Numerical Model Study of In Vivo Magnetic Nanoparticle Tumor Heating.

Iron oxide nanoparticles are currently under investigation as heating agents for hyperthermic treatment of tumors. Major determinants of effective heating include the biodistribution and minimum iron oxide loading required to achieve adequate heating at practically achievable magnetic field strengths. These inter-related criteria ultimately determine the practicality of this approach to tumor treatment. Further, in our experience the currently used treatment assessment criterion for hyperthermia treatment-cumulative equivalent minutes at 43 °C, CEM43 -provides an inadequate description of the expected treatment effectiveness. OBJECTIVES: Couple numerical models to experimental measurements to study the relative heating effectiveness described by cell death predictions. METHODS: FEM numerical models were applied to increase the understanding of a carefully calibrated series of experiments in mouse mammary adenocarcinoma. RESULTS: The numerical model results indicate that minimum tumor loadings between approximately 1.3 to 1.8 mg of Fe per cm3 of tumor tissue are required to achieve the experimentally observed temperatures in magnetic field strengths of 32 kA/m (rms) at 162 kHz. CONCLUSION: We show that including multiple cell death processes operating in parallel within the numerical models provides valuable perspective on the likelihood of successful treatment. SIGNIFICANCE: We show and believe that these assessment methods are more accurate than a single assessment figure of merit based only on the comparison of thermal histories, such as the CEM method.

Improving Accuracy in Arrhenius Models of Cell Death: Adding a Temperature-Dependent Time Delay.

The Arrhenius formulation for single-step irreversible unimolecular reactions has been used for many decades to describe the thermal damage and cell death processes. Arrhenius predictions are acceptably accurate for structural proteins, for some cell death assays, and for cell death at higher temperatures in most cell lines, above about 55 °C. However, in many cases--and particularly at hyperthermic temperatures, between about 43 and 55 °C--the particular intrinsic cell death or damage process under study exhibits a significant "shoulder" region that constant-rate Arrhenius models are unable to represent with acceptable accuracy. The primary limitation is that Arrhenius calculations always overestimate the cell death fraction, which leads to severely overoptimistic predictions of heating effectiveness in tumor treatment. Several more sophisticated mathematical model approaches have been suggested and show much-improved performance. But simpler models that have adequate accuracy would provide useful and practical alternatives to intricate biochemical analyses. Typical transient intrinsic cell death processes at hyperthermic temperatures consist of a slowly developing shoulder region followed by an essentially constant-rate region. The shoulder regions have been demonstrated to arise chiefly from complex functional protein signaling cascades that generate delays in the onset of the constant-rate region, but may involve heat shock protein activity as well. This paper shows that acceptably accurate and much-improved predictions in the simpler Arrhenius models can be obtained by adding a temperature-dependent time delay. Kinetic coefficients and the appropriate time delay are obtained from the constant-rate regions of the measured survival curves. The resulting predictions are seen to provide acceptably accurate results while not overestimating cell death. The method can be relatively easily incorporated into numerical models. Additionally, evidence is presented to support the application of compensation law behavior to the cell death processes--that is, the strong correlation between the kinetic coefficients, ln{A} and E(a), is confirmed.

FEM numerical model study of electrosurgical dispersive electrode design parameters.

Electrosurgical dispersive electrodes must safely carry the surgical current in monopolar procedures, such as those used in cutting, coagulation and radio frequency ablation (RFA). Of these, RFA represents the most stringent design constraint since ablation currents are often more than 1 to 2 Arms (continuous) for several minutes depending on the size of the lesion desired and local heat transfer conditions at the applicator electrode. This stands in contrast to standard surgical activations, which are intermittent, and usually less than 1 Arms, but for several seconds at a time. Dispersive electrode temperature rise is also critically determined by the sub-surface skin anatomy, thicknesses of the subcutaneous and supra-muscular fat, etc. Currently, we lack fundamental engineering design criteria that provide an estimating framework for preliminary designs of these electrodes. The lack of a fundamental design framework means that a large number of experiments must be conducted in order to establish a reasonable design. Previously, an attempt to correlate maximum temperatures in experimental work with the average current density-time product failed to yield a good match. This paper develops and applies a new measure of an electrode stress parameter that correlates well with both the previous experimental data and with numerical models of other electrode shapes. The finite element method (FEM) model work was calibrated against experimental RF lesions in porcine skin to establish the fundamental principle underlying dispersive electrode performance. The results can be used in preliminary electrode design calculations, experiment series design and performance evaluation.

