Computational fluid dynamics models and methods of use

Abstract

The present application provides methods for predicting freeze-thaw profiles across scales and geometries, generating predetermined freeze-thaw profiles in small-scale experiments using computational fluid dynamics models, and using small-scale freeze-thaw profiles to predict large-scale freeze-thaw profiles.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of U.S. Provisional Application No. 63 / 429,778, filed December 2, 2022, which is incorporated herein by reference in its entirety.

[0002] This application relates to methods for optimizing freeze-thaw processes to maintain the quality and stability of chemical compounds. The methods described herein are also useful for optimizing freeze-thaw processes to maintain the quality and stability of pharmaceutical agents. [Background technology]

[0003] The freeze-thaw process allows operational flexibility during the manufacturing of compounds, particularly drugs, to maintain quality attributes. For example, freezing stabilizes bulk drugs and reduces the possibility of microbial contamination during transport. Immobilizing protein molecules in a frozen matrix minimizes diffusion collisions that can cause aggregation in drugs. Freezing also reduces the rate of degradation reactions, particularly those involving free water, such as peptide bond hydrolysis and aspartic acid isomerization. Thus, freezing large quantities of drugs in batches allows formulation, fill, and finish processes to proceed according to real-time commercial and clinical demands.

[0004] The freeze-thaw process can also adversely affect the quality attributes of compounds, particularly drugs. Excessively cold temperatures can cause proteins to spontaneously unfold (e.g., cryodenaturation), and the freeze-thaw rate can alter the physical and chemical properties of the solution in ways that compromise protein stability. Therefore, optimizing the freeze-thaw process optimizes the quality attributes of drugs during the manufacturing process, storage, transportation, and delivery. Experiments can characterize the freeze-thaw process under a range of conditions and determine its effect on the quality attributes of drugs. Because the characteristics of the freeze-thaw process depend on the scale at which the freeze-thaw process occurs, experiments should be performed on a large scale. However, bulk drugs may not be available for large-scale studies early in development. Financial, time, and labor costs can also limit the investigation of large-scale freeze-thaw scenarios.

[0005] It will be appreciated that a need exists for improved methods to characterize the freeze-thaw process using a range of conditions across scales and to determine its effect on the quality attributes of compounds, particularly pharmaceutical agents. Summary of the Invention

[0006] Optimizing the freeze-thaw process to maintain the quality attributes of pharmaceutical compounds, particularly biopharmaceuticals, is a critical issue in pharmaceutical manufacturing processes, storage, transportation, and delivery. There is a need for improved methods for characterizing the freeze-thaw process using various conditions across scales to determine its effect on pharmaceutical quality attributes. This application provides methods for predicting the characteristics of the freeze-thaw process using various conditions across scales and replicating the characteristics of the freeze-thaw process in a small-scale freeze-thaw process. Thus, the effect of the freeze-thaw process on the quality attributes of a pharmaceutical can be determined with minimal financial, time, and labor costs, even when only small amounts of the pharmaceutical are available.

[0007] The present application provides a method for freezing a solution. In some exemplary embodiments, the method includes: (a) using a computational fluid dynamics model to predict a first freezing profile of a large volume of solution subjected to first freezing operating conditions, the first freezing profile including a predicted average temperature and total freezing time of the solution during freezing; (b) using the computational fluid dynamics model to fit a transient temperature boundary equation to the first freezing profile; (c) using the computational fluid dynamics model to predict a set temperature sequence that generates a predicted second freezing profile of a small volume of solution, the set temperature sequence being a condition for predicting the transient temperature boundary equation, and the second freezing profile including a predicted average temperature and total freezing time of the solution during freezing; and (d) freezing the small volume of solution using the set temperature sequence.

[0008] In one embodiment, the method further comprises determining at least one quality characteristic of the small amount of solution after freezing.

[0009] In one aspect, the solution comprises a pharmaceutical agent, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, an Fab region of an antibody, an antibody drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

[0010] In one aspect, the method further includes operating the temperature regulation system using a computational fluid dynamics model to generate a sequence of set temperatures for freezing small batches.

[0011] In one embodiment, the method further comprises measuring the temperature of at least one point of interest in the small volume throughout the freezing.

[0012] In one embodiment, the large scale volume is from about 0.2L to about 20L.

[0013] In one embodiment, the small-scale volume is about 20 mL to about 100 mL.

[0014] In one embodiment, the large scale quantity is in a large scale container having a volume of about 1 L to 20 L.

[0015] In one embodiment, the small-scale amount is in a small-scale container having a volume of about 30 mL to 100 mL.

[0016] In one embodiment, the large scale container is selected from the group comprising 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

[0017] In one embodiment, the small container is selected from the group comprising a 30 mL bag and a 100 mL bag.

[0018] The present application provides a method for thawing a solution. In some exemplary embodiments, the method includes: (a) using a computational fluid dynamics model to predict a first thawing profile of a large volume of solution subjected to first thawing operating conditions, the first thawing profile including a predicted average temperature and total thawing time of the solution during thawing; (b) using the computational fluid dynamics model to fit a transient temperature boundary equation to the first thawing profile; (c) using the computational fluid dynamics model to predict a set temperature sequence that generates a predicted second thawing profile of a small volume of solution, the set temperature sequence being a condition for predicting the transient temperature boundary equation, and the second thawing profile including a predicted average temperature and total thawing time of the solution during thawing; and (d) thawing the small volume of solution using the set temperature sequence.

[0019] In one embodiment, the method further comprises determining at least one quality attribute of the small amount of solution after thawing.

[0020] In one aspect, the solution comprises a pharmaceutical agent, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, an Fab region of an antibody, an antibody drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

[0021] In one aspect, the method further includes operating the temperature regulation system using a computational fluid dynamics model to generate a set temperature sequence for thawing the small volume of solution.

[0022] In one embodiment, the method further comprises measuring the temperature of at least one point of interest in the small volume throughout the thawing.

[0023] In one embodiment, the large scale volume is from about 0.2L to about 20L.

[0024] In one embodiment, the small-scale volume is about 20 mL to about 100 mL.

[0025] In one embodiment, the large scale quantity is in a large scale container having a volume of about 1 L to 20 L.

[0026] In one embodiment, the small-scale amount is in a small-scale container having a volume of about 30 mL to 100 mL.

[0027] In one embodiment, the large scale container is selected from the group comprising 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

[0028] In one aspect, the small-scale container is selected from the group consisting of a 30 mL bag and a 100 mL bag. The present application provides a method for freezing a solution. In some exemplary embodiments, the method includes: (a) using a computational fluid dynamics model to predict a freezing profile of a large-scale solution subjected to a set of freezing operating conditions; (b) determining whether freezing will occur within a required period of time; and (c) freezing the large-scale amount of the solution using the set of freezing operating conditions.

[0029] The present application provides a method for freezing and thawing a solution. In some exemplary embodiments, the method includes: (a) using a computational fluid dynamics model to predict a first freeze and thaw profile of a large volume of solution subjected to first freeze and thaw operating conditions, the first freeze and thaw profile including a predicted average temperature of the solution during freezing and thawing and a total freeze and thaw time; (b) using the computational fluid dynamics model to fit a transient temperature boundary equation to the first freeze and thaw profile; (c) using the computational fluid dynamics model to predict a set temperature sequence that generates a predicted second freeze and thaw profile of a small volume of solution, the set temperature sequence being a condition for predicting the transient temperature boundary equation, and the second freeze and thaw profile including a predicted average temperature of the solution during freezing and thawing and a total freeze and thaw time; and (d) freezing and thawing the small volume of solution using the set temperature sequence.

[0030] In one embodiment, the method further comprises thawing and determining at least one quality characteristic of the small amount of solution after thawing.

[0031] In one aspect, the solution comprises a pharmaceutical agent, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, an Fab region of an antibody, an antibody drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

[0032] In one aspect, the method further includes operating the temperature regulation system using a computational fluid dynamics model to generate set temperature sequences for thawing and defrosting the small volume.

[0033] In one embodiment, the method further comprises thawing and measuring the temperature of at least one point of interest in the small volume throughout the thawing.

[0034] In one embodiment, the large scale volume is from about 0.2L to about 20L.

[0035] In one embodiment, the small-scale volume is about 20 mL to about 100 mL.

[0036] In one embodiment, the large scale quantity is in a large scale container having a volume of about 1 L to 20 L.

[0037] In one embodiment, the small-scale amount is in a small-scale container having a volume of about 30 mL to 100 mL.

[0038] In one embodiment, the large scale container is selected from the group comprising 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

[0039] In one embodiment, the small container is selected from the group comprising a 30 mL bag and a 100 mL bag.

[0040] The present application provides a method for freezing and thawing a solution. In some exemplary embodiments, the method includes (a) using a computational fluid dynamics model to predict a freezing and thawing profile of a large-scale solution subjected to first freeze and thaw operating conditions, (b) determining whether freezing and thawing will occur within a required time period, and (c) freezing and thawing the large-scale amount of solution using the first freeze and thaw operating conditions.

[0041] The present application provides a method for thawing a solution. In some exemplary embodiments, the method includes (a) using a computational fluid dynamics model to predict a thawing profile of a large-scale solution subjected to first thawing operating conditions, (b) determining whether thawing will occur within a required time period, and (c) thawing the large-scale quantity of the solution using the first thawing operating conditions.

