Modeling of Ultrasound Stimulation of Adolescent Pancreas for Insulin Release Therapy

Abstract

Objectives:

Our previous published studies have focused on safety and effectiveness of using therapeutic ultrasound (TUS) for treatment of type 2 diabetes mellitus (T2DM) in preclinical models. Here we present a set of simulation studies to explore potential ultrasound application schemes that would be feasible in a clinical setting.

Methods:

Using the multiphysics modeling tool OnScale, we created 2D models of the human abdomen from CT images captured from one normal weight adolescent patient, and one obese adolescent patient. Based on our previous studies, the frequency of our TUS was 1 MHz delivered from a planar unfocused transducer. We tested five different insonation angles, as well as four ultrasound intensities combined with four different duty factors and five durations of application to explore how these variables effect the peak pressure and temperature delivered to the pancreas as well as surrounding tissue in the model.

Results:

We determined that ultrasound applied directly from the anterior of the patient abdomen at 5 W/cm² delivered consistent acoustic pressures to the pancreas at the levels which we have previously found to be effective at inducing an insulin release from preclinical models.

Conclusions:

Our modeling work indicates that it may be feasible to non-invasively apply TUS in clinical treatment of T2DM.

Introduction

Diabetes mellitus continues to be a worldwide epidemic of enormous proportions. An estimated 1.4 million new cases of diabetes were diagnosed among people ages 18 and older in 2019¹. Disease prevalence among adults continues to increase with approximately 37.3 million people in the US or 11.3% of the population of the country currently suffering from diabetes¹. Type 2 diabetes mellitus (T2DM), which accounts for 90 to 95% of diabetes cases, is defined by a combination of peripheral insulin resistance, inadequate insulin secretion by pancreatic beta cells, and abnormally high levels of glucagon secretion². For T2DM to develop, both insulin resistance and inadequate insulin secretion must be present, and the amount of insulin secreted from pancreatic beta cells must not be adequate to counteract the effects of insulin resistance resulting in hyperglycemia³. While insulin resistance is the more commonly known pathogenic feature of T2DM, it would not result in hyperglycemia (and ultimately T2DM) without an associated deficiency in insulin secretion^4,5.

Once believed to be a condition mostly prevalent in adulthood, T2DM has increasingly become more frequent in children and adolescents over the past few decades⁶. The incidence of youth T2DM, linked with obesity and declining physical activity, is increasing. As in adult T2DM, youth T2DM is associated with insulin resistance and progressive deterioration of beta cell function. In contrast to adult T2DM, the decline in beta cell function in youth T2DM is 3 to 4 times faster, and therapeutic failure rates are significantly higher⁷. Pharmacological management of T2DM routinely requires complex therapy with multiple medications and loses its effectiveness over time. This is especially problematic in young diabetic patients as they may require special attention to ensure treatment compliance. Thus, new modes of therapy are needed that will directly target the underlying causes of abnormal glucose metabolism.

Previous studies from our group have demonstrated that low-intensity TUS application can induce up to four-fold increase in insulin release in vitro compared to control while retaining comparable cell viability⁸. Subsequent terminal in vivo studies conducted in a murine model found a moderate but significant increase in blood insulin concentration immediately after sonication compared to sham⁹. However, before the technology can proceed into clinically-focused trials, we must investigate the clinical feasibility of anterior extracorporeal sonication of a human. The pancreas is a notoriously hard organ to image using ultrasound, thus clinical feasibility relies heavily on finding an appropriate acoustic window that avoids air-filled organs, minimizes standing waves, and prevents excessive temperature increases over 5°C¹⁰. Therefore, we will attempt to utilize finite-element models based on adolescent patients computer tomography (CT) images of two different body types to first find an optimal acoustic window and then to find parameters of duration, duty cycle, and intensity so as to achieve sufficient acoustic pressures to stimulate insulin release based on previous in vitro studies⁹ and minimize heating.

Materials and Methods

OnScale, a multiphysics finite-element analysis software (Redwood City, CA, USA), was used to develop a model of an axial slice of the human abdomen based CT images, shown in Figure 1, to simulate the range of acoustic pressures and temperature increases that the body would be exposed to during extracorporeal sonication. A potential clinical application was modeled of a 1 MHz unfocused ultrasound transducer which we have previously shown to induce a release of insulin from cultured rat insulinoma cells^8,11,12. Anonymized CT images taken with oral contrast agents were obtained from Children’s National Medical Center in Washington, DC from a normal weight 15-year-old male patient and an obese 16-year-old female patient following Children’s National Medical Center human subject guidelines. The ethical statement is not required for the study due to no direct involvement of humans or animals. The reference CT slice was chosen based on the location which produced the largest footprint of the pancreas. The model was first developed in Adobe Illustrator (San Jose, California, USA) by tracing components of organs in the CT reference image to approximate the anatomy in the chosen slice. Tracing was primarily performed by placing overlapping ellipses. The desired ratio between the pixel size and the model was calculated and all objects were scaled uniformly. This geometry could then be translated into the OnScale platform by defining ellipse shapes in the simulation with Cartesian coordinates.