Correlated parameter fit of arrhenius model for thermal denaturation of proteins and cells.

Thermal denaturation of proteins is critical to cell injury, food science and other biomaterial processing. For example protein denaturation correlates strongly with cell death by heating, and is increasingly of interest in focal thermal therapies of cancer and other diseases at temperatures which often exceed 50 °C. The Arrhenius model is a simple yet widely used model for both protein denaturation and cell injury. To establish the utility of the Arrhenius model for protein denaturation at 50 °C and above its sensitivities to the kinetic parameters (activation energy E a and frequency factor A) were carefully examined. We propose a simplified correlated parameter fit to the Arrhenius model by treating E a, as an independent fitting parameter and allowing A to follow dependently. The utility of the correlated parameter fit is demonstrated on thermal denaturation of proteins and cells from the literature as a validation, and new experimental measurements in our lab using FTIR spectroscopy to demonstrate broad applicability of this method. Finally, we demonstrate that the end-temperature within which the denaturation is measured is important and changes the kinetics. Specifically, higher E a and A parameters were found at low end-temperature (50 °C) and reduce as end-temperatures increase to 70 °C. This trend is consistent with Arrhenius parameters for cell injury in the literature that are significantly higher for clonogenics (45-50 °C) vs. membrane dye assays (60-70 °C). Future opportunities to monitor cell injury by spectroscopic measurement of protein denaturation are discussed.

Admittance to detect alterations in left ventricular stroke volume.

BACKGROUND: Implantable cardioverter-defibrillators monitor intracardiac electrograms (EGMs) to discriminate between ventricular and supraventricular tachycardias. The incidence of inappropriate shocks remains high because of misclassification of the tachycardia in an otherwise hemodynamically stable individual. Coupling EGMs with an assessment of left ventricular (LV) stroke volume (SV) could help in gauging hemodynamics during an arrhythmia and reducing inappropriate shocks. OBJECTIVE: The purpose of this study was to use the admittance method to accurately derive LV SV. METHODS: Ultrasonic flow probe and LV endocardial crystals were used in canines (n = 12) as the standard for LV SV. Biventricular pacing leads were inserted to obtain admittance measurements. A tetrapolar, complex impedance measurement was made between the Bi-V leads. The real and imaginary components of impedance were used to discard the myocardial component from the blood component to derive instantaneous blood conductance (Gb). Alterations in SV were measured during right ventricular pacing, dopamine infusion, and inferior vena cava occlusion. RESULTS: Gb tracks steady-state changes in SV more accurately than traditional magnitude (ie, |Y|, without removal of the muscle signal) during right ventricular pacing and dopamine infusion (P = .004). Instantaneous LV volume also was tracked more accurately by Gb than ∣Y∣ in the subset of subjects that underwent inferior vena cava occlusions (n = 5, P = .025). Finite element modeling demonstrates that admittance shifts more sensitivity of the measurement to the LV blood chamber as the mechanism for improvement (see Online Appendix). CONCLUSION: Monitoring LV SV is possible using the admittance method with biventricular pacing leads. The technique could be piggybacked to complement EGMs to determine if arrhythmias are hemodynamically unstable.

FEM numerical model analysis of magnetic nanoparticle tumor heating experiments.