[0042] The present application provides a method for freezing a solution. In some exemplary embodiments, the method includes: (a) using a computational fluid dynamics model to predict a freezing profile of a large-scale solution subjected to first freezing operating conditions; (b) determining whether freezing will occur within a required time period; and (c) freezing the large-scale amount of solution using the first freezing operating conditions.

[0043] In one embodiment, the computational fluid dynamics model may take into account environmental factors, which may include, for example, air currents, proximity to other surfaces of varying temperatures, relative humidity, pressure, and any combination thereof. [Brief explanation of the drawings]

[0044] [Figure 1] 1 illustrates an overview of a computational fluid dynamics model framework, in accordance with an illustrative embodiment; [Figure 2] 1 illustrates a model of a large solution in a large vessel and a small solution in a small vessel generated by a computational fluid dynamics model of the present disclosure, in accordance with an illustrative embodiment. [Figure 3] 1 illustrates a spatial domain within a large-scale vessel divided into separate volumes after spatial discretization, in accordance with an illustrative embodiment; [Figure 4] 10 illustrates predicted thermodynamic temperatures within a small-scale solution at points during a freezing process, according to an illustrative embodiment. [Figure 5] 10 illustrates predicted velocities within a large container partially filled with solution at points during a freeze-thaw process, according to an illustrative embodiment. [Figure 6]1 illustrates predicted thermodynamic temperatures within a large-scale container partially filled with a large-scale solution at two points during the freezing process according to an example embodiment. [Figure 7] An exemplary embodiment is shown in which the computational fluid dynamics model of the present disclosure can determine whether 3.5 L of solution in a 5 L Nalgene™ Polycarbonate Biotainer™ bottle containing high or low concentrations of drug substance or free drug substance can be frozen at freezing operating conditions within 48 hours. [Figure 8] 1 illustrates the predicted thermodynamic temperatures within the small-scale container at points during the freezing process and the final point (e.g., red sphere) at which the small-scale solution freezes, according to an example embodiment. [Figure 9] The weighted spatial averaging of the large-scale freeze-thaw process, generation of set temperature sequences for a temperature regulation system, and prediction of expected temperature profiles of the large-scale and small-scale freeze-thaw processes performed by the computational fluid dynamics model of the present disclosure in accordance with exemplary embodiments shows that the small-scale freeze-thaw process allows for representing the large-scale freeze-thaw process in spatially averaged quantities across scales and geometries. [Figure 10] 1 shows an example of transient equations fitted by the disclosed computational fluid dynamics model to the predicted temperatures of a large-scale solution during a freezing process, set as transient temperature boundary conditions while predicting a temperature progression scheme for a temperature regulation system in a small-scale experiment intended to replicate the freeze-thaw rates of a large-scale process, according to an exemplary embodiment, and adjusting the temperature regulation system to produce the predicted temperature progression scheme during the small-scale experiment. [Figure 11] An exemplary embodiment is shown in which a computational fluid dynamics model approximates the physics of the freeze-thaw process for large-scale and small-scale solutions in 1 L-5 L polycarbonate bottles and 30 mL bags, respectively, and the freeze-thaw profile of a large-scale solution can be reproduced in a small-scale solution using the Benchtop Freezing Platform. [Figure 12]10 illustrates the total freezing time of solutions in large and small containers to the total freezing time predicted by a computational fluid dynamics model, according to an illustrative embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0045] Maintaining the quality and stability of chemical compounds, particularly biopharmaceuticals, during manufacturing processes, storage, transportation, and patient administration can be challenging yet essential. Bulk drug substances undergo a series of processing steps to convert the purified drug substance into a final dosage form in an appropriate container closure system or delivery device (e.g., formulation, fill, and finish processes). The formulation, fill, and finish processes include freezing and thawing the bulk drug substance (e.g., bulk freeze-thaw), formulating the purified drug substance to the desired concentration with excipients, filtering, filling into a container closure system, lyophilization (if necessary), testing, labeling and packaging, storage, transportation, and delivery (e.g., patient administration). As a result, biopharmaceuticals are vulnerable to numerous sources of chemical and physical instability during the formulation, fill, and finish processes that can impair their efficacy.

[0046] Low temperatures can cause proteins to spontaneously unfold (e.g., cold denaturation) by weakening the hydrophobic effect. The Gibbs free energy function can explain the cold denaturation temperature, which has an inverted parabolic shape. The negative free energy of unfolding favors thermal denaturation at temperatures above and below the high and low thresholds, respectively. For example, the hydrophobic effect stabilizes globular protein globules with an inner hydrophobic core, despite the preference of polar and nonpolar residues for alternative geometric positions. Therefore, lowering the temperature reduces the stabilization provided by the hydrophobic effect, causing cold denaturation below the low threshold. In addition to the absolute temperature, the rate at which freezing occurs can adversely affect protein stability by altering the physical and chemical properties of the solution.

[0047] Slow freezing rates can exclude proteins and excipients from the ice-liquid interface, leading to increased concentrations of excipients and proteins in the liquid near the ice crystals (e.g., freeze concentration). Such increases in excipient concentration can alter the protein structure. Increasing the concentration of excipients near the ice crystals can alter the pH and destabilize the protein, as low-solubility buffer components can precipitate. Furthermore, increased protein concentration increases the likelihood of aggregation and precipitation. Similar to slow freezing rates, slow thawing rates can stress and damage proteins. Extremely small ice crystals can recrystallize during the slow thawing process, and proteins can denature at the ice-liquid interface.

[0048] The freeze concentration generated during freezing can destabilize the protein again during thawing. Therefore, a faster thawing process that minimizes recrystallization and freeze concentration is typically preferred. For example, a mixing process sufficient to homogenize the solution without shearing and denaturing the protein at the air-liquid interface can accelerate the thawing process without adversely affecting the quality of the product. Similarly, a faster freezing rate can reduce freeze concentration, but a fast freezing process can compromise the stability of the protein.

[0049] A rapid freezing rate exposes proteins to a large ice-liquid interface by forming extremely small ice crystals that adsorb proteins onto their surfaces. Proteins concentrated on the surface of the crystals at the ice-liquid interface can partially unfold and aggregate. In addition, a rapid freezing rate can trap air in the ice, and subsequent thawing can denature proteins at the air-liquid interface. Therefore, during biopharmaceutical manufacturing, careful evaluation and optimization of freeze-thaw process parameters can prevent bulk freeze-thaw processes from compromising the quality of drug substances.

[0050] Measuring the temperature of a solution at one or more points of interest during a freeze-thaw process can determine a freeze-thaw profile. These data can determine the average temperature and rate of freezing or thawing of a solution over the duration of the freeze-thaw process. Large scales magnify the formation of freeze concentrate. Therefore, experiments investigate freeze concentrate formation during large-scale freeze-thaw processes. Therefore, investigating the effects of various freeze-thaw operating conditions on the quality attributes of pharmaceutical protein products in large-scale freeze-thaw processes can require extensive amounts of physical materials and labor. However, large quantities of pharmaceutical protein products may not be available during the early development stage, hindering the ability to optimize freeze-thaw operating conditions for large-scale manufacturing processes, storage, and transportation.

[0051] Disclosed herein is a method for predicting the freeze-thaw rate of a large-scale solution subjected to a set of freeze-thaw operating conditions, using the small-scale solution to reproduce the freeze-thaw rate of a small-scale amount of solution, and determining the effect of the freeze-thaw rate on the quality attributes of the small-scale amount of solution. The examples described below demonstrate that the total freezing time of a large-scale freezing process differed by approximately 3.57% from the prediction of the disclosed computational fluid dynamics model. In addition, the disclosed computational fluid dynamics model reproduced the freezing rate of a small-scale freezing process in a small-scale freezing experiment. The actual and predicted total freezing times of the small-scale freezing process differed by approximately 2.86% and approximately 2.38%, respectively. Consequently, the disclosed method can be used to determine the effect of a large-scale freeze-thaw process on the quality attributes of a pharmaceutical product without the cost of conducting a large-scale study. The disclosure also provides a method for determining whether a set of freezing operating conditions is suitable for freezing or thawing a quantity of solution within a predetermined amount of time.

[0052] Unless otherwise explained, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although the practice or testing can use methods and materials similar or equivalent to those described herein, specific methods and materials are described herein.

[0053] The terms "a" and "an" should be understood to mean "at least one," and the terms "about" and "approximately" should be understood to allow for standard variation as understood by one of ordinary skill in the art, and when ranges are provided, the endpoints are included. As used herein, the terms "include," "includes," and "including" are intended to be open-ended and are understood to mean "comprise," "comprises," and "comprising," respectively.

[0054] In an exemplary embodiment, the present disclosure provides a method for freezing or thawing a solution. The solution may contain, for example, an ingredient, drug or pharmaceutical, active ingredient, pharmaceutical product, biological product, small molecule drug, active pharmaceutical ingredient, excipient, or any combination thereof, having at least one quality characteristic that the freezing or thawing process can preserve, replicate, or predict. The pharmaceutical product may be a pharmaceutical formulation including an excipient.

[0055] As used herein, the term "composition" refers to a pharmaceutical agent formulated together with one or more pharmaceutically acceptable vehicles.

