Method and system for determining respiratory tract and pulmonary deposition of inhaled substances

Abstract

A computer-implemented method for determining airway deposition of an inhaled substance in a zone of a subject's lungs is provided, the method comprising: receiving a patient dataset for the subject including a parameter set and corresponding values ​​of two or more parameters, wherein the parameters in the parameter set form at least four dimensionless numbers in a dimensionless correlation specific to the zone; and determining the airway deposition of the inhaled substance in the zone of the subject's lungs from the dimensionless correlation and the corresponding values ​​of the parameters in the parameter set.

Description

[Technical Field]

[0001] The present invention relates to the field of determining respiratory tract deposition of inhaled substances. [Background technology]

[0002] Inhaled substances are used in clinical practice to treat diseases such as asthma or chronic obstructive pulmonary disease. The effectiveness of the treatment is related to airway deposition, i.e., the zone(s) of deposition and the amount of deposition within each zone.

[0003] In vivo scintigraphy is the gold standard for assessing airway deposition (1), but it requires exposing the subject to radiolabeled compounds and repeating with different formulations.

[0004] Computational fluid dynamics (CFD) can be used to predict deposition of inhaled substances, but it can be computationally expensive because it simulates airflow within a 3D model of the lung (e.g., Non-Patent Document 2). [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Carvalho et al, Int J Pharm, 2011; 406: 1-10; Conway J. Adv Drug Deliv Rev 2012; 64: 357-368 [Non-patent document 2] Van Holsbeke et al, Ther Adv Respir Dis 2018, Vol. 12: 1-15 Summary of the Invention [Problem to be solved by the invention]

[0006] There is a need for new methods for determining airway deposition that are computationally inexpensive, have comparable accuracy to existing methods, are patient-specific, and take into account different formulations and inhalation flows. [Means for solving the problem]

[0007] 1. A computer-implemented method for determining airway deposition of an inhaled substance within a lung zone of a subject, comprising: - receiving a patient data set for the subject including a parameter set and corresponding values ​​for two or more parameters, the parameters in the parameter set forming at least four dimensionless numbers in a zone-specific dimensionless correlation; - determining airway deposition of the inhaled substance in the zone of the subject's lung from the dimensionless correlation and the corresponding values ​​of the parameters in the parameter set; A method is provided herein, comprising:

[0008] According to a preferred embodiment, - The first component of the dimensionless correlation is a dimensionless number (π 0,zone ) and The second component of the dimensionless correlation is a dimensionless group containing at least four dimensionless numbers of the sought zone.

[0009] According to a preferred embodiment, the dimensionless correlation has the form of Equation 1: π 0,zone =c0(π1 c1 ×π2 c2 ×π3 c3 ×...×π m cm ) [Formula 1] In Equation 1, - π 0,zone is a dimensionless number (first component) that is deposition within the zone, - c0(π1 c1 ×π2 c2 ×π3 c3 ×...×π m cm) is the dimensionless group (second component), - π 1~m Each π in is a dimensionless number of zones, - Each c in c1~cm is a dimensionless exponent, m is at least 4, 4 to 20, preferably 4 to 9, more preferably 4, 5 or 6; - c0 is the correlation multiplier, - Zone π1~π m Each of π, each of c1 to cm, and c0 are determined from multiple patient record data sets and regression analysis.

[0010] According to a preferred embodiment, the zones π1 to π m Each of π, c in c1 to cm, and c0 are - filling the dimensionless group of Equation 1 with at least 6, preferably between 6 and 20, dimensionless numbers selected from a pool of dimensionless numbers; - conducting multiple rounds of regression analysis, each round comprising: - adjusting the values ​​of c0, c1~cm until converging on a solution for deposition of multiple patient record data sets; - Substituting a portion (e.g., 2 to 5) of the dimensionless numbers in the dimensionless group with different dimensionless numbers selected from a pool of dimensionless numbers; and - repeating the adjustment and substitution until the improvement in convergence (intraclass correlation) is minimal; is calculated by

[0011] According to a preferred embodiment, the pool of dimensionless numbers is: Includes TIFF2025538705000001.tif62170.

[0012] According to a preferred embodiment, the dimensionless number in Equation 1 is: Selected from TIFF2025538705000002.tif21170.

[0013] According to a preferred embodiment, the parameters and dimensionless numbers in the parameter set include those of Table AA1, selected according to the zone of the subject's lung in which airway deposition is desired.

[0014] [Table 1]

[0015] According to a preferred embodiment, - The zone is an IT zone, - Equation 1 is TIFF2025538705000004.tif10170, - c1>c2>c3>c4>cm, In Equation 1, the terms with m>4 are optional.

[0016] According to a preferred embodiment, - The zone is a PR zone, - Equation 1 is TIFF2025538705000005.tif12170, - c1>c2>c3>c4>cm, In Equation 1, the terms with m>4 are optional.

[0017] According to a preferred embodiment, - The zone is a DI zone, - Equation 1 is TIFF2025538705000006.tif11170, - c1>c2>c3>c4>cm, In Equation 1, the terms with m>4 are optional.

[0018] According to a preferred embodiment, - The zone is an RLL zone, - Equation 1 is TIFF2025538705000007.tif7170, - c1>c2>c3>c4>cm, In Equation 1, the terms with m>4 are optional.

[0019] According to a preferred embodiment, - The zone is an LLL zone, - Equation 1 is TIFF2025538705000008.tif11170, - c1>c2>c3>c4>cm, In Equation 1, the term m>4 is optional, or Or, - the zone is a RUL zone, - Equation 1 is TIFF2025538705000009.tif10170, - c1>c2>c3>c4>cm, In Equation 1, the term m>4 is optional, or Or, - The zone is a LUL zone, - Equation 1 is TIFF2025538705000010.tif12170, - c1>c2>c3>c4>cm, In Equation 1, the term m>4 is optional, or Or, - the zone is an RML zone, - Equation 1 is TIFF2025538705000011.tif12170, - c1>c2>c3>c4>cm, In Equation 1, the term m>4 is optional, or Or, - The zone is an ET zone, - Equation 1 is TIFF2025538705000012.tif11170, - c1>c2>c3>c4>cm, In Equation 1, the term m>4 is optional, or Or, - The zone is a TL zone, - Equation 1 is TIFF2025538705000013.tif10170, - c1>c2>c3>c4>cm, In Equation 1, the terms with m>4 are optional.

[0020] Also provided is a method for determining airway deposition of an inhaled substance in the lungs of a subject, comprising: - receiving a patient data set for the subject, the patient data set including parameter sets and corresponding values ​​for two or more parameters; - determining airway deposition of the inhaled substance in the lungs of the subject from the patient dataset; Including, Also provided herein are methods wherein the parameter set includes at least two parameters from Table B.

[0021] The parameter set is - at least one parameter from the Image subgroup of the library of parameters of Table B; - at least one parameter from the inhaler subgroup library of parameters of Table B; - at least one parameter from the Flow Subgroup Library of Parameters in Table B; - at least one parameter from the physical properties and constants library of parameters of Table B; may include:

[0022] The parameter set is - at least one of the images IM1, IM2, IM3, IM4 and IM6 from the image subgroup of Table B, - at least one of the inhalers IN1, IN2 and IN5 from the inhaler subgroup of Table B, - at least one of F1, F2 and F4 from the flow subgroup of Table B, - at least one of the physical properties and constants PC1, PC2 and PC3 of Table B; may include:

[0023] What we are asking for is, - applying a set of parameters to the dimensionless correlation; - determining airway deposition of the inhaled substance in the lungs of the subject from the patient data set applied to a dimensionless correlation; Preferably,

[0024] Preferably, - the first component of the dimensionless correlation (e.g., y-axis) is a dimensionless number (π0) representing airway deposition, - the second component of a dimensionless correlation (e.g., the x-axis) is a dimensionless group containing one or more dimensionless numbers, - one or more dimensionless numbers differ from the dimensionless number of the first component, - One or more dimensionless numbers are determined from the parameters in the parameter set.

[0025] At least some, and preferably all, of the dimensionless numbers in the second component of the dimensionless correlation can be determined using ratios and / or using Buckingham's pi theorem.

[0026] The dimensionless exponent(s) of the dimensionless correlation can be determined using regression analysis and multiple patient record data sets, where the patient record data sets include recorded values ​​of deposition, parameters of the parameter set, and recorded values ​​of each parameter in the parameter set.

[0027] Preferably, the dimensionless correlation is determined according to a particular airway zone; the zone is the intrathoracic (IT) zone, the parameter set comprises the PPG6 parameters in Table A, and the dimensionless number comprises the PPG6 dimensionless number in Table A; or the zone is the extrathoracic (ET) zone, the set of parameters includes the PPG7 parameters in Table A, and the dimensionless number includes the PPG7 dimensionless number in Table A, or the zone is a distal (DI) zone, the set of parameters includes the parameters of PPG8 in Table A, and the dimensionless number includes the dimensionless number of PPG8 in Table A; or - the zone is a peripheral (PR) zone, the parameter set includes the PPG9 parameters in Table A, and the dimensionless number includes the PPG9 dimensionless number in Table A, or The zone is a total lobe (TL) zone, the parameter set includes the parameters of PPG10 in Table A, and the dimensionless number includes the dimensionless number of PPG10 in Table A.