Iron oxide nanoparticles are currently under investigation as heating agents for hyperthermic treatment of tumors. Major determinants of effective heating include the biodistribution of magnetic materials, the minimum iron oxide loading required to achieve adequate heating, and practically achievable magnetic field strengths. These are inter-related criteria that ultimately determine the practicability of this approach to tumor treatment. Currently, we lack fundamental engineering design criteria that can be used in treatment planning and assessment. Coupling numerical models to experimental studies illuminate the underlying physical processes and can separate physical processes to determine their relative importance. Further, adding thermal damage and cell death process to the models provides valuable perspective on the likelihood of successful treatment. FEM numerical models were applied to increase the understanding of a carefully calibrated series of experiments in mouse mammary carcinoma. The numerical models results indicate that tumor loadings equivalent to approximately 1 mg of Fe3O4 per gram of tumor tissue are required to achieve adequate heating in magnetic field strengths of 34 kA/m (rms) at 160 kHz. Further, the models indicate that direct intratumoral injection of the nanoparticles results in between 1 and 20% uptake in the tissues.

Comparative analysis of mathematical models of cell death and thermal damage processes.

The standard method for assessing hyperthermia treatment has been calculation of cumulative equivalent minutes at 43 °C, CEM43 and its variations. This parameter normalises treatment thermal histories rather than predicts treatment results. Arrhenius models have been widely used in analysing higher temperature thermal treatments and successfully employed to predict irreversible thermal alterations in structural proteins. Unfortunately, in many, but not all cases they fail to represent thermally induced damage or cell death at hyperthermic temperatures, 43-50 °C, exhibiting significant over-prediction of the initial 'shoulder' region. The failure arises from the simplifying assumptions used to derive the irreversible reaction format that has been used in thermal damage studies. Several successful multi-parameter fit methods have been employed to model cell survival data. The two-state statistical thermodynamic model was derived from basic thermodynamic principles. The three-state model results from relaxing the assumptions under the Arrhenius formulation that result in an irreversible reaction. In other cell processes studied in vitro the irreversible Arrhenius model holds, and is sufficient to provide an accurate and useful estimate of thermal damage and cell death. It is essential in numerical model work to include multiple thermal damage processes operating in parallel to obtain a clear image of the likely outcome in tissues. Arrhenius and other C(t) models have that capability, while a single value for CEM43, does not.

Analysis of the spatial sensitivity of conductance/admittance catheter ventricular volume estimation.

Conductance catheters are known to have a nonuniform spatial sensitivity due to the distribution of the electric field. The Geselowitz relation is applied to murine and multisegment conductance catheters using finite element models to determine the spatial sensitivity in a uniform medium and simplified left ventricle models. A new formulation is proposed that allows determination of the spatial sensitivity to admittance. Analysis of FEM numerical modeling results using the Geselowitz relation provides a true measure of parallel conductance in simplified left ventricle models for assessment of the admittance method and hypertonic saline techniques. The spatial sensitivity of blood conductance (Gb) is determined throughout the cardiac cycle. Gb is converted to volume using Wei's equation to determine if the presence of myocardium alters the nonlinear relationship through changes to the electric field. Results show that muscle conductance (Gm) from the admittance method matches results from the Geselowitz relation and that the relationship between Gb and volume is accurately fit using Wei's equation. Single-segment admittance measurements in large animals result in a more evenly distributed sensitivity to the LV blood pool. The hypertonic saline method overestimates parallel conductance throughout the cardiac cycle in both murine and multisegment conductance catheters.

Nanoparticles in Medicine: Selected Observations and Experimental Caveats.