[0056] As used herein, the terms "drug" and "pharmaceutical product" can include the biologically active ingredient of a drug product. Drugs and pharmaceutical products can refer to any substance or combination of substances used in a drug product intended to provide pharmacological activity or otherwise have a direct or indirect effect on the diagnosis, cure, mitigation, treatment, or prevention of disease, or to have a direct or indirect effect on restoring, correcting, or modifying physiological function in an animal. Non-limiting methods for preparing drugs and pharmaceutical products can include using fermentation processes, recombinant DNA, isolation and recovery from natural sources, chemical synthesis, biosynthesis, polymerase chain reaction, or a combination thereof. In some exemplary embodiments, drugs and pharmaceutical products are drugs, chemical compounds, nucleic acids, nucleotides, nucleosides, oligonucleotides, toxins, peptides, proteins, fusion proteins, antibodies, antibody fragments, Fab regions of antibodies, antibody-drug conjugates, or pharmaceutical protein products, or a combination thereof.

[0057] As used herein, the terms "protein" and "pharmaceutical protein product" can include any amino acid polymer having covalently linked amide bonds. A protein comprises one or more amino acid polymer chains, commonly known in the art as "polypeptides." A "polypeptide" refers to a polymer composed of amino acid residues, related naturally occurring structural variants, and synthetic non-naturally occurring analogs thereof, linked via peptide bonds. A "synthetic peptide or polypeptide" refers to a non-naturally occurring peptide or polypeptide. Synthetic peptides or polypeptides can be synthesized, for example, using an automated polypeptide synthesizer. Various solid-phase peptide synthesis methods are known to those skilled in the art. A protein can comprise one or more polypeptides to form a single functional biomolecule. Proteins can include antibody fragments, nanobodies, recombinant antibody chimeras, cytokines, chemokines, peptide hormones, etc. Proteins of interest can include biotherapeutic proteins, recombinant proteins used in research or therapy, trap proteins and other chimeric receptor Fc fusion proteins, chimeric proteins, antibodies, monoclonal antibodies, polyclonal antibodies, human antibodies, and bispecific antibodies. Proteins can be produced using recombinant cell-based production systems, such as insect baculovirus systems, yeast systems (e.g., Pichia), mammalian systems (e.g., CHO cells and CHO derivatives such as CHO-K1 cells). For a recent review discussing biotherapeutic proteins and their production, see Ghaderi et al., "Production platforms for biotherapeutic glycoproteins. Occurrence, impact, and challenges of non-human sialylation" (Darius Ghaderi et al., 28 Biotechnology and Genetic Engineering Reviews 147-176 (2012)), the teachings of which are incorporated herein in their entirety.Proteins can be classified based on composition and solubility and thus include simple proteins such as globular and fibrous proteins, complex proteins such as nucleoproteins, glycoproteins, mucoproteins, chromoproteins, phosphoproteins, metalloproteins, and lipoproteins, and derived proteins such as primary derived proteins and secondary derived proteins.

[0058] In some exemplary embodiments, the proteins and pharmaceutical protein products may be recombinant proteins, antibodies, bispecific antibodies, multispecific antibodies, antibody fragments, monoclonal antibodies, fusion proteins, scFvs, and combinations thereof.

[0059] As used herein, the term "recombinant protein" refers to a protein produced as a result of transcription and translation of a gene carried on a recombinant expression vector introduced into a suitable host cell. In certain exemplary embodiments, the recombinant protein may be an antibody, e.g., a chimeric antibody, a humanized antibody, or a fully human antibody. In certain exemplary embodiments, the recombinant protein may be an antibody of an isotype selected from the group consisting of IgG (e.g., IgG1, IgG2, IgG3, IgG4), IgM, IgA1, IgA2, IgD, or IgE. In certain exemplary embodiments, the antibody molecule is a full-length antibody (e.g., an IgG1 or IgG4 immunoglobulin), or the antibody may be a fragment (e.g., an Fc fragment or a Fab fragment).

[0060] As used herein, the term "antibody" includes immunoglobulin molecules comprising four polypeptide chains, two heavy (H) chains and two light (L) chains interconnected by disulfide bonds, and multimers thereof (e.g., IgM). Each heavy chain comprises a heavy chain variable region (abbreviated herein as HCVR or VH) and a heavy chain constant region. The heavy chain constant region comprises three domains, CH1, CH2, and CH3. Each light chain comprises a light chain variable region (abbreviated herein as LCVR or VL) and a light chain constant region. The light chain constant region comprises one domain (CL1). The VH and VL regions can be further subdivided into regions of hypervariability called complementarity-determining regions (CDRs), interspersed with more conserved regions called framework regions (FRs). Each VH and VL is composed of three CDRs and four FRs arranged from amino terminus to carboxy terminus in the following order: FR1, CDR1, FR2, CDR2, FR3, CDR3, and FR4. In different embodiments of the present invention, the FRs of an anti-big ET-1 antibody (or antigen-binding portion thereof) can be identical to human germline sequences or can be naturally or artificially modified. An amino acid consensus sequence can be defined based on a parallel analysis of two or more CDRs. The term "antibody," as used herein, also includes antigen-binding fragments of a complete antibody molecule. The terms "antigen-binding portion" of an antibody, "antigen-binding fragment" of an antibody, and the like, as used herein, include any naturally occurring, enzymatically obtainable, synthetic, or genetically engineered polypeptide or glycoprotein that specifically binds to an antigen to form a complex. Antigen-binding fragments of antibodies can be derived from complete antibody molecules using any suitable standard technique, such as proteolytic or recombinant genetic engineering techniques, involving the manipulation and expression of DNA encoding antibody variable domains and, optionally, constant domains. Such DNA is known and / or readily available from, for example, commercial sources, DNA libraries (including, for example, phage antibody libraries), or can be synthesized.The DNA can be sequenced and manipulated chemically or by using molecular biology techniques, for example, to arrange one or more variable and / or constant domains in a suitable configuration, or to introduce codons, generate cysteine ​​residues, modify, add or delete amino acids, etc.

[0061] As used herein, "antibody fragment" includes a portion of an intact antibody, such as, for example, the antigen-binding or variable region of an antibody. Examples of antibody fragments include, but are not limited to, Fab fragments, Fab' fragments, F(ab')2 fragments, scFv fragments, Fv fragments, dsFv diabodies, dAb fragments, Fd' fragments, Fd fragments, and isolated complementarity-determining region (CDR) regions, as well as triabodies, tetrabodies, linear antibodies, single-chain antibody molecules, and multispecific antibodies formed from antibody fragments. An Fv fragment is a combination of the variable regions of an immunoglobulin heavy and light chain, and an ScFv protein is a recombinant single-chain polypeptide molecule in which the variable regions of an immunoglobulin light and heavy chain are connected by a peptide linker. In some exemplary embodiments, an antibody fragment contains sufficient amino acid sequence of the parent antibody for the fragment to bind to the same antigen as the parent antibody, and in some exemplary embodiments, the fragment binds to the antigen with an affinity comparable to that of the parent antibody and / or competes with the parent antibody for binding to the antigen. Antibody fragments may be produced by any means. For example, antibody fragments may be enzymatically or chemically produced by fragmentation of an intact antibody and / or recombinantly produced from a gene encoding a partial antibody sequence. Alternatively, or in addition, antibody fragments may be wholly or partially synthetically produced. Antibody fragments may optionally comprise single-chain antibody fragments. Alternatively, or in addition, antibody fragments may comprise multiple chains linked together, for example, by disulfide bonds. Antibody fragments may optionally comprise multimolecular complexes. Functional antibody fragments typically comprise at least about 50 amino acids, more typically at least about 200 amino acids.

[0062] The term "bispecific antibody" includes antibodies capable of selectively binding two or more epitopes. Bispecific antibodies generally comprise two different heavy chains, each of which specifically binds to a different epitope, either on two different molecules (e.g., antigens) or on the same molecule (e.g., the same antigen). When a bispecific antibody is capable of selectively binding two different epitopes (a first epitope and a second epitope), the affinity of the first heavy chain for the first epitope is generally at least one to two, or three or four orders of magnitude lower than the affinity of the first heavy chain for the second epitope, or vice versa. The epitopes recognized by a bispecific antibody can be on the same or different targets (e.g., on the same or different proteins). Bispecific antibodies can be generated, for example, by combining heavy chains that recognize different epitopes of the same antigen. For example, nucleic acid sequences encoding heavy chain variable sequences that recognize different epitopes of the same antigen can be fused to nucleic acid sequences encoding different heavy chain constant regions, and such sequences can be expressed in cells that express immunoglobulin light chains.