[0028] Preferably, the dimensionless correlation is determined according to a particular airway zone; the zone is the right upper lobe (RUL) zone, the parameter set includes the parameters of PPG11 in Table A, and the dimensionless number includes the dimensionless number of PPG11 in Table A, or the zone is the right middle lobe (RML) zone, the set of parameters includes the PPG12 parameters in Table A, and the dimensionless number includes the PPG12 dimensionless number in Table A; or the zone is the right lower lobe (RLL) zone, the set of parameters includes the parameters of PPG13 in Table A, and the dimensionless number includes the dimensionless number of PPG13 in Table A; or the zone is the left upper lobe (LUL) zone, the set of parameters includes the PPG14 parameters in Table A, and the dimensionless number includes the PPG14 dimensionless number in Table A, or the zone is the left lower lobe (LLL) zone, the parameter set includes the PPG15 parameters in Table A, and the dimensionless number includes the PPG15 dimensionless number in Table A.

[0029] Further provided herein is a computing device or system configured to perform the methods described herein.

[0030] Further provided herein is a computer program or computer program product having instructions that, when executed by a computing device or computing system, cause the computing device or computing system to perform the methods described herein. [Brief explanation of the drawings]

[0031] [Figure 1] 1 is a graph showing multiple patient record data sets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record data sets (dotted line), and test data for the intrathoracic (IT) zone (triangles). [Figure 2] 1 is a graph showing multiple patient record datasets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record datasets (dotted line), and distal (DI) zone test data (triangles). [Figure 3] 1 is a graph showing multiple patient record datasets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record datasets (dotted line), and peripheral (PR) zone test data (triangles). [Figure 4] 1 is a graph showing multiple patient record datasets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record datasets (dotted line), and test data for the whole lobe (TL) zone (triangles). [Figure 5] 1 is a graph showing multiple patient record datasets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record datasets (dotted line), and test data (triangles) from the right upper lung (RUL) zone. [Figure 6]1 is a graph showing multiple patient record datasets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record datasets (dotted line), and test data (triangles) for the right middle lung (RML) zone. [Figure 7] 1 is a graph showing multiple patient record datasets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record datasets (dotted line), and test data (triangles) for the right left lung (RLL) zones. [Figure 8] 1 is a graph showing multiple patient record datasets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record datasets (dotted line), and test data (triangles) for the left upper lung (LUL) zone. [Figure 9] 1 is a graph showing multiple patient record datasets (training data) (black dots), a best fit line (dimensionless correlation) of the multiple patient record datasets (dotted line), and test data (triangles) for the left lower lung (LLL) zone. [Figure 10] 1 is a graph showing the computational speed of the dimensionless correlation of the present method (known as Rapid Deposition Analysis (RDA)) compared to the state-of-the-art method, Computational Fluid Dynamics (CFD). Note the logarithmic scale. [Figure 11] Figure 1 shows the mean and standard deviation of deposition by zone obtained by NDA and CFD for 18 test points (18 patients). The extremes of the box represent quartiles (the lower quartile is where 25% of the data are below that value, and the upper quartile is where 25% of the data are above that value). The horizontal line indicates the median, and the triangle indicates the mean. The whiskers extend from the box to the most extreme data points that are less than or equal to 1.5 times the interquartile range. All data points outside this range are visualized as individual points. The mean and standard deviation are also shown on the x-axis of each plot. [Figure 12]1 is a graph of the cross-correlation of deposition in RML as a function of π for various quantities of Equation 1a in Example 1. [Figure 13] 1 is a graph showing the average deposition results calculated using the present method (RDA) compared to using CFD when the quantity of π in Equation 1 was 4. [Figure 14] 1 is a graph showing the average deposition results calculated using the present method (RDA) compared to using CFD when the quantity of π in Equation 1 was 20. DETAILED DESCRIPTION OF THE INVENTION

[0032] Figures 1-14 are non-inhaler specific (all inhaler types combined).

[0033] Before describing the present systems and methods of the present invention, it is to be understood that the invention is not limited to the particular systems and methods or combinations being described, as such systems and methods and combinations may, of course, vary. It is also to be understood that the terminology used herein is not intended to be limiting, as the scope of the present invention will be limited only by the appended claims.

[0034] As used herein, the singular forms "a," "an," and "the" include both singular and plural referents unless the context clearly dictates otherwise.

[0035] As used herein, the terms "comprising," "comprises," and "comprised of" are synonymous with "including," "includes," or "containing," and "contains," and are inclusive or open-ended and do not exclude additional, unrecited members, elements, or method steps. As used herein, the terms "comprising," "comprises," and "comprised of" are understood to include the terms "consisting of," "consists," and "consists of."

[0036] The recitation of numerical ranges by endpoints includes all recited values ​​and fractions subsumed within the respective ranges, as well as the recited endpoints.

[0037] As used herein, the term "about" or "approximately" when referring to a measurable value such as a parameter, amount, duration, etc., is meant to encompass variations of no more than + / - 10%, preferably no more than + / - 5%, more preferably no more than + / - 1%, and even more preferably no more than + / - 0.1% of the specified value, insofar as such variations are appropriate for the practice of the disclosed invention. It should also be understood that values ​​to which the modifier "about" or "approximately" pertain are themselves preferably specifically disclosed.

[0038] The terms "one or more" or "at least one" in relation to one or more members or at least one member of a group of members is clear in itself, but by way of further example, the term encompasses, inter alia, any one of the members, or any two or more of the members, such as any three or more, four or more, five or more, six or more, or seven or more of the members, up to and including all of the members.

[0039] All documents cited herein are incorporated by reference in their entirety, and in particular the teachings of all documents specifically mentioned herein are incorporated by reference.

[0040] Unless otherwise defined, all terms used in disclosing the present invention, including technical and scientific terms, have the meanings commonly understood by one of ordinary skill in the art to which this invention belongs. To better understand the teachings of the present invention, term definitions are included by way of further guidance.

[0041] In the following sections, various aspects of the invention are defined in more detail. Each aspect so defined may be combined with any one or more of the other aspects, unless expressly indicated to be incompatible. In particular, any feature indicated as being preferred or advantageous may be combined with any one or more of the other features indicated as being preferred or advantageous.

[0042] Throughout this specification, the reference to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described with respect to this embodiment is included in at least one embodiment of the present invention. Thus, the phrases "in one embodiment" or "in an embodiment" appearing in various places throughout this specification are not necessarily all referring to the same embodiment, but may refer to the same embodiment. Furthermore, particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments, as would be apparent to one of ordinary skill in the art from this disclosure. Furthermore, although some embodiments described herein include some features and not others included in other embodiments, it is understood by one of ordinary skill in the art that combinations of features from different embodiments are within the scope of the present invention and are intended to form different embodiments. For example, in the appended claims, any of the embodiments described in the claims may be used in any combination.

[0043] In this specification of the present invention, reference is made to the accompanying drawings, which form a part of this specification and which show, by way of example only, specific embodiments in which the present invention may be practiced. Parenthetical or bold reference numbers associated with respective elements are merely illustrative of those elements and are not intended to limit the scope of those elements. Unless otherwise specified, all figures and drawings herein are not to scale and are chosen to illustrate various embodiments of the present invention. In particular, dimensions of the various components are shown for illustrative purposes only, and relationships between the dimensions of the various components should not be inferred from the drawings unless so specified.

[0044] It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present invention. Therefore, the following detailed description is not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims.

[0045] 1. A method for determining airway deposition of an inhaled substance in the lungs of a subject, comprising: - receiving a patient data set for the subject, the patient data set including parameter sets and corresponding values ​​for two or more parameters; - determining airway deposition of the inhaled substance in the lungs of the subject from the patient dataset; Including, A method is provided herein wherein the parameter set includes at least two parameters from Table B.

[0046] The inventors have discovered that subject parameters can be mapped to different dimensionless numbers of dimensionless correlations specific to the subject's zones, and that these dimensionless correlations are predictive of deposition within the zones. Different dimensionless correlations can be formed depending on the zone. It has not previously been understood that dimensionless numbers are predictive of deposition within different locations, i.e., different zones, of the lung. Using correlations instead of computational fluid dynamics (CFD) to predict deposition significantly increases the speed at which deposition can be calculated.

[0047] Airway deposition can be determined for one airway zone among multiple zones (also referred to herein as a "zone"). In other words, the airway deposition determination is specific to one zone. Multiple airway deposition determinations can be performed for different zones.