Medically useful nanoparticles measure 1-100 nm in at least one dimension and are engineered and manufactured for specific diagnostic and treatment applications. Most nanoparticles used currently used in medicine are engineered and manufactured for specific purposes. Medically significant nanoparticles are composed of a 1) central core that is usually the medically active component, 2) one or more layers of organic or inorganic materials that forms a capsule (corona) covering the core and 3) an outer surface layer that interacts with the environment and/or targeted cells and tissues. Effective nanoparticle function in the living, intact animal or human requires electrochemical stability necessary to bypass the reticuloendothelial system (RES) and avoid filtration through the renal glomerulus into the urine. Nanoparticles are present in "natural" as well as the manufacturing and clinical environments thus could pose as significant toxins because of their small sizes, their chemical and drug content and potential effect of causing long term disease including allergies, chronic inflammation and cancer. Currently published studies have focused on the effects of nanoparticles on cells in the extremely artificial environments of cell cultures. More clinical and preclinical studies documenting the short term and long term effects nanoparticle in the intact experimental animal and human are needed.

Application of the Geselowitz relationship to the murine conductance catheter.

Conductance catheters are known to have a nonuniform spatial sensitivity due to the distribution of the electric field. The Geselowitz relation is applied to the murine conductance catheter using a finite element model to determine catheter's spatial sensitivity in uniform media. Further analysis of FEM numerical modeling results using the Geselowitz relation provides a true measure of parallel conductance in a simplified murine left ventricle for assessment of the admittance method and hypertonic saline techniques. The spatial sensitivity of blood conductance (G(b)) is determined throughout the cardiac cycle. G(b) is converted to volume using Wei's equation to determine if the presence of myocardium alters the nonlinear relationship through changes to the electric field shape. Results show that the admittance method correctly calculates G(b) in comparison to the Geselowitz relation, and that the relationship between G(b) and volume is accurately fit using Wei's equation.

A bio-telemetric device for measurement of left ventricular pressure-volume loops using the admittance technique in conscious, ambulatory rats.

This paper presents the design, construction and testing of a device to measure pressure-volume loops in the left ventricle of conscious, ambulatory rats. Pressure is measured with a standard sensor, but volume is derived from data collected from a tetrapolar electrode catheter using a novel admittance technique. There are two main advantages of the admittance technique to measure volume. First, the contribution from the adjacent muscle can be instantaneously removed. Second, the admittance technique incorporates the nonlinear relationship between the electric field generated by the catheter and the blood volume. A low power instrument weighing 27 g was designed, which takes pressure-volume loops every 2 min and runs for 24 h. Pressure-volume data are transmitted wirelessly to a base station. The device was first validated on 13 rats with an acute preparation with 2D echocardiography used to measure true volume. From an accuracy standpoint, the admittance technique is superior to both the conductance technique calibrated with hypertonic saline injections, and calibrated with cuvettes. The device was then tested on six rats with 24 h chronic preparation. Stability of animal preparation and careful calibration are important factors affecting the success of the device.

Left ventricular epicardial admittance measurement for detection of acute LV dilation.

There are two implanted heart failure warning systems incorporated into biventricular pacemakers/automatic implantable cardiac defibrillators and tested in clinical trials: right heart pressures, and lung conductance measurements. However, both warning systems postdate measures of the earliest indicator of impending heart failure: left ventricular (LV) volume. There are currently no proposed implanted technologies that can perform LV blood volume measurements in humans. We propose to solve this problem by incorporating an admittance measurement system onto currently deployed biventricular and automatic implantable cardiac defibrillator leads. This study will demonstrate that an admittance measurement system can detect LV blood conductance from the epicardial position, despite the current generating and sensing electrodes being in constant motion with the heart, and with dynamic removal of the myocardial component of the returning voltage signal. Specifically, in 11 pigs, it will be demonstrated that 1) a physiological LV blood conductance signal can be derived; 2) LV dilation in response to dose-response intravenous neosynephrine can be detected by blood conductance in a similar fashion to the standard of endocardial crystals when admittance is used, but not when only traditional conductance is used; 3) the physiological impact of acute left anterior descending coronary artery occlusion and resultant LV dilation can be detected by blood conductance, before the anticipated secondary rise in right ventricular systolic pressure; and 4) a pleural effusion simulated by placing saline outside the pericardium does not serve as a source of artifact for blood conductance measurements.

Heating mechanisms in gold nanoparticles at radio frequencies.