[0063] A typical bispecific antibody has two heavy chains, each with three heavy-chain CDRs followed by a CH1 domain, a hinge, a CH2 domain, and a CH3 domain, and an immunoglobulin light chain that does not confer antigen-binding specificity but can associate with each heavy chain, or can associate with each heavy chain and bind to one or more of the epitopes bound by the heavy-chain antigen-binding region, or can associate with each heavy chain and allow binding of one or both of the heavy chains to one or both epitopes. BsAbs can be divided into two major classes: those that possess an Fc region (IgG-like) and those that lack an Fc region, the latter usually being smaller than Fc-containing IgG and IgG-like bispecific molecules. IgG-like bsAbs can have different forms such as, but not limited to, triomab, knobs-into-holes IgG (kih IgG), crossMab, orth-Fab IgG, dual variable domain Ig (DVD-Ig), two-in-one or dual acting Fab (DAF), IgG single chain Fv (IgG-scFv), or κλ body. Different non-IgG-like formats include tandem scFvs, diabody formats, single-chain diabodies, tandem diabodies (TandAbs), dual affinity retargeting molecules (DARTs), DART-Fc, nanobodies, or antibodies produced by the dock-and-lock (DNL) methodology (Gaowei Fan, Zujian Wang & Mingju Hao, Bispecific antibodies and their applications, 8 JOURNAL OF HEMATOLOGY & ONCOLOGY 130; Dafne Muller & Roland E. Kontermann, Bispecific Antibodies, HANDBOOK OF THERAPEUTIC ANTIBODIES 265-310 (2014)), the teachings of which are incorporated herein in their entirety).

[0064] As used herein, a "multispecific antibody" refers to an antibody that has binding specificities for at least two different antigens. Such molecules typically bind only two antigens (e.g., bispecific antibodies, bsAbs), although antibodies with additional specificities, such as trispecific antibodies and KIH trispecifics, can also be addressed by the systems and methods disclosed herein.

[0065] The term "monoclonal antibody" as used herein is not limited to antibodies produced through hybridoma technology. Monoclonal antibodies may be derived from a single clone, including any eukaryotic, prokaryotic, or phage clone, by any means available or known in the art. Monoclonal antibodies useful in the present disclosure can be prepared using a wide variety of techniques known in the art, including the use of hybridoma, recombinant, and phage display technologies, or a combination thereof.

[0066] In some exemplary embodiments, proteins and pharmaceutical protein products can be produced from mammalian cells. Mammalian cells can be of human or non-human origin and include primary epithelial cells (e.g., keratinocytes, cervical epithelial cells, bronchial epithelial cells, tracheal epithelial cells, renal epithelial cells, and retinal epithelial cells), established cell lines and their lineages (e.g., 293 embryonic kidney cells, BHK cells, HeLa cervical epithelial cells and PER-C6 retinal cells, MDBK (NBL-1) cells, 911 cells, CRFK cells, MDCK cells, CHO cells, BeWo cells, Chang cells, Detroit 562 cells, HeLa229 cells, HeLa S3 cells, Hep-2 cells, KB cells, LSI80 cells, LS174T cells, NCI-H-548 cells, RPMI2650 cells, SW-13 cells, T24 cells, WI-28 cells, and the like).VA13, 2RA cells, WISH cells, BS-CI cells, LLC-MK2 cells, Clone M-3 cells, 1-10 cells, RAG cells, TCMK-1 cells, Yl cells, LLC-PKi cells, PK(15) cells, GH i cells, GH3 cells, L2 cells, LLC-RC256 cells, MHiCi cells, XC cells, MDOK cells, VSW cells, and TH-I, B1 cells, BSC-1 cells, RAf cells, RK cells, PK-15 cells, or derivatives thereof), Fibroblasts from any tissue or organ (including, but not limited to, heart, liver, kidney, colon, intestine, esophagus, stomach, nervous tissue (brain, spinal cord), lung, vascular tissue (arteries, veins, capillaries), lymphatic tissue (lymph glands, pharyngeal adenoids, tonsils, bone marrow, and blood), spleen), as well as fibroblasts and fibroblast-like cell lines (e.g., CHO cells, TRG-2 cells, IMR-33 cells, Don cells, GHK-21 cells, citrullinemia cells, Dempsey cells, Detroit 551 cells, Detroit 510 cells, Detroit 525 cells, Detroit 529 cells, Detroit 532 cells, Detroit 539 cells, Detroit 548 cells, Detroit 573 cells, HEL299 cells, IMR-90 cells, MRC-5 cells, WI-38 cells, WI-26 cells, Midi cells, CHO cells, CV-1 cells, COS-1 cells, COS-3 cells, COS-7 cells, Vero cells, DBS-FrhL-2 cells, BALB / 3T3 cells The cells may include, for example, mouse L cells, F9 cells, SV-T2 cells, M-MSV-BALB / 3T3 cells, K-BALB cells, BLO-11 cells, NOR-10 cells, C3H / IOTI / 2 cells, HSDMiC3 cells, KLN205 cells, McCoy cells, mouse L cells, line 2071 (mouse L) cells, LM line (mouse L) cells, L-MTK' (mouse L) cells, NCTC clones 2472 and 2555, SCC-PSA1 cells, Swiss / 3T3 cells, Indian muntjac cells, SIRC cells, Cn cells, and Jensen cells, Sp2 / 0, NS0, NS1 cells, or derivatives thereof.

[0067] In some exemplary embodiments, the compositions can be used to treat, prevent, and / or ameliorate a disease or disorder. Exemplary, non-limiting diseases and disorders that can be treated and / or prevented by administration of the pharmaceutical formulations of the present invention include infections, respiratory disorders, pain resulting from any condition associated with neurogenic, neuropathic, or nociceptive pain, genetic disorders, congenital disorders, cancer, dermatitis herpetiformis, chronic idiopathic urticaria, scleroderma, hypertrophic scarring, Whipple's disease, benign prostatic hyperplasia, pulmonary disorders such as mild, moderate, or severe asthma, allergic reactions, Kawasaki disease, sickle cell disease, Churg-Strauss syndrome, Graves' disease, preeclampsia, Sjogren's syndrome, autoimmune lymphoproliferative syndrome, autoimmune hemolytic anemia, Barrett's disease, and others. esophagus, autoimmune uveitis, tuberculosis, nephrosis, arthritis including rheumatoid arthritis, inflammatory bowel disease including Crohn's disease and ulcerative colitis, systemic lupus erythematosus, inflammatory diseases, HIV infection, AIDS, LDL apheresis, diseases caused by PCSK9 activating mutations (gain-of-function mutations, "GOF"), disorders caused by heterozygous familial hypercholesterolemia (heFH), primary hypercholesterolemia, dyslipidemia, cholestatic liver disease, nephrotic syndrome, hypothyroidism, obesity, atherosclerosis, cardiovascular disease, neurodegenerative diseases, neonatal-onset multisystem inflammatory disorder (NOM)ID / CINCA), Muckle-Wells syndrome (MWS), familial cold autoinflammatory syndrome (FCAS), familial Mediterranean fever (FMF), tumor necrosis factor receptor-associated periodic fever syndrome (TRAPS), systemic-onset juvenile idiopathic arthritis (Still's disease), type 1 and type 2 diabetes, autoimmune diseases, motor neuron diseases, eye diseases, sexually transmitted diseases, tuberculosis, diseases or conditions that are ameliorated, inhibited, or alleviated by VEGF antagonists, diseases or conditions that are ameliorated, inhibited, or alleviated by PD-1 inhibitors, diseases or conditions that are ameliorated, inhibited, or alleviated by interleukin antibodies, diseases or conditions that are ameliorated, inhibited, or alleviated by NGF antibodies, diseases or conditions that are ameliorated, inhibited, or alleviated by PCSK9 antibodies, diseases or conditions that are ameliorated, inhibited, or alleviated by ANGPTL antibodies, diseases or conditions that are ameliorated, inhibited, or alleviated by activin antibodies, diseases or conditions that are ameliorated, inhibited, or alleviated by GDF antibodies, Fel d The disease or condition may be ameliorated, inhibited, or alleviated by a C1 antibody, a disease or condition ameliorated, inhibited, or alleviated by a CD antibody, a disease or condition ameliorated, inhibited, or alleviated by a C5 antibody, or a combination thereof.

[0068] In some exemplary embodiments, the composition can be administered to a patient. Administration can be via any route acceptable to those skilled in the art. Non-limiting administration routes include oral, topical, or parenteral. Administration via certain parenteral routes can involve introducing the formulation of the present invention into the patient's body through a needle or catheter propelled by a sterile syringe or some other mechanical device, such as a continuous infusion system. The composition can be administered using a syringe, infuser, pump, or any other device recognized in the art for parenteral administration. The composition can also be administered as an aerosol for absorption through the lungs or nasal cavity. A solution can also be administered for absorption through mucous membranes, such as by oral administration.

[0069] In some exemplary embodiments, the formulation may further comprise excipients, including, but not limited to, buffering agents, bulking agents, tonicity agents, solubilizing agents, and preservatives. Other additional excipients can also be selected based on function and compatibility with the formulation, as described, for example, in Remington: The Science and Practice of Pharmacy, (2005); US Pharmacopeia: National Formulary; Louis Sanford Goodman et al., Goodman & Gilmans, The Pharmacological Basis of Therapeutics (2001); Kenneth E. Avis, Herbert A. Lieberman & Leon Lachman, Pharmaceutical Dosage Forms: Parenteral Medications (1992); Praful Agrawala, Pharmaceutical Dosage Forms: Tablets. Volume 1, 79 Journal of Pharmaceutical Sciences 188 (1990); Herbert A. Lieberman, Martin M. Rieger & Gilbert S. Banker, Pharmaceutical Dosage Forms: Disperse Systems (1996); Myra L. Weiner & Louis A. Kotkoskie, Excipient toxicity and safety (2000).