[0048] The multiple zones include: total lobe (TL), intrathoracic (IT), extrathoracic (ET), distal (DI), peripheral (PR), right upper lobe (RUL), right middle lobe (RML), right lower lobe (RLL), left upper lobe (LUL), and left lower lobe (LLL). These zones and the airways they contain are known in the art.

[0049] As understood in the art, a lobe is a segment of the lung. The right lung has three major lobes (RUL, RML, RLL), while the left lung, which is slightly smaller due to the asymmetrical positioning of the heart, has two lobes (LUL and LLL).

[0050] As understood in the art, total lobar (TL) means (RUL+RML+RLL+LUL+LLL), intrathoracic (IT) refers to the airways below (inferior) the upper part of the trachea (including central, distal and peripheral), extrathoracic (ET) refers to the airways above (superior) the upper part of the trachea, and central (CL) refers to the airways extending from the upper part of the trachea down to the major bronchi, as can be seen on a CT scan.

[0051] Distal (DI) refers to airways that branch off from the main bronchi and are visible on CT scans. These airways are typically airways with diameters greater than 1-2 mm. These airways extend as far as the 7th to 10th branching order. Peripheral (PR) refers to airways that cannot be distinguished on CT scans. In terms of particle deposition, particles are deposited in the peripheral (PR) airways once they exit the distal (DI) airway model. As used herein, the upper airway refers to the combined oral cavity, pharynx, and larynx.

[0052] As understood in the art, an airway is a conduit for air between a subject's mouth / nose and lungs that has a lumen. Airways that lie within a zone can have a surface area, which refers to the total surface (inner wall) of the airway lumen within the zone. Airways that lie within a zone can have a volume, which refers to the total volume of the airway lumen within the zone.

[0053] According to one embodiment, airway deposition is determined for one zone in a preference ranking (ranking from most preferred to least preferred) of IT(PPG6)>PR(PPG9)>DI(PPG8). According to one embodiment, airway deposition is determined for one airway zone or for at least the IT(PPG6) airway zone.

[0054] Respiratory tract deposition (also known herein as "deposition," or "De," or "π0") refers to the amount of inhaled substance that is deposited within a zone of a subject. It is expressed as a fraction, ratio, or percentage of the delivered dose, i.e., the dose (by mass) deposited within the zone relative to the total dose (by mass) inhaled by the subject. It is a dimensionless number (i.e., it has no units).

[0055] Inhalants are liquid aerosols or powder aerosols. Inhalants are typically administered using an inhaler. Inhalants typically contain an active agent. Common types of inhalers include dry powder inhalers (DPIs), nebulizers, and metered dose inhalers (MDIs). In dry powder inhalers (DPIs), the inhalant is a dry powder, and inhalation by the patient is the primary force driving the dry powder movement. In nebulizers, the inhalant is a liquid driven by inhalation, and inhalation by the patient is the primary force driving the liquid movement. In metered dose inhalers (MDIs), the inhalant is a liquid, and part of the force driving the liquid movement is a pressurized propellant. Examples of inhalants include insulin, salbutamol, Promixin, and tobramycin. Examples of commercially available inhalers containing one or more active agents include Ellipta DPI (fluticasone furoate + vilanterol), Seretide MDI (fluticasone furoate + salmeterol), Symbicort Turbohaler DPI (budesonide + formoterol fumarate), and Quinsair Zirela nebulizer.

[0056] The parameter set includes parameters that are critical to airway deposition, especially within the zone.

[0057] The parameter set includes at least two parameters from the library of parameters in Table B. The parameter set preferably includes at least 9, preferably 9 to 17, of the parameters from Table B. Each parameter in Table B has a value (tested or recorded) related to a patient inhaling a substance. Some parameters relate to the physiology of the patient (e.g., the Image subgroup in Table B). Some parameters relate to the inhaler and aerosol used by the patient (e.g., the Inhaler subgroup in Table B). Some parameters relate to airflow or substance flow during inhalation by the patient (e.g., the Flow subgroup in Table B). Some parameters are physical properties and constants (e.g., the Physical Properties and Constants in Table B). It is understood that a parameter set can include one or more parameters not listed in Table A or Table B in addition to some of the parameters from the library of parameters in Table B, or in addition to the parameters of a PPG in Table A.

[0058] Preferably, at least two parameters from the library of parameters in Table B form at least one dimensionless number. Preferably, the parameters from the library of parameters in Table B form at least four dimensionless numbers, between four and twenty dimensionless numbers, preferably between four and nine dimensionless numbers, and more preferably four, five, or six dimensionless numbers. A dimensionless number (DN / π) is a mathematical term that has no dimensions, i.e., no units. One way to create a dimensionless number is to divide two parameters that have the same primary dimension. For example, the ratio of IM1 to IM2 in Table B forms the dimensionless number DN6 in Table C. For example, the ratio of IM4 to IM6 in Table B forms the dimensionless number DN3 in Table C. Another way to create a dimensionless number is to use Buckingham's pi theorem, as described elsewhere herein.

[0059] The parameter set is - at least one parameter from the Image subgroup of the library of parameters of Table B; - at least one parameter from the inhaler subgroup library of parameters of Table B; - at least one parameter from the Flow Subgroup Library of Parameters in Table B; - at least one parameter from the physical properties and constants library of parameters of Table B; may include:

[0060] The parameters of the Imaging subgroup (IM1-IM11) are defined in Table B. The parameters of the Imaging subgroup are patient specific. The parameters of the Inhaler subgroup (IN1-IN6) are defined in Table B. The parameters of the Flow subgroup (F1-F10) are defined in Table B. The parameters of the Physical Properties and Constants subgroup (PC1-PC12) are defined in Table B.

[0061] The parameter set is - at least one of the images IM1, IM2, IM3, IM4 and IM6 from the image subgroup; - at least one of the inhalers IN1, IN2 and IN5 from the inhaler subgroup, - at least one of F1, F2 and F4 from the flow subgroup; - at least one of the physical properties and constants PC1, PC2 and PC3; may include:

[0062] The parameter set is - at least IM1, IM2, IM3, IM4 and IM6 from the image subgroup, - at least IN1, IN2 and IN5 from the inhaler subgroup, - at least F1, F2 and F4 from the flow subgroup, - physical properties and constants of at least PC1, PC2 and PC3; may include:

[0063] A parameter set may include at least two parameters from one of primary parameter groups PPG1 through PPG15 of Table A.

[0064] The parameter set preferably includes at least two parameters, preferably 10 to 17 parameters, from one of the primary parameter groups PPG2 to PPG5 in Table A. The parameter set preferably forms at least four dimensionless numbers, 4 to 20 dimensionless numbers, preferably 4 to 9 dimensionless numbers, more preferably 4, 5 or 6 dimensionless numbers in the corresponding primary parameter group in Table A. For example, if the parameter set is selected from PPG3 in Table A and parameter A trachea , A min,ua and A branch , the parameters are two of the dimensionless numbers of PPG3 in Table A, namely A min,ua / A trachea , and A branch / A trachea can be formed.

[0065] The parameter set preferably includes at least two parameters, preferably all of the parameters, from one of the primary parameter groups PPG6 to PPG15 of Table A depending on the zone.

[0066] The parameter set preferably includes at least one parameter from primary parameter groups PPG6 to PPG15 in Table A1 depending on the zone. The parameter set preferably forms at least four dimensions in the corresponding primary parameter group in Table A1. The zone can be one or more of IT, PR, DI, RLL, LLL, RUL, LUL, RML, ET, or TL.

[0067] According to one aspect, a method is provided for airway deposition of an inhaled substance in multiple zones of a subject's lungs, using a method described herein applied to each zone of the multiple zones. The zones of the multiple zones can be two or more of IT, PR, DI, RLL, LLL, RUL, LUL, RML, ET, or TL. Preferably, the zones of the multiple zones include IT and, optionally, one or more of PR, DI, RLL, LLL, RUL, LUL, RML, ET, and TL. Preferably, the zones of the multiple zones include IT and PR and, optionally, one or more of DI, RLL, LLL, RUL, LUL, RML, ET, and TL. Even more preferably, the zones of the multiple zones include IT, PR, and DI and, optionally, one or more of RLL, LLL, RUL, LUL, RML, ET, and TL.

[0068] The parameter set for each zone preferably includes at least the parameters of the primary parameter groups PPG6 to PPG15 in Table A1 depending on the zone, and preferably forms at least four dimensions in the corresponding primary parameter group in Table A1.

[0069] It is understood that the parameter sets can be determined using dimensional analysis (also called non-dimensional analysis (NDA)). Typically, one parameter set is determined per zone. The parameter sets can be refined and therefore can change over time as additional patient records are used to determine the parameter sets (see below). Alternatively, once a parameter set is determined for a zone, the parameter set can remain unchanged.

[0070] The various primary parameter groups are shown in Table A. Each row of Table A contains one primary parameter group.

[0071] Primary parameter group 1 (PPG1) in Table A includes parameters from the parameter library of Table C, each of which has been found to be important for determining deposition within one or more zones.