Gold nanoparticles are under study as a potentially viable mechanism for hyperthermia tumor treatment in two regimes of the electromagnetic spectrum: laser and radio frequency excitation. Gold nanoparticles, nanorods and nanoshells have been applied with visible laser sources that excite the particles at or near their plasmon resonance frequency, and this mechanism has been well studied. The physical processes that describe the experimentally observed heating at radio frequencies (13.56 MHz) are not as well understood. Differing results have been reported in semi-solid phantom materials and liquid phase suspensions. This numerical modeling study was undertaken to inspect the relative importance of several candidate physical processes.

FEM numerical model study of heating in magnetic nanoparticles.

Electromagnetic heating of nanoparticles is complicated by the extremely short thermal relaxation time constants and difficulty of coupling sufficient power into the particles to achieve desired temperatures. Magnetic field heating by the hysteresis loop mechanism at frequencies between about 100 and 300 kHz has proven to be an effective mechanism in magnetic nanoparticles. Experiments at 2.45 GHz show that Fe3O4 magnetite nanoparticle dispersions in the range of 1012 to 1013 NP/mL also heat substantially at this frequency. An FEM numerical model study was undertaken to estimate the order of magnitude of volume power density, Qgen (W m-3) required to achieve significant heating in evenly dispersed and aggregated clusters of nanoparticles. The FEM models were computed using Comsol Multiphysics; consequently the models were confined to continuum formulations and did not include film nano-dimension heat transfer effects at the nanoparticle surface. As an example, the models indicate that for a single 36 nm diameter particle at an equivalent dispersion of 1013 NP/mL located within one control volume (1.0 × 10-19 m3) of a capillary vessel a power density in the neighborhood of 1017 (W m-3) is required to achieve a steady state particle temperature of 52 °C - the total power coupled to the particle is 2.44 µW. As a uniformly distributed particle cluster moves farther from the capillary the required power density decreases markedly. Finally, the tendency for particles in vivo to cluster together at separation distances much less than those of the uniform distribution further reduces the required power density.

Nanoparticle based cancer treatment: can delivered dose and biological dose be reliably modeled and quantified?

Essential developments in the reliable and effective use of heat in medicine include: 1) the ability to model energy deposition and the resulting thermal distribution and tissue damage (Arrhenius models) over time in 3D, 2) the development of non-invasive thermometry and imaging for tissue damage monitoring, and 3) the development of clinically relevant algorithms for accurate prediction of the biological effect resulting from a delivered thermal dose in mammalian cells, tissues, and organs. The accuracy and usefulness of this information varies with the type of thermal treatment, sensitivity and accuracy of tissue assessment, and volume, shape, and heterogeneity of the tumor target and normal tissue. That said, without the development of an algorithm that has allowed the comparison and prediction of the effects of hyperthermia in a wide variety of tumor and normal tissues and settings (cumulative equivalent minutes/ CEM), hyperthermia would never have achieved clinical relevance. A new hyperthermia technology, magnetic nanoparticle-based hyperthermia (mNPH), has distinct advantages over the previous techniques: the ability to target the heat to individual cancer cells (with a nontoxic nanoparticle), and to excite the nanoparticles noninvasively with a non-injurious magnetic field, thus sparing associated normal cells and greatly improving the therapeutic ratio. As such, this modality has great potential as a primary and adjuvant cancer therapy. Although the targeted and safe nature of the noninvasive external activation (hysteretic heating) are a tremendous asset, the large number of therapy based variables and the lack of an accurate and useful method for predicting, assessing and quantifying mNP dose and treatment effect is a major obstacle to moving the technology into routine clinical practice. Among other parameters, mNPH will require the accurate determination of specific nanoparticle heating capability, the total nanoparticle content and biodistribution in the target cells/tissue, and an effective and matching alternating magnetic field (AMF) for optimal and safe excitation of the nanoparticles. Our initial studies have shown that appropriately delivered and targeted nanoparticles are capable of achieving effective tumor cytotoxicity at measured thermal doses significantly less than the understood thermal dose values necessary to achieve equivalent treatment effects using conventional heat delivery techniques. Therefore conventional CEM based thermal dose - tissues effect relationships will not hold for mNPH. The goal of this effort is to provide a platform for determining the biological and physical parameters that will be necessary for accurately planning and performing safe and effective mNPH, creating a new, viable primary or adjuvant cancer therapy.