[0070] As used herein, the volume of a "large-scale solution" can have a volume of about 0.2 L to about 100 L, about 1 L to about 75 L, about 2 L to about 50 L, about 5 L to about 25 L, about 0.2 L, about 0.5 L, about 1 L, about 2 L, about 3 L, about 4 L, about 5 L, about 7.5 L, about 10 L, about 15 L, about 16.6 L, about 20 L, about 25 L, about 30 L, about 40 L, about 50 L, about 60 L, about 70 L, about 75 L, about 80 L, about 90 L, or about 100 L.

[0071] Large-scale solutions include approximately 0.2L to approximately 100L, approximately 1L to approximately 75L, approximately 2L to approximately 50L, approximately 5L to approximately 25L, approximately 0.2L, approximately 0.5L, approximately 1L, approximately 2L, approximately 3L, approximately 4L, approximately 5L, approximately 7.5L, approximately 8.3L, approximately 10L, It can be in a container (eg, a bulk container) having a volume of about 15 L, about 16.6 L, about 20 L, about 25 L, about 30 L, about 40 L, about 50 L, about 60 L, about 70 L, about 75 L, about 80 L, about 80 L, or about 100 L.

[0072] As used herein, the volume of a "small scale solution" can be about 1 mL to about 200 mL, about 5 mL to about 100 mL, about 10 mL to 75 mL, about 25 mL to about 50 mL, about 1 mL, about 2 mL, about 3 mL, about 4 mL, about 5 mL, about 7.5 mL, about 10 mL, about 15 mL, about 20 mL, about 25 mL, about 30 mL, about 40 mL, about 50 mL, about 60 mL, about 70 mL, about 75 mL, about 80 mL, about 90 mL, about 100 mL, about 125 mL, about 150 mL, about 175 mL, or about 200 mL.

[0073] The small-scale solution can be in a container (e.g., a small-scale container) having a volume of about 30 mL to about 250 mL, about 50 mL to about 200 mL, about 75 mL to about 175 mL, about 100 mL to about 150 mL, about 30 mL, about 40 mL, about 50 mL, about 75 mL, about 100 mL, about 125 mL, about 150 mL, about 200 mL, or about 250 mL.

[0074] As used herein, a "freezing profile" refers to any one or more quantitative measures of a freezing process that can be used to quantitatively determine at least one freezing rate. Exemplary embodiments quantitatively determine the freezing rate throughout the freezing process until the solution is frozen. In some embodiments, the freezing rate can be measured directly. In some embodiments, the freezing rate can be determined indirectly by measuring at least one physical quantity of the freezing process. Illustrative, non-limiting examples of quantitative measures that can be used to determine the thawing rate include thermodynamic temperature, electrical conductivity, osmolality, evaporation, condensation, direct or indirect observation of crystal formation, density, flow rate, viscosity, and any combination thereof.

[0075] As used herein, "freezing rate" refers to the rate at which a solution decreases in thermodynamic temperature. For example, the freezing rate can be the instantaneous rate at which the thermodynamic temperature of a point in a solution decreases during the freezing process, the instantaneous rate at which the average thermodynamic temperature of a quantity of solution decreases during the freezing process, the average rate at which the thermodynamic temperature of a point in a solution decreases throughout the freezing process (e.g., from the time the solution is first subjected to freezing conditions to the time the entire solution is first frozen), or the average rate at which the average thermodynamic temperature of a quantity of solution decreases throughout the freezing process (e.g., from the time the solution is first subjected to freezing conditions to the time the entire solution is first frozen).

[0076] As used herein, a "thawing profile" refers to any quantitative measure of the thawing process that can be used to quantitatively determine at least one thawing rate. Exemplary embodiments quantitatively determine the thawing rate throughout the thawing process until the solution is thawed. In some embodiments, the thawing rate can be measured directly. In some embodiments, the thawing rate can be determined indirectly by measuring at least one physical quantity of the thawing process. Illustrative, non-limiting examples of quantitative measures that can be used to determine the thawing rate include thermodynamic temperature, electrical conductivity, osmolality, evaporation, condensation, direct or indirect observation of crystalline melting, density, flow rate, viscosity, and any combination thereof.

[0077] As used herein, "thawing rate" refers to the rate at which a solution increases in thermodynamic temperature. For example, the thawing rate can be the instantaneous rate at which the thermodynamic temperature of a point in a solution increases during the thawing process, the instantaneous rate at which the average thermodynamic temperature of a quantity of solution increases during the thawing process, the average rate at which the thermodynamic temperature of a point in a solution increases throughout the thawing process (e.g., from the time the solution is first subjected to thawing conditions to the time the entire solution is first thawed), or the average rate at which the average thermodynamic temperature of a quantity of solution increases throughout the thawing process (e.g., from the time the solution is first subjected to thawing conditions to the time the entire solution is first thawed).

[0078] As used herein, "freezing operating conditions" refers to the thermal and mechanical properties of the material inputs into a freezing system, as well as the operating conditions of the freezing system (e.g., freezing operating conditions) that may affect the freezing process. Exemplary, non-limiting freezing operating conditions that may be included in the freezing operating conditions include temperature, convection mode, volume of solution, mechanical properties of the solution, thermal properties of the solution, geometry of the solution, volume of the container, mechanical properties of the container, thermal properties of the container, geometry of the container, air between the fill level and the upper boundary of the container, adjacent airflow mechanisms, proximity of the container to other containers in the freezing environment, and any combination thereof.

[0079] As used herein, "thaw operating conditions" refers to the thermal and mechanical properties of the material input into the thaw system and the operating conditions of the thaw system (e.g., thaw operating conditions) that may affect the thawing process. Exemplary, non-limiting thaw operating conditions that may be included in the thaw operating conditions include temperature, convection mode, volume of solution, mechanical properties of the solution, thermal properties of the solution, geometry of the solution, volume of the container, mechanical properties of the container, thermal properties of the container, geometry of the container, air between the fill level and the upper boundary of the container, adjacent airflow mechanisms, proximity of the container to other containers in the freezing environment, and any combination thereof.

[0080] As used herein, a "transient temperature boundary equation" is an equation fitted to the predicted average thermodynamic temperature of a large-scale solution during a freeze-thaw process. Predicting the freeze-thaw profile of a large-scale solution can provide the predicted average thermodynamic temperature of the large-scale solution during the freeze-thaw process (e.g., the transient thermodynamic temperature of the solution during the freeze-thaw process) throughout the freeze-thaw process. The disclosed computational fluid dynamics model can replicate the predicted average thermodynamic temperature of the large-scale solution during the freeze-thaw process in the small-scale solution by predicting and subjecting the small-scale solution to a set temperature sequence. The disclosed computational fluid dynamics model can set the transient temperature boundary equation as a boundary condition while predicting a set temperature sequence that reproduces the freeze-thaw profile of the large-scale solution in the small-scale solution. Thus, the transient temperature boundary equation informs the disclosed computational fluid dynamics model of the average thermodynamic temperature that must be generated in the small-scale solution at each point during the freeze-thaw process in order for the set temperature progression to reproduce the large-scale freeze-thaw profile.

[0081] The present invention is not limited to the aforementioned solutions, compositions, drugs, pharmaceuticals, proteins, pharmaceutical protein products, proteins, polypeptides, synthetic polypeptides, recombinant proteins, antibodies, antigen-binding portions, antigen-binding fragments, antibody fragments, bispecific antibodies, multispecific antibodies, formulations, excipients, cells, large-scale solutions, small-scale solutions, freezing profiles, freezing rates, thawing profiles, thawing rates, freezing operating conditions, thawing operating conditions, or transient temperature boundary equations; and the solutions, compositions, drugs, pharmaceuticals, proteins, pharmaceutical protein products, proteins, polypeptides, synthetic polypeptides, recombinant proteins, antibodies, antigen-binding portions, antigen-binding fragments, antibody fragments, bispecific antibodies, multispecific antibodies, formulations, excipients, cells, large-scale solutions, small-scale solutions, freezing profiles, freezing rates, thawing profiles, thawing rates, freezing operating conditions, thawing operating conditions, or transient temperature boundary equations may be selected by any suitable means.

[0082] Existing methods for determining the freeze-thaw rate of a large-scale freeze-thaw process and its effect on pharmaceutical quality attributes require large quantities of pharmaceutical material. Problematically, producing the necessary amount of pharmaceutical material for large-scale testing requires significant financial, labor, material, time, and other resources. Thus, resource limitations can hinder the optimization of large-scale freeze-thaw operating conditions. In contrast, exemplary embodiments of the present disclosure can provide site-specific modeling of pharmaceutical freeze-thaw processes within containers across scales and geometries within a range of freeze-thaw operating conditions. Furthermore, exemplary embodiments of the present disclosure can reproduce the freeze-thaw rate of a large-scale pharmaceutical freeze-thaw process in small-scale experiments. Thus, the effect of large-scale freeze-thaw rates on pharmaceutical quality attributes can be determined using minimal amounts of pharmaceutical material. Consequently, exemplary embodiments of the present disclosure enable more rigorous and cost-effective optimization of large-scale pharmaceutical freeze-thaw operating conditions than existing methods.