[0072] Primary parameter group 2 (PPG2) in Table A includes parameters known to be important for determining deposition in one or more zones. These parameters include those most frequently found to be determinants of airway deposition in various zones and parameters that are less frequently found but are found in dimensionless numbers with higher weightings (indexes). Table A also lists the dimensionless numbers formed from the parameters in PPG2.

[0073] Primary parameter group 3 (PPG3) in Table A includes parameters experimentally known to be most critical to airway deposition. These parameters include those most frequently found as determinants of airway deposition in various zones, as well as parameters less frequently found in dimensionless numbers with higher weightings (indexes). PPG3 corresponds to the Examples herein. Table A also shows the dimensionless numbers formed from the parameters of PPG3.

[0074] Primary parameter group 4 (PPG4) in Table A contains parameters that have been experimentally found to be most critical for respiratory tract deposition. These parameters are the most frequently found to be determinants of respiratory tract deposition in nearly all of the various zones. Table A also shows dimensionless numbers formed from the PPG4 parameters.

[0075] Primary parameter group 5 (PPG5) in Table A contains parameters that have been experimentally found to be most critical for respiratory tract deposition. These parameters are the most frequently found determinants of respiratory tract deposition and are present in the most of the various zones. Table A also shows dimensionless numbers formed from the PPG5 parameters.

[0076] Primary Parameter Group 6 (PPG6) in Table A or Table A1 includes parameters that have been experimentally found to be most critical for airway deposition in the intrathoracic (IT) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG6.

[0077] Primary parameter group 7 (PPG7) in Table A or Table A1 contains parameters that have been experimentally found to be most critical for airway deposition in the extrathoracic (ET) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG7.

[0078] Primary Parameter Group 8 (PPG8) in Table A or Table A1 contains parameters that have been experimentally found to be most critical to airway deposition in the distal (DI) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG8.

[0079] Primary Parameter Group 9 (PPG9) in Table A or Table A1 contains parameters that have been experimentally found to be most critical for airway deposition in the peripheral (PR) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG9.

[0080] Primary Parameter Group 10 (PPG10) in Table A or Table A1 includes parameters that have been experimentally found to be most critical for airway deposition in the total lobe (TL) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG10.

[0081] Primary parameter group 11 (PPG11) in Table A or Table A1 includes parameters that have been experimentally found to be most critical for airway deposition in the right upper lobe (RUL) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG11.

[0082] Primary parameter group 12 (PPG12) in Table A or Table A1 includes parameters experimentally found to be most critical for airway deposition in the right middle lobe (RML) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG12.

[0083] Primary parameter group 13 (PPG13) in Table A or Table A1 contains parameters that have been experimentally found to be most critical for airway deposition in the right lower lobe (RLL) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG13.

[0084] Primary parameter group 14 (PPG14) in Table A or Table A1 includes parameters that have been experimentally found to be most critical for airway deposition in the left upper lobe (LUL) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG14.

[0085] Primary parameter group 15 (PPG15) in Table A or Table A1 includes parameters that have been experimentally found to be most critical for airway deposition in the left lower lobe (LLL) zone. Table A or Table A1 also shows dimensionless numbers formed from the parameters of PPG15.

[0086] The subject's patient data set is - parameters of the parameter set, - the value(s) of each parameter in the parameter set, Includes.

[0087] The airway deposition of the inhaled substance in the lungs of the subject is determined from the patient data set applied to a dimensionless correlation. The dimensionless correlation is a mathematical correlation between the airway deposition and a parameter in the parameter set. The dimensionless correlation is preferably zone-specific. For example, RUL is the dimensionless correlation intrathoracicmay be different from

[0088] In particular, the airway deposition of an inhaled substance in the lungs of a subject is determined from a dimensionless correlation: - the first component of the correlation (e.g., y-axis) is a dimensionless number (π0) representing airway deposition, The second component of the correlation (e.g., the x-axis) is a dimensionless group containing one or more dimensionless numbers that are different from the dimensionless numbers in the first component. The one or more dimensionless numbers are formed from parameters in the parameter set.

[0089] The dimensionless correlation can be expressed as: π0=c0(π1 c1 ×π2 c2 ×π3 c3 ×...×π m cm ) [Formula 1] In this formula, - Deposition within the zone is expressed as a dimensionless number (π0) (first component), - c0(π1 c1 ×π2 c2 ×π3 c3 ×...×π m cm ) is the dimensionless group (second component), - π 1~m Each π in is a dimensionless number, - π1 c1 ~π m cm Each π c is a dimensionless term, Each c in c1 to ccm is a dimensionless exponent (herein referred to as "exponent"), c0 is the correlation multiplier (herein "multiplier"), m has a value of at least 4, a value of 4 to 20, preferably a value of 4 to 9, more preferably a value of 4, 5 or 6. The π0 of the zone is π 0,zone It can be expressed as:

[0090] Thus, a dimensionless correlation comprises a dimensionless group of one or more dimensionless numbers, each formed from one or more of the parameters in the set of parameters.

[0091] A dimensionless group may include one or more dimensionless numbers from the list in Table C. A dimensionless group may include at least one dimensionless number from one of the primary parameter groups (PPG1 to PPG15) (Table A). A dimensionless group preferably includes at least two dimensionless numbers, preferably six to nine dimensionless numbers, from one of the primary parameter groups (PPG3 to PPG5) (Table A). A dimensionless group preferably includes at least two dimensionless numbers, preferably all of the dimensionless numbers, from one of the primary parameter groups (PPG6 to PPG15) (Table A), depending on the zone.

[0092] It is understood that the dimensionless numbers within a dimensionless group starting from any set of parameters can be found using Buckingham's Pi Theorem, known in the art from, for example, Buckingham, Nature 96.2406 (1915): 396-397, or Gibbings, John Cecil. Dimensional analysis. Springer Science & Business Media, 2011.

[0093] Each of c in c1 to cm and the multiplier c0 can be determined using regression analysis and multiple patient record data sets.

[0094] The process of determining dimensionless correlations, which includes one or more steps of determining the first order dimensions of the parameters, forming dimensionless numbers, forming dimensionless groups, and deriving multipliers and exponents of the dimensionless correlations, is known as dimensional analysis or dimensionless analysis (NDA). By way of background, a dimensionless number (DN / π) is a mathematical term that has no dimensions, i.e., no units. Preferably, the number of dimensionless numbers in a dimensionless group is at least one or two. The number of dimensionless groups in the second component is one. Each dimensionless number (DN / π) in a dimensionless group contains one or more parameters, and a non-exhaustive list of parameters is provided in the library of Table B. One or more dimensionless numbers (π1, π2, π3, ..., π) that form a dimensionless group are m ) is determined by Buckingham's pi theorem. In Tables A and C, for example, the dimensionless numbers are determined using Buckingham's pi theorem. If other parameters not listed in Table B are determined, Buckingham's pi theorem can be used to determine the dimensionless numbers from this theorem, optionally in combination with one or more parameters listed in Table B. The values ​​of c0, c1~cm are determined by solving nonlinear least-squares equations.

[0095] The inventors have found that a second component of the dimensionless correlation, expressed as one or more dimensionless numbers (DN / π), allows the problem of zonal airway deposition to be reduced to a two-component correlation.

[0096] The dimensionless numbers for each primary parameter group are given in Table A. If a new primary parameter group is formed that contains a parameter not listed in the parameter library in Table B, the corresponding dimensionless number can be found by taking ratios or by using Buckingham's pi theorem.

[0097] A general application of Buckingham's pi theorem is as follows:

[0098] A primary parameter group is formed, which may include, for example, at least some or all of the parameters from the parameter library of Table B, and optionally one or more additional parameters not shown in Table B. Alternatively, the primary parameter group may include at least some, and preferably all, of the parameters of one of the primary parameter groups of Table A or Table A1, and optionally one or more additional parameters not shown in Table B. As an example, the primary parameter group may be PPG3 in Table A.

[0099] For each parameter in the primary parameter group, its primary dimension(s) are determined, i.e., M (mass), L (length) and / or t (time) and / or Θ (temperature) (see column Primary Dimensions in Table B).

[0100] The number of primary dimensions (j) in the primary parameter group (typically three (M, L, T) or four (M, L, T, Θ) primary dimensions) is determined, for example, based on Table A, PPG3, i.e., j=4.

[0101] The number of parameters (n) in the deposition and primary parameter group is determined (eg, based on Table A, PPG3: n=34).

[0102] The minimum number (k) of dimensionless numbers in the deposition and primary parameter group (k=nj) is determined (for example, based on Table A, PPG3: k=34−4=30 (at least)).