Figure 1.

a) An axial slice from an abdominal CT of the obese patient and b) the reconstructed model in OnScale. In the model, a therapeutic ultrasound transducer can be seen on the left side of the patient.

The simulation software considers acoustic wave propagation along with both longitudinal and transverse wave propagation. Similar models of biological structures have previously been validated by our laboratory and others^13,14,15. The simulation grid size was determined by methods previously reported^16,17. A grid size of one fifteenth the wavelength of the ultrasound frequency being propagated has been shown to effectively represent the actual propagation of ultrasound waves without being too computationally expensive. To avoid unrealistic echoes and reflection from within the transducer, the transducer material was modeled as a vacuum. Material properties used in our simulations are listed in Table 1 and parameters were obtained from published data¹⁸. Materials’ density and speed of sound were primarily used to determine the pressure field in the model while material wave damping and specific heat were used to determine the ultrasound energy loss or absorption per voxel and heating respectively.

Table 1.

Values of tissue physical properties used for our simulation studies.

	Abbreviation	Density (kg/m3)	Speed of Sound (m/s)	Dilatational Wave Damping (dB/cm)	Specific Heat (J/Kg*K)
Pancreas	panc	1087	1591	0.829	3164
Bone	bon	1908	1880	4.74	1313
Liver	lvr	1079	1585	0.6	3540
Kidney	kdny	1066	1554.3	0.243	3763
Fat	fat	911	1440.2	1.8	2348
Stomach	bwl	1000	1560	0.002	4200
Skin	skin	1109	1624	3.5	3391
Muscle	musc	1090	1588.4	0.7	3421
Spleen	spleen	1079	1585	0.6	3540
Blood	aorta	1050	1578.2	0.21	3617
Gel	gel	1000	1560	0.1	4200
Water	wart	1000	1560	0.002	4200

To determine the optimal method of applying ultrasound to the pancreas, we tested a number of application angles, ultrasound intensities, pulsing schemes and application times. Transducer angles were determined relative to the geometric center of the model. The applied frequency was 1 MHz and the active diameter of a modeled flat, single-element unfocused ultrasound transducer was 1.5 cm. Intensities of 1, 5, 7.5 and 10 W/cm² were tested along with duty cycles of 10%, 25%, 50% and 100% and 1, 2, 3, 4, and 5 minute application times. These parameters were investigated to find the optimal combination that would deliver an adequate pressure without causing excessive heating to the skin or internal organs. To explore suitable insonation angles for the optimal acoustic window, the angles directly from the right hand side of the patient, 45° from the right, directly from the top, 45° from the left and directly from the left hand side of the patient were used. These directions are analogous to the East, North East, North, North West and West directions on the model shown in Figure 2.

Figure 2.

An array of images which shows the material geometry (top row), maximum pressure map (middle row), and maximum temperature map (bottom row). Each column represents one of the five different insonation angles tested.

The maximum temperature and pressure induced by each of the ultrasound intensities and pulsing schemes and insonation angles were determined for the entire model as well as for the pancreas itself. This analysis was performed in MATLAB 2020a (The Mathworks, Natick, MA, USA). To extract the maximum pressure and temperature from the pancreas, an oblong region of interest (ROI) was selected for each patient (Figure 3a) that encompasses the head of the pancreas which is the largest tissue mass of the pancreas and would be a likely target for ultrasound therapy on the pancreas. The target pressure at the pancreas is approximately 210 kPa which is the pressure we have previously shown to induce a release of insulin from cultured rat insulinoma cells (via only mechanicals effects of ultrasound) and which also does not decrease cell viability^8,11,12.

Figure 3.

a) The pressure map (in Pa) of the left 45° insonation angle displayed in MATLAB with the head of the pancreas ROI for analysis highlighted. b) The pressure map for the left 45° insonation angle as viewed in OnScale with different organ outlines displayed.

Results

The results of acoustic simulations can be seen in Table 2 and Table 3. For each simulated intensity and insonation angle, the average and maximum pressure at the pancreas ROI was recorded. For both the normal weight and obese patient, an ultrasound intensity of 1 MHz at 5 W/cm² applied directly from the top of the supine patient’s abdomen created a maximum pressure closest to the 210 kPa previously shown to be effective at releasing insulin from cultured beta cells^8,11,12 (Table 2 & Table 3, bold and underlined entry).