[0083] For example, FIG. 1 illustrates an overview of a computational fluid dynamics model of the present disclosure, according to an exemplary embodiment. A system of equations representing the physics of material inputs undergoing freeze-thaw operating conditions can govern the computational fluid dynamics model of the present disclosure. User input can provide information about the material inputs undergoing freeze-thaw operating conditions to the computational fluid dynamics model of the present disclosure. Information about the material inputs undergoing freeze-thaw operating conditions can include, but is not limited to, the geometry of the container and the mechanical and thermal properties of the material inputs, including any and all portions of the composition formulation. For example, FIG. 2 illustrates a representation of a large-scale solution (e.g., about 0.2 L to about 100 L) in a large-scale container (e.g., about 0.5 L to about 100 L) having a rectangular cube geometry in a computational fluid dynamics model of the present disclosure, according to an exemplary embodiment. FIG. 2 also illustrates a representation of a small-scale solution in a small-scale container (e.g., about 30 mL to about 250 mL) having an inflated bag geometry in a computational fluid dynamics model of the present disclosure, according to an exemplary embodiment. User input can also provide information about the freeze-thaw operating conditions to the computational fluid dynamics model of the present disclosure. Information about freeze-thaw operating conditions can include container temperature, convection mode, adjacent airflow, density, and proximity to each other.

[0084] The computational fluid dynamics models of the present disclosure can be modeled using, for example, the fluid simulation software ANSYS Fluent (ANSYS, Inc., Cannonsburg, Pennsylvania). For a comprehensive overview of modeling options available within ANSYS Fluent that are compatible with the computational fluid dynamics models of the present disclosure, see the ANSYS Fluent Theory Guide, Release 2021 R1, January 2021, ANSYS, Inc., the teachings of which are incorporated herein in their entirety, and the ANSYS Fluent User's Guide, Release 2021 R1, January 2021, ANSYS, Inc., the teachings of which are incorporated herein in their entirety. The system of equations governing the computational fluid dynamics models of the present disclosure can model, for example, mass transfer and heat transfer. Equations included in the governing system can include, for example, the Navier-Stokes equations, the mass conservation equation, the momentum conservation equation, the energy conservation equation, the energy equation, the turbulence equation, the species equation, the equations of inverse diffusion, and equations modeling thermal and solutal buoyancy. The shell conduction method can be used, for example, to model the material of the boundary imposed by the container to account for the effects of the container material without solving for the material structure. The mushy zone approximation method can be used, for example, to model the freezing front within the container so that the freezing of the liquid is spatially advanced based on the modeled freezing operating conditions. Multiphase flow simulation can be used, for example, to model stagnant air between the solution fill level and the upper boundary of the container. The fluid volume method can be used, for example, to model the gas-liquid interface. The interfacial diffusion-preventing surface model can be used, for example, to account for significant differences between the viscosities of air and solution.

[0085] The computational fluid dynamics model of the present embodiment can use information about the material inputs and freeze-thaw operating conditions to determine a solution to a selected system of equations. The solution to the governing system of equations can provide a physical measure of the freeze-thaw process within a vessel subjected to the freeze-thaw operating conditions. However, determining an analytical solution to the selected system of equations can be difficult. Instead, the computational fluid dynamics model of the present disclosure can use space and time discretization to determine a numerical solution that approximates the analytical solution to the selected system of equations.

[0086] Spatial discretization divides the spatial domain within a container into discrete volumes at points while the container is undergoing freeze-thaw operating conditions. FIG. 3 illustrates the spatial domain of a large-scale container divided into discrete volumes after spatial discretization at points while the container is undergoing freezing operating conditions, according to an exemplary embodiment. The computational fluid dynamics model of the present disclosure can determine a numerical solution that approximates (e.g., predicts) the average value of the analytical solution within each discrete volume of the discretized spatial domain within the container (e.g., location-specific). For example, FIG. 4 illustrates the predicted thermodynamic temperature of a small-scale solution within a small-scale container at points while the small-scale container is undergoing freezing operating conditions, according to an exemplary embodiment. Additionally, FIG. 5 illustrates the predicted velocity within a large-scale container partially filled with a large-scale solution at points while the large-scale container is undergoing freezing operating conditions, according to an exemplary embodiment. Thus, the computational fluid dynamics model of the present disclosure can predict the physical measures of the freeze-thaw process for the entire spatial domain within a container undergoing freeze-thaw operating conditions across scales and geometries.

[0087] The time discretization performs spatial discretization at regular intervals while the container undergoes freeze-thaw operating conditions. The computational fluid dynamics model can use interpolation to approximate analytical solutions at time points between successive spatial discretization operations. For example, FIG. 6 shows predicted thermodynamic temperatures within a large-scale solution within a large-scale container at two points while the large-scale container undergoes freezing operating conditions, according to an exemplary embodiment. Thus, the computational fluid dynamics model of the present disclosure can approximate (e.g., predict) physical measures of the freeze-thaw process within a container undergoing freeze-thaw operating conditions throughout the spatial-temporal domain.

[0088] The numerical solution determined by the disclosed computational fluid dynamics model can predict the thermodynamic temperature of a solution in a container subjected to freeze-thaw operating conditions. For example, Figures 4-6 show the thermodynamic temperatures of a solution predicted by the disclosed computational fluid dynamics model when subjected to modeled freezing operating conditions, according to exemplary embodiments. The thermodynamic temperatures of a solution subjected to freeze-thaw operating conditions can determine the total freeze-thaw time, the initial freeze point, the initial thaw point, the final freeze point, the final thaw point, the time to center freeze, the time to center thaw, and the temperature profile at the edge of the solution. For example, Figure 7 shows that the disclosed computational fluid dynamics model can predict whether 48 hours is sufficient time for freezing operating conditions to freeze 3.5 L of high- or low-concentration drug substance / free drug substance solution in a 5 L polycarbonate bottle. User input can provide information about the material inputs and freezing operating conditions to the computational fluid dynamics model shown in Figure 7, including the position of the 5 L polycarbonate bottle relative to the other bottles in the freezing operating conditions. The computational fluid dynamics model shown in Figure 7 can make conservative predictions by modeling the theoretical last point of a solution to freeze (i.e., the center of the solution). In addition, Figure 8 shows the last point of freezing (e.g., the red sphere) in a small-scale solution subjected to freezing operating conditions predicted by the computational fluid dynamics model of the present disclosure, according to an exemplary embodiment. The numerical solution determined by the computational fluid dynamics model of the present disclosure can also approximate the freeze-thaw rate of a solution subjected to freeze-thaw operating conditions.

[0089] Spatially weighting the predicted physical measures of a solution undergoing freeze-thaw operating conditions and interpolation can provide average physical measures while the solution is undergoing freeze-thaw operating conditions. For example, FIG. 9 shows that the disclosed computational fluid dynamics model, according to an exemplary embodiment, can predict an average representation of a large-scale solution undergoing freeze-thaw operating conditions, including average temperature, using weighted averaging. Furthermore, weighted averaging enables the disclosed computational fluid dynamics model to model the freeze-thaw process of a solution across scales and geometries. For example, FIG. 2 shows a representation of a large-scale solution in a large-scale container with a rectangular cube geometry and a small-scale solution in a small-scale container with an inflated bag geometry within the disclosed computational fluid dynamics model, according to an exemplary embodiment. Additionally, FIGS. 5-7 show the physical measures of a large-scale solution in a large-scale container with a vertical cube geometry predicted by the disclosed computational fluid dynamics model, according to an exemplary embodiment. In contrast, FIGS. 4 and 8 show the physical measures of a small-scale solution in a small-scale container with an inflated bag geometry predicted by the disclosed computational fluid dynamics model, according to an exemplary embodiment.

[0090] In some embodiments, the average physical measure of a solution subjected to freeze-thaw operating conditions can be a freeze-thaw profile. In some embodiments, the freeze-thaw profile can include a predicted average temperature and total freeze-thaw time of a solution subjected to freeze-thaw operating conditions. Figure 9 also shows that the computational fluid dynamics model of the present disclosure can develop a set temperature sequence to represent an average amount of a large-scale solution subjected to freeze-thaw operating conditions in a small-scale solution. In some embodiments, the small-scale solution subjected to the set temperature sequence developed by the computational fluid dynamics model reproduces the predicted average temperature profile (e.g., predicted freeze-thaw profile) of the large-scale solution in the small-scale solution.

[0091] In some embodiments, a computational fluid dynamics model can develop a set temperature sequence by first fitting an equation to the predicted freeze-thaw profile of a large-scale solution. Figure 10 illustrates an exponential equation fitted to the average thermodynamic temperature of a freezing profile of a large-scale solution by a computational fluid dynamics model of the present disclosure, according to an exemplary embodiment. In some embodiments, the computational fluid dynamics model can then set the equation as a transient temperature boundary condition when predicting the set temperature sequence and the freeze-thaw profile of a small-scale solution subjected to the set temperature sequence. In one aspect, a computational fluid dynamics model of the present disclosure can refine a set temperature sequence prediction until the predicted total freeze-thaw time of the small-scale solution differs by no more than about 10% from the predicted total freeze-thaw time of the large-scale solution. In another aspect, a computational fluid dynamics model of the present disclosure can refine a set temperature sequence prediction until the predicted average temperature of the small-scale solution differs by no more than about 10% from the predicted average temperature of the large-scale solution at any point during the freeze-thaw process.

