (D).

Claims

CLAIMS1. A method for calculating perfusion metrics, wherein the perfusion metrics are calculated using a concentration (c) of a tracer, wherein the method comprising: a) determining blood flow for a target circulatory area (VOI) and calculating an arterial input function (AIF) for the target circulatory area (VOI), wherein the target circulatory area (VOI) includes a peripheral compartment (z), b) determining changes in a tissue attenuation curve (TAC) for the target circulatory area (VOI) using the arterial input function (AIF), and c) calculating perfusion metrics based on specific tissue attenuation curves (TAC) for the target circulatory area (VOI) using a computed arterial input function (AIF), wherein the computation of the arterial input function (AIF) comprises the steps of selecting a pharmacokinetic model, wherein the selection of the pharmacokinetic model comprises selecting a class (CM, CMC) and order (zz) pharmacokinetic model, wherein the pharmacokinetic model class is selected from a parallel distribution model (CM) from a central compartment (z) to one or more peripheral compartments or a serial distribution model (CMC) from a central compartment (z) in series through one or more intermediate compartments (z) to one or more peripheral compartments, and a order (zz) of the pharmacokinetic model is the number of compartments (z) in the selected pharmacokinetic model, the selection of kinetic parameters and the initial concentration of the (Q (0)) tracer substance for the selected pharmacokinetic model, and the computation of arterial input function (AIF) at the inlet to the target circulatory area (VOI) using the solution of the selected pharmacokinetic model.

2. The method for calculating perfusion metrics according to claim 1, wherein the concentration of the tracer substance in compartment (z) is described by the equationwherein: VLis the value of the volume of distribution available for the tracer substance in the compartment (z), c(is the transient value of the concentration of the tracer substance in the compartment (z), and qtn, qout>cin>cout describes the size of the volumetric flow rate (q) with a given concentration (c) at the inflow (in) to and outflow (out) from the compartment (z).

3. The method for calculating perfusion metrics according to any of claims 1 -2, wherein the class of the kinetic model is a parallel distribution (CM) model, wherein the concentration of the tracer substance for the central compartment is in the formand for the peripheral compartments4. The method for calculating perfusion metrics according to claim 3, wherein the concentration of the tracer substance in compartment (z) is described by the equationwherein the change in concentration in the compartment (z) is dci / dt, the flow arriving from the preceding compartment is ( / Cj-i(tj-i), and from the subsequent one (ki+1 tci+1), and the flows backflowing from each of them+ kL i+1) c(. and c is the concentration, k is the reaction rate constants, t is the time, and the indices i-l, i, i+1 are the preceding, current, and subsequent compartments, respectively.

5. The method for calculating perfusion metrics according to claim 3 or 4, wherein the equation describing the concentration of the tracer substance includes the excretion of the tracer substance from the body.

6. The method for calculating perfusion metrics according to claim 5, wherein the equation includes excretion of the tracer substance from the body bywherein — (7Q0) cLis a fraction of the tracer substance excreted from the body.

7. The method for calculating perfusion metrics according to claim 6, wherein the tracer substance is excreted from the body exclusively from the central compartment.

8. The method of calculating perfusion metrics according to claim 5 - 7, wherein the excretion of the tracer substance from the body is described by the Michaelis-Menten formalism or is captured by using the Hill-Langmuir equation.

9. The method for calculating perfusion metrics of claim 8, wherein the Hill-Langmuir equation is in the formwhere vmaxdetermines the maximum elimination rate of the tracer substance, and z, KDare the empirical constants.

10. The method of calculating the perfusion metrics of claim 7, wherein the parallel distribution (CM) model is a two -compartment (2CM) or three -compartment (3CM) model, wherein the two- compartment (2CM) model comprises a central compartment and a single peripheral compartment, and wherein the tracer substance concentration at the central compartment is in the formand for the peripheral compartment it is in the formand where k21it is the rate constant between the peripheral compartment and the central compartment, k12is the rate constant between the central compartment and the peripheral compartment, k10is the rate constant of elimination of the tracer substance from the central compartment.

11. The method of calculating perfusion metrics according to any of claims 1 -2, wherein the class of the kinetic model is a serial distribution model (CMC), and the concentration in a given compartment (z) is shaped on the basis of a cascade of compartments preceding a given compartment, the return transport of the tracer substance is negligible and there is no excretion of the tracer substance from the body, and the determination of the kinetic parameters for any compartment (z) is in the form ofwherein i is in the range from 1 to n.