[0103] Select j repeat variables from the primary parameter group. None of the repeat variables can be dimensionless (e.g., N outlet , FPF, GSD, α cannot be chosen). No two iteration variables can have the same overall dimension (e.g., V FRC or TV inh (Both L 3) cannot be chosen). Two iteration variables can share a common dimension. It is generally advantageous to choose parameters whose primary dimensions relate to mass, geometry, and kinematics. Geometry refers to parameters related to the structure of the zone, and is usually one of the image subgroups in Table B. Kinetics refers to parameters that cause motion, such as velocity and airflow (e.g., Table A, based on PPG3: j=4).

[0104] Dimensionless number (π1~π k-1 ) To construct a dimensionless number (e.g., π1), form a holding expression that includes the repeating variables and one "remaining parameter" from the primary parameter group that is not one of the repeating variables. Rearrange the parameters represented as the primary dimension in the holding expression to form a dimensionless number and optionally remove a parameter.

[0105] This process is repeated for the next dimensionless number in the primary parameter group (e.g., π2). The retained expression contains the same repeated variables, with one "remaining parameter" being a parameter not used so far (e.g., based on Table A, PPG3: the dimensionless numbers (DNs) shown from PPG3 are derived from the parameters of PPG3).

[0106] At the end of applying Buckingham's pi theorem, there are at least k dimensionless numbers (π0 and π1 to π k-1 ) exists, and π1~π k-1 Each π in is defined in terms of the parameters in the primary parameter group.

[0107] The patient record dataset is - Recorded values ​​of deposition, - parameters of the parameter set, - the recorded value(s) for each parameter in the parameter set; Includes.

[0108] The recorded values ​​are values ​​previously determined for the patient. The plurality of recorded values ​​are obtained from a plurality of patient record data sets. The plurality of patient record data sets are used to derive multipliers and exponents in the dimensionless correlation.

[0109] The recorded deposition includes an indication of the zone of deposition. The recorded deposition can be determined from medical imaging (e.g., single photon emission computed tomography (SPECT)) and gamma scintigraphy using radiolabeled aerosols. These methods are known in the art (e.g., Conway, Joy. (2012). Lung imaging - two dimensional gamma scintigraphy, SPECT, CT and PET. Advanced drug delivery reviews. 64. 357-68. 10.1016 / j.addr.2012.01.013). Alternatively or additionally, the recorded deposition can be determined from medical imaging and computational fluid dynamics (CFD). These methods are known in the art (e.g., De Backer et al., J Aerosol Med Pulm Drug Deliv. 2010 Jun;23(3):137-48; Usmani, Omar S., et al. "Predicting lung deposition of extrafine inhaled corticosteroid-containing fixed combinations in patients with chronic obstructive pulmonary disease using functional respiratory imaging: An in silico study." Journal of aerosol medicine and pulmonary drug delivery 34.3 (2021): 204-211).

[0110] It is understood that the patient record dataset may include values ​​for some or all of the parameters in the parameter library (Table B). A portion of the parameters available in the patient record dataset is used to fill the parameter set. Typically, if a patient record dataset is missing parameter values ​​for one or more parameters in the parameter set, the patient record dataset will not be used in the regression analysis.

[0111] The patient's parameter value(s) (test values) are used to determine deposition. The parameter value(s) in the patient record (recorded values) are used to determine the dimensionless correlation, specifically the multiplier value and each exponent value in Equation 1.

[0112] The patient parameter value(s) (test or record), which are imaging parameters (e.g., IM-IM11 in Table B), can be determined from medical images (e.g., slice CT scans or volumetric CT scans). These methods are known in the art. See, for example, "Machine learning algorithms utilizing quantitative CT features may predict eventual onset of bronchiolitis obliterans syndrome after lung transplantation." Academic radiology 25.9 (2018): 1201-1212; De Backer, Wilfried, et al. "Functional respiratory imaging assessment of glycopyrrolate and formoterol fumarate metered dose inhalers formulated using co-suspension delivery technology in patients with COPD." Therapeutic advances in respiratory disease 14 (2020): 1753466620916990.

[0113] The patient's parameter value(s), which are the inhaler parameters (e.g., IN1-IN6 in Table B), can be determined (tested or recorded) from inhaler manufacturer data or from Next Generation Impactor (NGI) technology. The Next Generation Impactor™, or NGI™, has a cascade impactor that classifies inhaler aerosols based on their size. The output of the NGI™ is typically a list of the absolute mass of aerosol deposited at each stage by the impactor with a diameter range associated with that stage. Based on these two, a size histogram of the aerosol emitted from the inhaler can be constructed.

[0114] The value(s) of the patient's parameter(s), which are flow parameters (e.g., F1-F10 in Table B), can be determined (tested or recorded) from, for example, the manufacturer's recommendations on how to inhale / breathe while using the inhaler, or from how the patient actually inhales / breathes while using the inhaler. This depends on the inhaler used.

[0115] The values ​​(tested or recorded) of the patient's parameters, which may be physical properties or constants (e.g., PC1-PC12 in Table B). Typically, these are values ​​that can be set as constants. The constants can be obtained from thermodynamic tables. However, it is within the scope of this disclosure that one or more of the parameters may vary according to the patient's environment, e.g., room temperature.

[0116] For the dimensionless groups in Equation 1, the values ​​of the multipliers and each exponent in Equation 1 can be determined using regression analysis based on multiple patient record data sets.

[0117] For example, if the dimensionless group in Eq. - at least one dimensionless number from the list in Table C, - at least one dimensionless number from one of the primary parameter groups PPG1 and PPG2 (Table A), - at least two dimensionless numbers, preferably six to nine dimensionless numbers, from one of the primary parameter groups PPG3 to PPG5 (Table A), - at least two dimensionless numbers, preferably all of the dimensionless numbers, from one of the primary parameter groups PPG6 to PPG15 (Table A) depending on the zone, - at least four dimensionless numbers from one of the primary parameter groups PPG6 to PPG15 (Table A1), Or, - any of the above in addition to one or more dimensionless numbers not listed in Table C, where the multiplier and each exponent in Equation 1 can be determined using regression analysis based on multiple patient record data sets.

[0118] Regression analysis is known in the art. Generally speaking, the values ​​of the multipliers and each exponent in Equation 1 are iteratively adjusted (e.g., toward higher or lower values) so that the value of the dimensionless group (when multiple patient record datasets are applied) approaches the value of deposition (π0) (in the multiple patient record dataset). Typically, convergence to a solution can be reached within a certain number of iterations.

[0119] Various types of regression analysis are suitable for determining the values ​​of the multipliers and exponents. A preferred type of regression analysis is the non-linear least-squares (NLSQ) protocol. In particular, the Levenberg-Marquardt method or algorithm (JJ More, "The Levenberg-Marquardt Algorithm: Implementation and Theory," Numerical Analysis, ed. G.A. Watson, Lecture Notes in Mathematics 630, Springer Verlag, pp. 105-116, 1977) is most preferred. During or as a result of the regression analysis, one or more values ​​of c1~cm may tend toward 0, thereby eliminating one or more dimensionless quantities.

[0120] To impart zone specificity to the dimensionless correlation, the multiple patient record data sets used in the regression analysis are pre-filtered to include only patient record data sets with deposition values ​​specific to the zone of interest.

[0121] While Buckingham's Pi Theorem allows at least k-1 dimensionless numbers ("full set") in a dimensionless group to be created from a first-order parameter set, the inventors have found that using more than four dimensionless numbers or terms does not result in a significant increase in accuracy, but does result in an improvement. Preferably, the number of dimensionless numbers or terms in a dimensionless group of dimensionless correlations is preferably between four and nine, more preferably four, five, or six. Thus, the number of coefficients is between four and nine, more preferably four, five, or six. Having a limited number of exponents allows for faster convergence of the process of finding values ​​for the multipliers and exponents.

[0122] A dimensionless group may thus include a reduced set of dimensionless numbers or terms ("reduced set") selected from a full set of dimensionless numbers ("full set"). The reduced set preferably includes a quantity of dimensionless numbers or terms equal to the term limit (m). The term limit (m) of the reduced set is preferably 4 to 9, more preferably 4, 5, or 6.

[0123] The reduced set is determined using a remove and replace protocol. In the remove and replace protocol, the dimensionless groups of the dimensionless correlations in Equation 1 are initially populated with replaceable dimensionless terms or sets of dimensionless numbers ("replaceable sets") randomly selected from the full set until the number (m) of dimensionless numbers or terms present in the dimensionless group is 6 or greater, preferably 6-12, and more preferably 8-10. In a first round, a regression analysis as described herein is performed using multiple patient record data sets on the dimensionless correlations whose dimensionless groups contain the replaceable sets of dimensionless numbers or terms. The regression analysis adjusts the values ​​of c0, c1~cm until convergence on a solution, and values ​​for the multiplier c0 and exponent c1~cm are determined. The first-round interclass correlation (ICC) is determined.

[0124] In the second round, a dimensionless number or term of an alternative quantity is randomly removed from the replacement set of the first round, and a different dimensionless number of the alternative quantity is added randomly selected from the full set. This alternative quantity can have a value between 3 and 5. In the second round, the regression analysis adjusts the values ​​of c0, c1~cm until it converges to a solution, providing a second set of weight values ​​for c0, c1~cm. The intraclass correlation (ICC) is determined (typically greater than 0.9).