[0092] In some embodiments, the small-scale solution can be subjected to a set temperature sequence predicted to replicate the freeze-thaw profile of the large-scale solution. In one aspect, the computational fluid dynamics model can operate a temperature regulation system to generate the set temperature sequence. In an exemplary embodiment depicted in FIG. 11 , the computational fluid dynamics model can operate a Celsius® S3 Benchtop Freezing Platform (Sartorius Stedim Biotech GmbH, Gottingen, Germany) to replicate the freeze-thaw profile of a large-scale solution in a 1 L or 5 L polycarbonate bottle (Thermo Fisher Scientific, Waltham, Massachusetts) on a small-scale solution in a 30 mL bag. In one aspect, the temperature of at least one point of interest in the small-scale solution can be measured during the freeze-thaw process. In another aspect, the measured temperature of at least one point of interest in the small-scale solution can be measured while the small-scale solution is undergoing the set temperature sequence. In yet another aspect, the measured temperature of at least one point of interest in the small-scale solution undergoing the set temperature sequence can be used to determine the average temperature of the small-scale solution while undergoing the set temperature sequence. In another aspect, the average temperature of the small-scale solution subjected to the set temperature sequence can be used to determine the total freeze-thaw time, and the actual freeze-thaw profile of the small-scale solution can include the total freeze-thaw time and the average temperature of the small-scale solution subjected to the set temperature sequence.

[0093] In one aspect, a large-scale solution modeled by a computational fluid dynamics model can be subjected to the modeled freeze-thaw operating conditions while measuring the temperature of at least one point of interest. In another aspect, the measured temperature of at least one point of interest in the large-scale solution subjected to a set of freeze-thaw operating conditions can be used to determine an average temperature of the large-scale solution. In yet another aspect, the average temperature of the large-scale solution during the freeze-thaw process can be used to determine a total freeze-thaw time for the solution, and an actual freeze-thaw profile for the large-scale solution can include the total freeze-thaw time and average temperature of the large-scale solution subjected to the set of freeze-thaw operating conditions.

[0094] In one aspect, the total freeze-thaw times of the actual and predicted large-scale and small-scale freeze-thaw profiles may not differ from each other by more than about 10%. In another aspect, the average temperatures of the actual and predicted large-scale and small-scale freeze-thaw profiles at a point during the freeze-thaw process may not differ from each other by more than about 10%. Figure 2 depicts an exemplary embodiment in which the actual and predicted total freeze-thaw times of a large-scale solution in a 5 L polycarbonate bottle and a small-scale solution in a 100 mL bag may differ by less than about 6.67%.

[0095] The present disclosure provides the benefit of determining the effect of large-scale freeze-thaw rates on the quality characteristics of freeze-thaw sensitive materials without conducting large-scale experiments. Thus, in one embodiment, a small amount of at least one quality characteristic can be determined after a freeze-thaw process. The quality characteristic of the present disclosure can be a physical, chemical, biological, or microbiological property or characteristic that should be within an appropriate limit, range, or distribution to ensure the desired product quality.

[0096] For example, in one aspect, the solution can comprise a pharmaceutical agent, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, an Fab region of an antibody, an antibody drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody. Thus, the disclosed method provides a robust and cost-effective way to optimize large-scale pharmaceutical freeze-thaw processes to ensure the quality, safety, and efficacy of drugs for patients. Shell Conduction

[0097] In some embodiments, the shell conduction method can be used to model the material of the boundary imposed by the vessel and account for the vessel's material effects without solving for the material structure. The shell conduction method can account for thermal mass in transient thermal analysis problems. The shell conduction method can also enable heat conduction through multiple junctions. The shell conduction method can be applied to boundaries and interior walls. Using fluid simulation software such as ANSYS Fluent (ANSYS, Inc., Cannonsburg, Pennsylvania), the shell conduction method can model heat conduction in the plane and normal to the boundary imposed by the wall. The shell conduction method can model thin sheets without the need to mesh the wall thickness in a preprocessor. Users can turn on or off conjugate heat transfer for any wall when the shell conduction method is used. Specifying the thickness and material properties of the wall boundary in ANSYS Fluent and enabling the shell conduction method can cause ANSYS Fluent to grow a layer of prismatic or hexagonal cells in the wall, depending on the type of face mesh used. Modeling a wall-imposed boundary without using the shell conduction method and without specifying the thickness of the boundary imposed by the vessel may cause the vessel material to present no thermal resistance to heat transfer in the model. Alternatively, specifying the thickness of the boundary imposed by the vessel without using the shell conduction method may only produce an appropriate thermal resistance across the boundary imposed by the vessel in the normal direction. Large-scale containers

[0098] In some embodiments, the computational fluid dynamics model is capable of predicting the location-specific physical quantities of the freeze-thaw process for the entire spatial domain within a large-scale vessel having a volume across its geometry ranging from about 1 L to about 20 L. In some embodiments, the computational fluid dynamics model is capable of predicting the location-specific physical quantities of the freeze-thaw process for a large-scale solution having a volume across its geometry ranging from about 0.75 L to about 15 L.

[0099] Exemplary, non-limiting, large-scale containers for which the computational fluid dynamics model can predict the location-specific physical quantities of the freeze-thaw process for the entire spatial domain within the container include a 1 L polycarbonate bottle, a 2 L polycarbonate bottle, a 5 L polycarbonate bottle, a 10 L polycarbonate bottle, a 20 L polycarbonate bottle, a 1 L bag, a 2 L bag, an 8.3 L bag, and a 16.6 L bag. Exemplary, non-limiting, large-scale container geometries for which the computational fluid dynamics model can predict the location-specific physical quantities of the freeze-thaw process for the entire spatial domain within the container. In one aspect, the large-scale container is a container with a square geometry, and in one aspect, the small-scale container is a solution with a bag geometry, where the solution inside the bag causes expansion. Small Containers

[0100] In some embodiments, the computational fluid dynamics model can predict the location-specific physical quantities of the freeze-thaw process for the entire spatial domain within a small-scale container having a volume ranging from about 30 mL to about 100 mL across its geometry. In some embodiments, the computational fluid dynamics model can predict the location-specific physical quantities of the freeze-thaw process for a small-scale solution ranging from about 20 mL to about 100 mL across its geometry.

[0101] Exemplary, non-limiting, small-scale containers for which the computational fluid dynamics model can predict the location-specific physical quantities of the freeze-thaw process for the entire spatial domain within the container include 30 mL bags and 100 mL bags. Exemplary, non-limiting, small-scale containers for which the computational fluid dynamics model can predict the location-specific physical quantities of the freeze-thaw process for the entire spatial domain within the container include bag geometries where the solution inside the bag causes expansion.

[0102] The present invention will be more fully understood by reference to the following examples, which should not, however, be construed as limiting the scope of the invention. Example 1

[0103] Temperature probes monitored the temperature of the large-scale volume of solution at multiple points of interest throughout the freeze-thaw process to determine the freezing rate. Information about the freeze-thaw rates informed a computational fluid dynamics (CFD) model of the freeze-thaw system. The CFD model was designed to provide location-specific predictions of the freeze-thaw rates of the solution at all locations within the vessel across scales and geometries. The CFD model was also designed to control a temperature regulation system such that the small-scale freeze-thaw rates of the solution mimicked the large-scale freeze-thaw rates.

[0104] The CFD model was validated, in part, by comparing the total freezing time of the large-scale solution in a 5 L Nalgene™ Polycarbonate Biotainer™ bottle with the total freezing time of the large-scale solution in a 5 L Nalgene™ Polycarbonate Biotainer™ bottle predicted by the CFD model (e.g., "Predicted Large-Scale Freezing Profile"). The predicted total freezing time (e.g., 6.75 hours) and the actual total freezing time (e.g., 7 hours) of the large-scale solution differed by 3.57%, as seen in FIG. 12 (e.g., "Large-Scale Experiment"). The CFD model then fit an equation to the predicted average thermodynamic temperature in the large-scale freezing profile and set the equation as the transient temperature boundary condition. The CFD model then predicted the freezing profile of the small-scale solution in a 100 mL Celsius® Pak simultaneously subjected to a set temperature sequence (e.g., "Predicted Small-Scale Freezing Profile") and developed a set temperature sequence such that the predicted small-scale freezing profile mimicked the predicted large-scale freezing profile. The CFD model then generated small-scale inputs that could manipulate the setpoint temperature of the Celsius® S3 Benchtop Freezing Platform according to the developed temperature progression scheme, as seen in Figure 11. The CFD model was then further validated by freezing a small-scale amount of solution in a 100 mL Celsius® Pak using the Celsius® S3 Benchtop Freezing Platform manipulated by the small-scale inputs and comparing the predicted and actual total freezing times of the small-scale solution with the actual total freezing times of the large-scale solution, as seen in Figure 12. The predicted and actual total freezing times of the small-scale solution (e.g., 6.83 hours) and the actual total freezing times (e.g., 7.2 hours) differed by 2.43% and 2.86%, respectively, from the actual total freezing times of the large-scale solution, as seen in Figure 12.