Table 2.

The average and maximum pressure delivered to the pancreas of the normal weight patient.

Average and Maximum Pressure at the Pancreas - Normal Weight Patient (kPa)
	1 W/cm2		5 W/cm2		7.5 W/cm2		10 W/cm2
	Average	Max	Average	Max	Average	Max	Average	Max
Right	26.93	134.56	60.21	300.88	73.74	368.50	85.15	425.51
Right 45°	43.50	188.08	97.26	420.56	119.12	515.09	137.55	594.77
Top	16.09	118.88	35.99	265.83	44.07	325.57	50.89	375.94
Left 45°	15.76	40.80	35.23	91.24	43.15	111.74	49.82	129.03
Left	18.88	44.55	42.22	99.62	51.70	122.01	59.70	140.89

Table 3.

The average and maximum pressure delivered to the pancreas of the obese patient.

Average and Maximum Pressure at the Pancreas - Obese Patient (kPa)
	1 W/cm2		5 W/cm2		7.5 W/cm2		10 W/cm2
	Average	Max	Average	Max	Average	Max	Average	Max
Right	27.31	77.89	61.07	174.16	74.80	213.31	86.37	246.31
Right 45°	41.65	164.88	93.13	368.68	114.06	451.54	131.71	521.39
Top	34.83	133.70	77.89	298.96	95.39	366.15	110.15	422.80
Left 45°	26.69	147.83	59.68	330.57	73.10	404.86	84.41	467.49
Left	18.70	37.93	41.82	84.82	51.22	103.89	59.14	119.96

During the course of this study, we ran a total of 800 thermal simulations considering our five insonation angles, four ultrasound intensities, four duty factors, five total application times for both of our two patients. In Figure 4, we show the maximum temperature at the site of the pancreas for the normal weight patient (Figure 4a) and the obese patient (Figure 4c) as well as the maximum temperature in the whole simulated body region for the normal weight patient (Figure 4b) and obese patient (Figure 4d). In both cases, the highest temperatures occurred outside of the pancreas. These high temperatures were localized to the area of skin just beneath the transducer as can be seen in Figure 2. As expected, an increase in duty factor as well as time of application is correlated with an increase in peak temperature in the pancreas as well as the surface of the skin. However, our thermal simulations indicate that there are combinations of duty factors and application times that can keep the maximum skin temperature below 46 °C. Notably, in our simulations, ultrasound applied for up to 5 minutes 10% duty factor induced a maximum temperature throughout the simulation of 45.70 °C in the normal weight patient. At a 10% duty factor, one minute application of ultrasound induced a maximum temperature of 45.6 °C in the obese patient.

Figure 4.

The maximum pressure simulated in the normal weight patient pancreas (a) and in the overall simulation (b) applying ultrasound from the top of the patient at 5 W/cm². Similarly, the maximum pressure simulated in the obese patient at the pancreas (c) and in the overall simulation (d).

Discussion

Our simulation studies have shown the feasibility of delivering therapeutic ultrasound to the human pancreas while maintaining safety to the organ as well as the surrounding tissue. For example, at the temperature of 46°C, it would take 1 hour to produce normal human skin tissue death¹⁹. Cumulative equivalent minutes at 43°C (CEM43) is the standard metric for thermal dose assessment that correlates well with tissue thermal damage. The available CEM43 data for tissues present in our model are shown below based on review by Yarmolenko et al.²⁰. At CEM43 between 41 and 80 min, a minor acute muscle damage was observed, with chronic and significant damage observed at CEM43 higher than 80 min. CEM43 of 41–80 min caused acute and minor damage to liver tissue, while CEM43 of 320 min caused thermal coagulation of pig liver. CEM43 lower than 20 min induced acute and significant damage in the small intestine, while at CEM43 above 80 min, significant and chronic damage was observed. Kidney damage was reported for CEM43 between 70 and 2.3×10¹⁹ min. No burns were observed in human skin at CEM43 of 240 min, however heat at CEM43 between 480 and 960 min caused immediate superficial burns. No thermal damage data are available for stomach and pancreas.

In the context of CME43, our simulation studies show that we are able to maintain the total heating of the muscle, liver, intestines, kidneys and any other organ below the requisite levels for thermal damage. As our previous studies have shown, a cumulative ultrasound application time of 5 minutes at approximately 210 kPa can reliably induce an increase in extracellular insulin^8,12. Our previous amperometry studies have also shown that the release of insulin induced by ultrasound is effectively instantaneous. This indicates that during the entire time ultrasound is being applied, the ultrasound is contributing to the therapeutic dose which we have experimentally shown to be 5 minutes of treatment with an induced pressure of 210 kPa. Though none of our simulation parameters were able to be applied continuously for a full 5 minutes without a detrimental thermal increase, we are confident that longer pauses between the pulsing schemes and natural cooling effects of the body will facilitate an ultrasound application in a reasonable timeframe which results in a 5 minute application of ultrasound inducing a 210 kPa pressure field at the pancreas.