12. The method for calculating perfusion metrics according to claim 11, wherein n = 3, 4, 5, 6, 7, 8, or 9.

13. The method of calculating perfusion metrics according to claim 11 or 12, wherein the approximation of the arterial input function (AIF) is in the form14. The method of calculating perfusion metrics of any of claims 1-13, wherein the selection of kinetic parameters includes the use of experimentally determined tracer substance kinetics, use safety clinical trials of the tracer substance, kinetic parameter approximation, use of analytical models, and / or use of a regression model.

15. The method of calculating perfusion metrics according to claim 14, wherein the selection of kinetic parameters is performed using the regression model, wherein each in the set of parameters Y = {k12, ... } is defined as a function of Y = / (X, b) + e X predictors describing the general medical and hemodynamic features of the patient and parameters b with a certain random error e, wherein the set of X predictors is determined by general medical data, as well as empirical indicators associated with the general medical data.

16. The method for calculating perfusion metrics according to claim 15, wherein the general medical data consists of or includes the following elements: sex, age Y, weight W, height H, and the empirical indicators consist of or include the following elements: body mass index BMI = W / H2, body surface area, and basal metabolic rate.

17. The method of calculating perfusion metrics according to claim 15 or 16, wherein the set of X predictors is complemented by hemodynamic indicators and parameters.

18. The method for calculating perfusion metrics according to claim 17, wherein the hemodynamic indicators and parameters are selected from a group comprising: HR pulse (1 / min), IBI cardiac cycle duration (sec), characteristic blood pressure levels in the form of systolic pressure SYS (mm Hg), diastolic DIA (mm Hg), and / or PP= SYS-DIA pulse (mm Hg), and / or mean arterial pressure MAP=DIA+PP / 3, a continuously recorded peripheral or central arterial pressure wave.

19. The method of calculating perfusion metrics according to any of claims 15-18, wherein the empirical indicators are associated with cardiac output or result from the Liljestran -Zander model.

20. The method of calculating the perfusion metrics of claim 19, wherein the empirical indicators associated with the cardiac output are selected from the group comprising: SV stroke volume, CO cardiac output, flow parameters, coronary flow, coronary unit flow, cerebral flow, cerebral unit flow, cardiac index, and cerebral index.

21. The method of calculating the perfusion metrics of any one of claims 1 - 20, wherein the concentration of the substance is expressed in conventional units, radiodensity, or relative X-ray attenuation capacity.

22. The method of calculating perfusion metrics according to claim 21, wherein the concentration of the substance is expressed on a Hounsfield Units (HU) scale.

23. The method of calculating the perfusion metrics of any one of claims 1 - 22, wherein the computation of the arterial input function (AIF) includes, as a final step, approximation by an analytical model or a gamma probability density distribution function.

24. The method for calculating perfusion metrics according to any one of claims 1 - 23, wherein the concentration (c) of the tracer substance includes the influence of patient-specific hemodynamic features and / or factors selected from the group consisting of or comprising: (1) renal impairment, (2) hydration, and (3) individual factors including the following elements: age, sex, and associated medical conditions.

25. The method for calculating perfusion metrics according to claim 24, wherein the patient-specific hemodynamic characteristics are determined by at least one element selected from the list comprising: (1) time parameters of cardiac contraction as cycle length (IBI, sec) or frequency (HR, 1 / min), (2) course of changes in cycle pressure values, including systolic (SYS, mm Hg) and diastolic (DIA, mm Hg), (3) cardiac output parameters as stroke volume (SV, ml), cardiac output (CO, 1 / min), and (4) coronary artery flow parameters (CBF, ml / s).

26. The method of calculating the perfusion metrics of any of claims 1 - 25, wherein the method further comprises a circulatory system model described by a set of interconnected functional blocks of a model with lumped-parameters, wherein the lumped-parameters are described by a system of equations balancing the change in volume flow rate and pressure between the conventional input and output aswherein the in and out indices denote the parameters of the flow state at the conventional inlet and outlet, and the symbols R, L, C determine the total resistance, inertance and compliance, respectively.

27. The method of calculating the perfusion metrics of any one of claims 1 - 26, wherein the model further comprises a model of three pulmonary circulation compartments and five systemic circulation compartments, or the model comprises a systemic circulation comprising two compartments and a pulmonary circulation comprising one compartment.

28. The method of calculating perfusion metrics according to any one of claims 1 - 26, wherein the model further comprises an atrioventricular cardiac model, separately for the pulmonary circulation and separately for the systemic circulation.

29. The method of calculating perfusion metrics according to claim 28, wherein the blood volume flow flowing through any heart cavity isE dV dpvpydE dt dt E dt’wherein E is a variable elastance model expressed as E(t) = dpv / dV, and the transient pressure within the cardial cavity is pv= E(t) ■ (Vv— y0).

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