[0105] The CFD model included a system of governing equations with simplifying assumptions to mathematically describe the underlying physics of the freezing system, as seen in Figure 1. The system of equations modeled mass transfer, heat transfer, and material properties within the freezing system. User input provided information about the material inputs and operating conditions to the CFD model equations, as seen in Figure 1. Material information included the vessel geometry and mechanical and thermal properties of the material inputs, as seen in Figure 1. Operating condition information included temperature, convection mode, adjacent airflow mechanisms, and the vessel's proximity to other vessels within the freezing operating conditions, as seen in Figure 1. The numerical solution approximated the sequential solution of the different equations within the system of governing equations for the CFD model using spatial discretization with a time advancement scheme, as seen in Figure 1. The spatial discretization spatially averaged regions within the vessel across the spatial domain at discrete times during the simulation of the freezing process, as seen in Figure 1. The spatially averaged fields provided an approximation of the continuous solution of the different equations at discrete times, as can be seen in Figure 1 .

[0106] Temporal spatialization implemented a continuous spatial discretization technique for the span of the time domain for the simulation of the freezing process, as seen in Figure 1. As a result, the CFD model was able to provide location-specific approximations of the physical quantities of the freezing process, including the freeze-thaw rate at any point within the container, after receiving information about the freezing system from user input. Weighted spatial averaging inside the freezing domain allowed the CFD model to reduce the average representation of the bulk volume of a 5 L Nalgene™ Polycarbonate Biotainer™ bottle to a 100 mL Celsius™ Pak, as seen in Figure 9. Thus, the 100 mL Celsius™ Pak was an average representation of the bulk volume of a 5 L Nalgene™ Polycarbonate Biotainer™ bottle.

[0107] The shell conduction method was used to model a 5L Nalgene™ Polycarbonate Biotainer™ bottle material and a 100mL Celsius® Pak™ material to account for the effects of the bottle material without the extensive cost of solving for the material structure. The 100mL Celsius® Pak model containing the solution mimicked the heat transfer rate of the 5L Nalgene™ Polycarbonate Biotainer™ bottle, reflecting the expansion caused by the solution and the more moderate convective heat transfer gradient across the sides and bottom. The shell conduction method can account for thermal mass in transient thermal analysis problems. The shell conduction method can also allow for heat conduction through multiple junctions. The shell conduction method can be applied to boundary and interior walls. Using the fluid simulation software ANSYS Fluent, the shell conduction method can model heat conduction in the plane and normal to the boundary imposed by the wall. The shell conduction method can model thin sheets without the need to mesh the wall thickness in a preprocessor. Users can turn on or off conjugate heat transfer for any wall when the shell conduction method is used. Specifying wall boundary thickness, material properties, and enabling the shell conduction method in ANSYS Fluent can cause ANSYS Fluent to grow a layer of prismatic or hexagonal cells for the wall, depending on the type of face mesh used. Modeling a wall-imposed boundary without using the shell conduction method and without specifying the thickness of the vessel-imposed boundary may cause the vessel material to present no thermal resistance to heat transfer. Alternatively, specifying the thickness of the vessel-imposed boundary without using the shell conduction method may only produce an appropriate thermal resistance across the vessel-imposed boundary in the normal direction.

[0108] ANSYS Fluent modeled the freezing front using the mushy zone approximation method available within ANSYS Fluent, as liquid freezing advances spatially based on the freezing operating conditions. A multiphase flow simulation modeled the air between the solution fill level and the cap of a 5 L Nalgene™ Polycarbonate Biotainer™ bottle. A fluid volume method modeled the gas-liquid interface, and an interfacial diffusion-resistant surface model accounted for significant differences between the viscosities of air and liquid. Example 2

[0109] The CFD model approximated whether a 3.5 L solution containing a high or low concentration of drug substance or free drug substance (e.g., user-specified) in a 5 L Nalgene™ Polycarbonate Biotainer™ bottle could freeze within 48 hours, as seen in Figure 7. The user provided the CFD model with information about the material inputs (e.g., the geometry of the 5 L Nalgene™ Polycarbonate Biotainer™ bottle and the mechanical and thermal properties of the material inputs). The user provided the CFD model with information about the freezing operating conditions, including the position of the 5 L Nalgene™ Polycarbonate Biotainer™ bottle relative to other bottles within the freezing operating conditions. The CFD model took a conservative approach and determined whether 48 hours was sufficient time for the center of the solution (e.g., the theoretical last point to freeze) to freeze. Given the user-provided information about the material inputs and the freezing operating conditions (not specified), the computational fluid dynamics model approximates that the solution will freeze within 48 hours.

Claims

1. 1. A method for freezing a solution, comprising: (a) predicting a first freezing profile of a large volume of the solution subjected to first freezing operating conditions using a computational fluid dynamics model, the first freezing profile including a predicted average temperature and total freezing time of the solution during freezing; (b) using the computational fluid dynamics model to fit a transient temperature boundary equation to the first freezing profile; (c) using the computational fluid dynamics model to predict a set temperature sequence that will produce a predicted second freezing profile for the small-scale volume of the solution; (i) the transient temperature boundary equation is a condition for predicting the set temperature sequence; (ii) predicting the second freezing profile, wherein the second freezing profile includes a predicted average temperature and total freezing time of the solution during freezing; (d) freezing the small amount of the solution using the set temperature sequence.

2. 10. The method of claim 1, further comprising determining at least one quality characteristic of the small amount of the solution after freezing.

3. 3. The method of claim 2, wherein the solution comprises a pharmaceutical agent, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, a Fab region of an antibody, an antibody drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

4. The method of claim 3 , further comprising using the computational fluid dynamics model to operate a temperature regulation system to generate the set temperature sequence for freezing the small batch.

5. 5. The method of claim 4, further comprising measuring the temperature of at least one point of interest in the small volume throughout freezing.

6. 6. The method of claim 5, wherein the large scale volume is from about 0.2 L to about 20 L.

7. 7. The method of claim 6, wherein the small volume is from about 20 mL to about 100 mL.

8. 6. The method of claim 5, wherein the large-scale quantity is in a large-scale vessel having a volume of about 1 L to about 20 L.

9. 9. The method of claim 8, wherein the small-scale amount is in a small-scale container having a volume of about 30 mL to about 100 mL.

10. 10. The method of claim 9, wherein the large scale container is selected from the group comprising 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

11. 11. The method of claim 10, wherein the small container is selected from the group consisting of a 30 mL bag and a 100 mL bag.

12. 1. A method for thawing a solution, comprising: (a) predicting a first thawing profile of a large volume of the solution subjected to first thawing operating conditions using a computational fluid dynamics model, the first thawing profile including a predicted average temperature and total thawing time of the solution during thawing; (b) using the computational fluid dynamics model to fit a transient temperature boundary equation to the first thawing profile; (c) using the computational fluid dynamics model to predict a set temperature sequence that produces a predicted second thawing profile for the small volume of the solution; (i) the transient temperature boundary equation is a condition for predicting the set temperature sequence; (ii) predicting the second thawing profile, wherein the second thawing profile includes a predicted average temperature of the solution during thawing and a total thawing time; (d) thawing the small volume of the solution using the set temperature sequence.

13. 13. The method of claim 12, further comprising determining at least one quality characteristic of the small amount of the solution after thawing.

14. 14. The method of claim 13, wherein the solution comprises a pharmaceutical agent, a drug, a chemical compound, a nucleic acid, a toxin, a peptide, a protein, a fusion protein, an antibody, an antibody fragment, a Fab region of an antibody, an antibody drug conjugate, a biopharmaceutical, a pharmaceutical protein product, or an antibody.

15. 15. The method of claim 14, further comprising using the computational fluid dynamics model to operate a temperature regulation system to generate the set temperature sequence for thawing the small volume.

16. 16. The method of claim 15, further comprising measuring the temperature of at least one point of interest in the small volume throughout thawing.

17. 17. The method of claim 16, wherein the large scale volume is from about 0.75 L to about 15 L.

18. 18. The method of claim 17, wherein the small volume is from about 20 mL to about 100 mL.

19. 17. The method of claim 16, wherein the large-scale quantity is in a large-scale container having a volume of about 1 L to about 20 L.

20. 20. The method of claim 19, wherein the small-scale amount is in a small-scale container having a volume of about 30 mL to about 100 mL.

21. 21. The method of claim 20, wherein the large scale container is selected from the group comprising 1 L polycarbonate bottles, 2 L polycarbonate bottles, 5 L polycarbonate bottles, 10 L polycarbonate bottles, 20 L polycarbonate bottles, 1 L bags, 2 L bags, 8.3 L bags, and 16.6 L bags.

22. 22. The method of claim 21, wherein the small container is selected from the group comprising a 30 mL bag and a 100 mL bag.

23. The method of claim 1 , wherein the computational fluid dynamics model takes into account environmental factors.

24. 24. The method of claim 23, wherein the environmental factors are selected from the group including air currents, proximity to other surfaces of varying temperature, relative humidity, pressure, and any combination thereof.

25. 1. A method for freezing a solution, comprising: (a) using a computational fluid dynamics model to predict the freezing profile of a large-scale solution subjected to freezing operating conditions; (b) determining that the freeze will occur within the required period; and (c) freezing a large amount of said solution using said freezing operating conditions.

26. 1. A method for thawing a solution, comprising: (a) predicting a thawing profile of a large-scale solution subjected to a first thawing operating condition using a computational fluid dynamics model; (b) determining that thawing will occur within the required time period; and (c) thawing a large quantity of said solution using said thawing operating conditions.

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