[0125] If the ICC improves in the second round compared to the first, the third round continues using the non-dimensional number or an exchangeable set of non-dimensional terms from the second round. If the ICC worsens in the second round compared to the first, the third round continues using the first round. Subsequent rounds proceed similarly to the previous rounds, with any necessary modifications. This process is repeated until the change in ICC becomes small, which typically occurs after 500 to 1000 rounds.

[0126] The dimensionless terms of the exchangeable set that are below the significance threshold are removed, thereby forming a reduced set of dimensionless numbers or terms, typically having preferably between 4 and 9, more preferably 4, 5 or 6 dimensionless numbers or terms. For example, if the contribution of a dimensionless term is less than 0.05%-0.2%, preferably less than 0.1%, of the total value (p0, RML), then this dimensionless term is removed.

[0127] The full set of dimensionless numbers or terms (also known as the pool of dimensionless numbers) described above may include the dimensionless numbers of Table C, preferably the dimensionless numbers of Table A, PPG2, more preferably the dimensionless numbers of Table A, PPG3, even more preferably the dimensionless numbers of Table A, PPG4, and most preferably the dimensionless numbers of Table A, PPG5.

[0128] According to one embodiment, the zones π1 to π mEach of π, c in c1 to cm, and c0 are - filling the dimensionless group of Equation 1 with at least nine dimensionless numbers (exchangeable set) selected from a pool of dimensionless numbers; - conducting multiple rounds of regression analysis, each round comprising: - adjusting the values ​​of c0, c1~cm until converging on a solution for deposition of multiple patient record data sets; - Substituting a portion (e.g., 2 to 5) of the dimensionless numbers in the dimensionless group with different dimensionless numbers selected from a pool of dimensionless numbers; and repeating the adjustments and substitutions until the improvement in convergence (intraclass correlation) is minimal or essentially nonexistent or tends to zero; is calculated by

[0129] An exemplary reduced set of dimensionless numbers for each zone is provided in Table A and Table A1 (PPG6-PPG15). The reduced set of dimensionless numbers described above preferably includes the zone-dependent dimensionless numbers of Table A or Table A1, namely, PPG6 (for IT zone deposition), PPG6 (for IT zone deposition), PPG7 (for ET zone deposition), PPG8 (for DI zone deposition), PPG9 (for PR zone deposition), PPG10 (for TL zone deposition), PPG11 (for RUL zone deposition), PPG12 (for RML zone deposition), PPG13 (for RLL zone deposition), PPG14 (for LUL zone deposition), and PPG15 (for LLL zone deposition).

[0130] According to one embodiment, - The zone is an IT zone, - Equation 1 is TIFF2025538705000014.tif12170, - c1>c2>c3>c4>cm.

[0131] According to one embodiment, - The zone is an IT zone, - Equation 1 is TIFF2025538705000015.tif11170, - c1>c2>c3>c4.

[0132] According to one embodiment, - The zone is a PR zone, -Equation 1 is TIFF2025538705000016.tif10170, - c1>c2>c3>c4>cm.

[0133] According to one embodiment, - The zone is a PR zone, - Equation 1 is TIFF2025538705000017.tif11170, - c1>c2>c3>c4.

[0134] According to one embodiment, - The zone is a DI zone, -Equation 1 is TIFF2025538705000018.tif11170, - c1>c2>c3>c4>cm.

[0135] According to one embodiment, - The zone is a DI zone, - Equation 1 is TIFF2025538705000019.tif11170, - c1>c2>c3>c4.

[0136] According to one embodiment, - The zone is an RLL zone, -Equation 1 is TIFF2025538705000020.tif8170, - c1>c2>c3>c4>cm.

[0137] According to one embodiment, - The zone is an RLL zone, - Equation 1 is TIFF2025538705000021.tif8170, - c1>c2>c3>c4.

[0138] According to one embodiment, - The zone is an LLL zone, - Equation 1 is TIFF2025538705000022.tif12170, - c1>c2>c3>c4>cm.

[0139] According to one embodiment, - The zone is an LLL zone, - Equation 1 is TIFF2025538705000023.tif12170, - c1>c2>c3>c4.

[0140] According to one embodiment, - the zone is a RUL zone, - Equation 1 is TIFF2025538705000024.tif11170, - c1>c2>c3>c4>cm.

[0141] According to one embodiment, - the zone is a RUL zone, - Equation 1 is TIFF2025538705000025.tif10170, - c1>c2>c3>c4.

[0142] According to one embodiment, - The zone is a LUL zone, - Equation 1 is TIFF2025538705000026.tif11170, - c1>c2>c3>c4>cm.

[0143] According to one embodiment, - The zone is a LUL zone, - Equation 1 is TIFF2025538705000027.tif12170, - c1>c2>c3>c4.

[0144] According to one embodiment, - the zone is an RML zone, - Equation 1 is TIFF2025538705000028.tif11170, - c1>c2>c3>c4>cm.

[0145] According to one embodiment, - the zone is an RML zone, - Equation 1 is TIFF2025538705000029.tif12170, - c1>c2>c3>c4.

[0146] According to one embodiment, - The zone is an ET zone, - Equation 1 is TIFF2025538705000030.tif11170, - c1>c2>c3>c4>cm.

[0147] According to one embodiment, - The zone is an ET zone, - Equation 1 is TIFF2025538705000031.tif11170, - c1>c2>c3>c4.

[0148] According to one embodiment, - The zone is a TL zone, - Equation 1 is TIFF2025538705000032.tif11170, - c1>c2>c3>c4>cm.

[0149] According to one embodiment, - The zone is a TL zone, - Equation 1 is TIFF2025538705000033.tif12170, - c1>c2>c3>c4.

[0150] The terms where m>4 are optionally present. These additional terms are determined as described above using regression analysis and multiple patient record data sets.

[0151] Those skilled in the art will appreciate that additional steps can be included to improve the accuracy of the prediction. For example, the sensitivity of the dimensionless correlation of a zone to the dimensionless number (DN) in that zone can be determined. This can be done by plotting deposition as a function of each DN. Using this technique, one can find the DN(s) at which "behavior changes" and identify the boundary (DN) at which the change in behavior (change in the shape of the plot) occurs. limit ) can also be found. The values ​​in the patient record dataset can be divided into two or three groups: DN behaviour may or may not be one of the DNs in the correlation, or may be a combination of at least two DNs. These groups (ranges) are behaviour <DN limit otherwise, DN behaviour >DN limit Then, find the correlation for each range individually. Then, the accuracy of the correlation can be improved, and the average maximum ICC for each zone can reach, for example, 0.95.

[0152] There is also provided a method for determining a derived dimensionless correlation, the derived dimensionless correlation being useful for determining airway deposition of an inhaled substance in the lungs of a subject (as described herein), the method comprising the steps of: - receiving a primary parameter group including a plurality of parameters from the parameter library of Table B. The primary parameter group may include: - at least nine parameters from the library of parameters in Table B, and optionally one or more parameters not listed in Table B; or - A parameter from one of the primary parameter groups (PPG1 to PPG5) of Table A, and optionally one or more parameters not listed in Table B. - performing a dimensionless analysis on the first-order parameter group to obtain a set of parameters and derived dimensionless correlations. - To construct dimensionless numbers from first-order parameter groups using Buckingham's pi theorem, thereby obtaining dimensionless correlations of the form π0=c0(π1 c1 ×π2 c2 ×π3 c3 ×...×π k-1 ck-1 ) [Formula 1] In this formula, - Deposition is expressed as a dimensionless number π0, - c0(π1 c1 ×π2 c2 ×π3 c3 ×...×π k ck-1 ) is a dimensionless group, - π 1~k-1 Each π in is a dimensionless number, - Each c in c1 to ck-1 is a dimensionless exponent, - k is the minimum number of dimensionless numbers in the dimensionless correlation, k is the number of parameters in the deposition and primary parameter group minus the number of primary dimensions in the primary parameter group, - c0 is the correlation multiplier, And, - To derive the values ​​of c0, c1~cm in the dimensionless correlation. π0=c0(π1 c1 ×π2 c2×π3 c3 ×...×π m cm ) [Formula 1a] In this formula, - Dimensionless number π1~π m is the dimensionless number π1~π in Eq. k is a subset of m has a value of at least 4, between 4 and 20, preferably between 4 and 9, more preferably 4, 5 or 6, and is less than k; - Dimensionless number π1~π m different subsets of π1 to π k Each different version of Equation 1a, including subsets with different combinations of dimensionless numbers from , is solved using regression analysis and multiple patient record datasets to obtain values ​​for the multiplier c0 and the exponent c1~cm. where: - The derived dimensionless correlation is the dimensionless number π1 to π that best fits multiple patient records. m , a version of Equation 1a including a multiplier c0 and an exponent c1~cm, The parameter set includes the parameters of the derived dimensionless correlation.