Models for thermal damage in tissues: processes and applications.

Irreversible thermal alterations in tissue function and structure are used in clinical applications to achieve diverse goals, from lower-temperature tumor ablation to higher-temperature tissue fusion and surgical cutting. The typical formulation in tumor hyperthermia studies, the thermal iso-effect dose, derives from cell-survival studies but describes a single process only over a limited range of temperatures and is thus not suitable for multiple higher-temperature events. Many other thermal damage processes have been described using the Arrhenius kinetic rate of formation approach, which has the advantage that it is inherently quantitative in nature and can easily be compared with quantitative markers of injury or histologic section. The vast majority of Arrhenius studies have been directed toward measurable cellular effects at relatively low temperatures. Some emphasis in this paper has been placed on what is known of higher-temperature processes to support the theme of this issue. This review compares and contrasts the two thermal-damage formulations and reviews methods to convert between them.

Accuracy considerations in catheter based estimation of left ventricular volume.

Cardiac volume estimation in the Left Ventricle from impedance or admittance measurement is subject to two major sources of error: parallel current pathways in surrounding tissues and a non uniform current density field. The accuracy of volume estimation can be enhanced by incorporating the complex electrical properties of myocardium to identify the muscle component in the measurement and by including the transient nature of the field non uniformity. Cardiac muscle is unique in that the permittivity is high enough at audio frequencies to make the muscle component of the signal identifiable in the imaginary part of an admittance measurement. The muscle contribution can thus be uniquely identified and removed from the combined muscle - blood measurement. In general, both error sources are transient and are best removed in real time as data are collected. This paper reviews error correction methods and establishes that the relative magnitudes of the error concerns are different in small and large hearts.

Ferrimagnetic nanoparticles enhance microwave heating for tumor hyperthermia therapy.

Localized tumor hyperthermia therapy has been intensively studied for the past three decades. One engineering limitation has been the difficulty of specifically targeting cancerous tissues in the normal tissue surroundings. Recent attention has turned to the deposition of nanoparticles in the tumor to enhance heating relative to its surroundings. The work in magnetic nanoparticles has focused on resonant hysteresis loop heating in the 100 to 300 kHz range, where that mechanism dominates - however extremely high magnetic field strengths are required to realize an advantage, up to 10(5) (A/m). We introduce experimental evidence that substantial advantages in heating can also be obtained at the microwave ISM frequency of 2.45 GHz when γ-hematite (Fe(2)O(3)) is dispersed in media at concentrations on the order of 10(12) particles/mL.

Comparison of conductance to volume equations: the gain coefficient alpha.

The conductance catheter technique is used to measure real-time pressure and volume data in a beating heart. There are three competing equations for transforming the raw conductance signal into volume: (1) Baan's equation, (2) The cuvette equation (i.e. Relative Volume Units), and (3) Wei's equation. This paper explores the accuracy of these three equations compared to ultrasound echo in mice, and discusses the reason for discrepancy regarding both Baan's equation and the cuvette equation. We conclude that Wei's equation is the most accurate, because its nonlinear mapping yields volumes in the range of physiologic norms.

Numerical models of laser fusion of intestinal tissues.

Numerical models of continuous wave Tm:YAG thermal fusion in rat intestinal tissues were compared to experiment. Optical and thermal FDM models that included tissue damage based on Arrhenius kinetics were used to predict birefringence loss in collagen as the standard of comparison. The models also predicted collagen shrinkage, jellification and water loss. The inclusion of variable optical and thermal properties is essential to achieve favorable agreement between predicted and measured damage boundaries.