[0153] The elimination and exchange protocol described above is used to reduce the number of dimensionless terms to preferably between 4 and 9, more preferably 4, 5 or 6.

[0154] The method is carried out in vitro. The method is preferably carried out in silico. The method is carried out using a computer. The method is a computer-implemented method.

[0155] Also provided is a computing device or system configured to perform the methods described herein.

[0156] There is further provided a computer program or computer program product having instructions which, when executed by a computing device or a computing system, cause the computing device or the computing system to perform (each of the steps of) the method described herein.

[0157] Further provided is a computer-readable medium having stored thereon a computer program (product) having instructions that, when executed by a computing device or computing system, cause the computing device or computing system to perform (each of the steps of) the method described herein.

[0158] A data stream representing a computer program or computer program product having instructions that, when executed by a computing device or computing system, cause the computing device or computing system to perform (each of the steps of) the method described herein.

[0159] table

[0160] [Table 2] TIFF2025538705000035.tif241170TIFF2025538705000036.tif32170

[0161] [Table 3]

[0162] [Table 4] TIFF2025538705000039.tif253170TIFF2025538705000040.tif251170TIFF2025538705000041.tif209170

[0163] [Table 5] TIFF2025538705000043.tif223170 [Example]

[0164] Example 1 (RML-PPG12) Multiple patient record data sets were obtained. Each patient record data set included measurements of each parameter in Table A PPG3 for that patient (the 34 parameters in Table A) and the patient's RML deposition value (π0). The values ​​of the 32 dimensionless numbers in Table A PPG3 were then calculated. Nine dimensionless numbers were selected (randomly or otherwise) from the 32 dimensionless numbers to form an "exchangeable set" and used in Equation 1a below. Each of π1 through π9 is a dimensionless number. π 0,RML =c0xπ1 c1 xπ2 c2 xπ3 c3 x....xπ9 c9 [Formula 1a]

[0165] Using known values ​​for each dimensionless number from multiple patient record datasets, values ​​for the multiplier c0 and each exponent c1–c9 were derived using a nonlinear least-squares protocol (NLLSP) incorporating the Levenberg-Marquardt method. In the first round, 1 was selected as the initial value for the multiplier c0 and each exponent c1–c9. The NLLSP iteratively adjusted the values ​​of (c0, c1–c9) until it converged to a solution, providing a first set of values ​​for c0, c1–c9. In the second round, the three dimensionless numbers with the least influence (lower exponents) were removed from the replacement set from the first round, and a total of three different dimensionless numbers were randomly selected and added from the 23 remaining dimensionless numbers. In the second round, the NLLSP adjusted the values ​​of c0, c1–c9 until it converged to a solution, providing a second set of weight values ​​for c0, c1–c9 determined from the intraclass correlation (ICC).

[0166] If the ICC improved in the second round compared to the first round, a third round continued using the replacement set from the second round, again removing three dimensionless numbers and adding three different dimensionless numbers randomly selected from the 20 remaining dimensionless numbers. If the ICC worsened in the second round compared to the first round, the third round continued using the first round. Subsequent rounds proceeded as in the previous rounds, with necessary modifications. This process was repeated until the change in ICC became small. After 500 rounds, the change in ICC became small. The ICC for PPG12 was 0.86.

[0167] π1 c1 ~π9 c9 The five dimensionless terms in are below the significance threshold, and their corresponding dimensionless terms are removed from Equation 1a, which is transformed into Equation 1b below. TIFF2025538705000044.tif12170This formula has the same dimensionless number as PPG12(RML) in Table A.

[0168] If the contribution of a dimensionless term was less than 0.1% of the total value (p0, RML), the dimensionless term was removed. The reduced set of dimensionless terms included four dimensionless terms.

[0169] The values ​​of c0, c1 to c4 in formula 1b are defined in Table D.

[0170] [Table 6]

[0171] Equation 1b is an example of a formula for determining RML deposition in the general population.

[0172] For patients with no known RML deposits using this method, the parameters in Table A1 PPG12(RML) were measured / determined, and from these parameter values, the dimensionless values ​​of Table A PPG12 were determined. The results are shown in Table E. In Table E, column B is the patient's measured DN(π) value, and column C is the value of DN in Equation 1b with the weightings in Table D applied.

[0173] [Table 7]

[0174] The patient values ​​were applied to equation 1b, i.e., π 0,RML =0.00166×1.235×133.54×2.033×4.598=2.56=Deposition in RML This becomes:

[0175] Deposition at RML was predicted to be 2.7 using CFD. The accuracy of the method was determined to be 94.53%.

[0176] Example 2 For each of the 19 patients with unknown RML deposits using the present method, the parameters in Table A1 PPG12(RML) were measured / determined, and from these parameters, values ​​for RML deposits were determined according to formula 1b in Example 1. The results (depPredicted[%]) are shown in Table F. Predictions using the present method were very similar to deposits determined using CFD (depCFD[%]), with mean values ​​of 2.56 vs. 2.26, respectively (90.3% agreement).

[0177] [Table 8]

[0178] Example 3 Regression analysis was performed to compare the different quantities of π in Equation 1a in Example 1. Equation 1a is compared to one π (π1 c1) and when formula 1a contains only π1 c1 ~π 23 c23 The intraclass correlation was evaluated as the quantity of π was gradually increased until it included π. The results are shown in Figure 12. The intraclass correlation did not improve significantly beyond four π terms in Eq. 1b, which means that a minimum of four dimensionless numbers can be used to predict deposition within each zone.

[0179] Example 4 A primary parameter group was formed containing all the parameters of PPG3 in Table A. Using dimensional analysis and Buckingham's pi theorem, dimensionless numbers were constructed.

[0180] For each parameter in the primary parameter group, its primary dimension(s) were determined: M (mass), L (length), t (time), and / or Θ (temperature). The number (j) of primary dimensions (four primary dimensions M, L, T, Θ) in the primary parameter group was determined. The number (n) of parameters in the deposition (De) and primary parameter group was determined based on the PPG3 = 34 parameters in Table A. The minimum number (k) of dimensionless numbers in the deposition and primary parameter group (k = nj) was determined as 34 - 4 = 30.

[0181] The dimensionless number (π) was written as the following equation: π0 = deposition, and π1,π2,π3...,π 30

[0182] Four iteration variables (parameters) were selected, three of which were mass (ρ a ), geometry (L ch (characteristic length, IM8)) and kinematics (u (flow velocity, F6)), and the fourth variable is the injection time (t inj , IN5) (see Table B for parameter codes).

[0183] To construct the dimensionless number (π1), the retention expression uses the iteration variables above and the absolute viscosity of air (μ in Table B). a and one remaining parameter, which was PC2).

[0184] therefore, π1=ρa A1 xL ch B1 xu C1 xt D1 xμ a 1 The dimensions are: TIFF2025538705000048.tif46170. Rearranging the above, TIFF2025538705000049.tif8170, which is equivalent to the Reynolds number (inverse form), shown as DN23 (Table C).

[0185] To construct the next dimensionless number (π2), the retained expression contains the same repeated variables, and one "remaining parameter" was chosen, g(PC10). After applying Buckingham's pi theorem, as exemplified above for π1, π2 was found to be the following expression, shown as DN25 (Table C): TIFF2025538705000050.tif11170

[0186] Some dimensionless numbers were created by dividing two parameters with the same linear dimension. Other dimensionless numbers were created by repeating the Buckingham Pi Theorem process described above. The total of 32 dimensionless numbers found are shown in Table A, PPG3.

[0187] The dimensionless numbers were placed into dimensionless correlations. π0=c0×π1 c1 ×π2 c2 ×π3 c3 ×...×π m cm [Formula 1a] In this formula, the m dimensionless numbers were chosen from 32 dimensionless numbers found using Buckingham's pi theorem.

[0188] First, nine dimensionless numbers were randomly selected from a set of 32 dimensionless numbers (exchangeable set), and values ​​for the multiplier c0 and each exponent c1–c9 were derived using a nonlinear least-squares protocol (NLLSP) incorporating the Levenberg-Marquardt method and multiple patient record datasets.

[0189] In the first round, an initial value of 1 was selected for the multiplier c0 and each exponent c1 through c9. The NLLSP iteratively adjusted the values ​​of (c0, c1 through c9) until convergence to a solution was achieved, providing a first set of values ​​for c0, c1 through c9. Convergence to a solution means that when multiple patient record datasets are applied to the dimensionless correlation (Equation 1a), the obtained value of π0 approaches the recorded value of deposition. Convergence to a solution is typically achieved within a certain number of iterations. The intraclass correlation (ICC) is determined (typically greater than 0.8).

[0190] In the second round, three dimensionless numbers were randomly removed from the first-round selection (the exchangeable set), and three different dimensionless numbers were randomly selected from the remaining (32 - 9 = 23) dimensionless numbers and added. In the second round, NLLSP iteratively adjusted the values ​​of c0, c1 through c9 until it converged to a solution, providing a second set of weight values ​​for c0, c1 through c9. The intraclass correlation (ICC) was determined (typically greater than 0.8).

[0191] If the ICC improved in the second round compared to the first round, a third round continued using the non-dimensional numbers (replaceable set) from the second round, again removing three non-dimensional numbers and adding three different non-dimensional numbers randomly selected from the remaining (32 - 9 - 3 = 20) non-dimensional numbers. If the ICC worsened in the second round compared to the first round, the third round continued using the first round. Subsequent rounds proceeded as in the previous rounds, with necessary modifications. This process was repeated until the change in ICC became small, which typically occurred after 500 rounds. The overall mean ICC was 0.92.

[0192] In this way, a dimensionless correlation with a reduced number of dimensionless numbers was arrived at. It was found that having more than four dimensionless numbers did not improve the predictive power of deposition. One dimensionless correlation was determined per zone.

[0193] The dimensionless numbers determined for each zone are listed in Table A, PPG6 through PPG15. The dimensionless numbers most frequently found as determinants of deposition across all zones, along with dimensionless numbers that are less frequently found but have higher weighting (indexes), are listed in Table A, PPG2 and PPG3. The dimensionless numbers most frequently found as determinants of deposition across almost all zones are listed in Table A, PPG4. The dimensionless numbers most frequently found as determinants of deposition across most zones are listed in Table A, PPG5. The dimensionless numbers found as determinants of deposition in zones IT, ET, DI, PR, TL, RUL, RML, RLL, RUL, LUL, and LLL are listed in Table A, PPG5 through PPG15, respectively. Table A1 lists the four most determinants of deposition in zones IT, ET, DI, PR, TL, RUL, RML, RLL, RUL, LUL, and LLL in PPG5 through PPG15.

[0194] After determining the dimensionless correlation for each zone, multiple unused patient record (study) data sets were applied to each dimensionless correlation, each unused patient record data set being one that had not been used in the regression analysis.

[0195] The dimensionless correlations per zone demonstrated a good fit to the training data (IT zone), Figure 2 (DI zone), Figure 3 (PR zone), Figure 4 (TL zone), Figure 5 (RUL zone), Figure 6 (RML zone), Figure 7 (RLL zone), Figure 8 (LUL zone), and Figure 9 (LLL zone). Note that results for the extrathoracic zone are not shown because they relate to the intrathoracic data (the extrathoracic zone is what remains after the extrathoracic zone is subtracted).

[0196] The results demonstrate a good fit of the dimensionless correlations to the training data by zone, as well as a good fit of the test data to the dimensionless correlations by zone. Table G shows the intraclass correlations (ICCs) for the training and test data for each of Figures 1-9. An ICC greater than 0.7 is considered a good fit.

[0197] [Table 9]

[0198] For a sample of 18 patients using the parameter set (each individually imaged, same inhaler / drug (IN parameters), same inhalation profile (F-number), same physical properties and constants (PC parameters)), the deposition obtained by the dimensionless correlation (NDA) described herein is similar to that obtained by computational fluid dynamics (CFD) (see mean and standard deviation in Figure 11).

[0199] The computational time for deposition using the dimensionless correlation (NDA) described herein is many times faster than achieving a similar level of accuracy using computational fluid dynamics (CFD) (see Figure 10). The computational time using NDA averaged approximately 30 seconds compared to an average of 42,000 seconds (11.5 hours) for CFD.

[0200] Example 5 Depositions in the extrathoracic (ET), intrathoracic (IT), distal (DI), peripheral (PR), right upper lobe (RUL), right middle lobe (RML), right lower lobe (RLL), left upper lobe (LUL), and left lower lobe (LLL) zones were determined using this method (RDA) for 19 different patients and compared with depositions determined for the same 19 patients using CFD.

[0201] Figure 13 shows the average results when the quantity of π in Equation 1 is 4. For each zone, the spread of deposition calculated using CFD and RDA is shown compared to CFD as bars with error bars, mean, standard deviation, and precision for RDA.

[0202] Figure 14 is similar to Figure 13 except that the number of π in Equation 1 is 20. The results demonstrate the high accuracy of the method compared to CFD and that increasing the number of π in Equation 1 from 4 to 20 only increases the accuracy slightly.

Claims

1. 1. A computer-implemented method for determining airway deposition of an inhaled substance within a lung zone of a subject, comprising: receiving a patient data set for the subject, the patient data set including a parameter set and corresponding values ​​for two or more parameters, the parameters in the parameter set forming at least four dimensionless numbers in a dimensionless correlation specific to the zone; determining the airway deposition of the inhaled substance in the zone of the lung of the subject from the dimensionless correlation and the corresponding values ​​of the parameters in the parameter set; A method comprising:

2. The first component of the dimensionless correlation is a dimensionless number (π ０，ｚｏｎｅ ) and The method of claim 1 , wherein a second component of the dimensionless correlation is a dimensionless group containing the at least four dimensionless numbers of the zone being sought.

3. The dimensionless correlation has the form of Equation 1: π ０，ｚｏｎｅ = c ０ (π １ ｃ１ × π ２ ｃ２ × π ３ ｃ３ ×... × π ｍ ｃｍ ) [Equation 1] In the formula 1, π ０，ｚｏｎｅ is a dimensionless number (first component) that is the deposition within the zone, c ０ (π １ ｃ１ ×π ２ ｃ２ ×π ３ ｃ３ ×... ×π ｍ ｃｍ ) is the dimensionless group (second component), π １～ｍ Each π is a dimensionless number for said zone, Each c in c1 to cm is an exponent of the dimensionless number, m is at least 4, 4 to 20, preferably 4 to 9, more preferably 4, 5 or 6; c ０ is a multiplier for the correlation, π of the zone １ ~π ｍ Each of π of c1 to cm, and c ０ 3. The method of claim 1 or 2, wherein σ is determined from a plurality of patient record data sets and regression analysis.

4. π of the zone １ ~π ｍ Each of π of c1 to cm, and c ０ teeth, filling said dimensionless group of Equation 1 with six or more, preferably six to twenty, dimensionless numbers selected from a pool of dimensionless numbers; conducting multiple rounds of regression analysis, each round comprising: c until convergence on a solution for deposition of said plurality of patient record data sets. ０ , adjusting the values ​​of c1 to cm; substituting a portion (e.g., 2 to 5) of the dimensionless numbers in the dimensionless group with different dimensionless numbers selected from the pool of dimensionless numbers; and repeating the adjustment and substitution until the improvement in convergence (intraclass correlation) is minimal; The method of claim 3, wherein the formula is determined by:

5. The pool of dimensionless numbers is The method of claim 4, comprising:

6. The dimensionless number in Equation 1 is The method according to any one of claims 3 to 5, wherein the compound is selected from the group consisting of:

7. The parameters and dimensionless numbers in the parameter set are selected according to the zone of the lung of the subject for which airway deposition is desired. Table 10 The method of any one of claims 1 to 6, comprising:

8. the zone is an IT zone, Equation 1 is: and c1>c2>c3>c4>cm, The method according to any one of claims 3 to 7, wherein in formula 1, the term m>4 is optionally present.

9. the zone is a PR zone, Equation 1 is: and c1>c2>c3>c4>cm, The method according to any one of claims 3 to 7, wherein in formula 1, the term m>4 is optionally present.

10. the zone is a DI zone, Equation 1 is: and c1>c2>c3>c4>cm, The method according to any one of claims 3 to 7, wherein in formula 1, the term m>4 is optionally present.

11. the zone is an RLL zone, Equation 1 is: and c1>c2>c3>c4>cm, The method according to any one of claims 3 to 7, wherein in formula 1, the term m>4 is optionally present.

12. the zone is an LLL zone, Equation 1 is: and c1>c2>c3>c4>cm, In the above formula 1, the term m>4 is optionally present or Or, the zone is a RUL zone; Equation 1 is: and c1>c2>c3>c4>cm, In the above formula 1, the term m>4 is optionally present or Or, the zone is a LUL zone; Equation 1 is: and c1>c2>c3>c4>cm, In the above formula 1, the term m>4 is optionally present or Or, the zone is an RML zone, Equation 1 is: and c1>c2>c3>c4>cm, In the above formula 1, the term m>4 is optionally present or Or, the zone is an ET zone, Equation 1 is: and c1>c2>c3>c4>cm, In the above formula 1, the term m>4 is optionally present or Or, the zone is a TL zone, Equation 1 is: and c1>c2>c3>c4>cm, The method according to any one of claims 3 to 7, wherein in formula 1, the term m>4 is optionally present.

13. A computing device or system configured to perform the method of any one of claims 1 to 12.

14. A computer program or computer program product having instructions which, when executed by a computing device or a computing system, cause said computing device or system to perform the method of any one of claims 1 to 12.

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