One of the major concerns regarding safety of therapeutic ultrasound application is the induced heating to the target organ and surrounding area. Though we have found some upper bounds in terms of application time and duty factor over which ultrasound can be applied to keep heating within an acceptable range, this range is likely greater than our simulations indicate. Though our model accounts for diffusion of heat throughout the system, we were not able to simulate the natural cooling effect of the circulatory system. Once this is taken into account, ultrasound will likely be able to be applied for a longer duty factor over a longer period of time while still keeping heating to below critical levels. In addition to the natural cooling capabilities of circulating blood, personalized treatment planning is another method not currently taken into account in this study which can be used to reduce heating to surrounding organs and structures. Treatment planning for ultrasound therapy could be thought of as akin to treatment planning for radiation therapy where each individual’s anatomy is taken into account when considering angle of approach of the specific therapy. Whether the ultrasound therapy is performed in the clinic or a transducer is attached to the patient in a patch format for at home application (Figure 5) appropriate individualized sonication angle will guarantee minimal heating to surrounding tissue and organs. The positive results from our two individual patients using our chosen range of insonation angles and intensities gives us further confidence to the robustness of this proposed treatment to a more diverse patient population.

Figure 5.

Envisioned TUS medical device for triggering of insulin release coupled with a constant glucose monitor.

One could argue that a large amount of heating to the surrounding tissue could be avoided if we had used focused transducers to concentrate ultrasound energy at the target organ of the pancreas. A disadvantage of using focused ultrasound is the accuracy that would be needed during application. We envision a final device which would consist of a patch that houses the therapeutic transducer and sits on the abdomen of the diabetic patient (Figure 5) which could be occasionally readjusted. Our group has already made strides toward realizing such a device in the form of safety and effectiveness studies in vitro^8,11,12,21 and in vivo⁹. Our unfocused ultrasound transducers mean that variations such as minute gradual changes in body mass index (BMI) or distention of the stomach perhaps after a meal are likely to have little effect on the most effective angle of insonation on the pancreas from our unfocused transducer as is evident by the fact that the same insonation angle for our normal weight and obese patient both deliver similar effective maximum pressures to the pancreas. With a focused transducer, the same focal length would not work for different patients with different BMIs, let alone the same patient at different times of the day. Further, we have shown that we are able to perform this treatment at ultrasound parameters that can likely elicit a therapeutic effect on the pancreas.

While the modeling of our ultrasound application was performed in 2D models which may be less realistic than a 3D or atlas approach, the 2D scenario allows us to explore a range of ultrasound parameters including intensity, duty cycle, application time and insonation angle in a manner which is both thorough and efficient. The fact that within the 800 scenarios simulated we found a combination of parameters which resulted in our target pressures in the pancreas gives us confidence that the freedom of another dimension will ease the burden of finding an appropriate acoustic window. This is due to the fact that the major anatomy features obstructs the pancreas access which are skin, adipose tissue, and the stomach, in which the latter of the three can be made acoustically transparent instructing the patient to drink water before treatment.

We chose to model various ultrasound intensities because unlike our in vitro and in vivo experiments, there is significantly more acoustically absorbing material between the transducer and target in a human compared to these other models. Ultimately, if the ultrasound intensity is increased enough, we are able to reach the target pressure at the target organ. Simply increasing the intensity of the ultrasound output however will result in unwanted and excessive heating in adipose tissue and at the interface of any incident bones. The variables of insonation angle, duty factor and application time then work to rectify the unwanted heating effects by combining an optimal angle of approach with a pulsing scheme to allow for natural dissipation of heat.

Ultrasound could either be applied following a similar regime as pharmacological management (few times a day, usually after meals), or used in a closed-loop system with wireless feedback from a constant glucose monitor (Figure 5). Our proposed approach may offer the capability of adjusting various ultrasound parameters (e.g. frequency, intensity, pulse duration, duty cycle) to deliver an optimal dose of insulin to the patient. We hope that this therapeutic strategy may eventually provide T2DM patients with a more personalized approach for the treatment and management of their condition.

Conclusions

In this work, we have outlined the process and results of a set of simulation studies on one normal weight patient, and one obese patient. During these simulation studies a total of 40 acoustic simulations and 800 thermal simulations were performed to completely characterize the effect of insonation angle and ultrasound pulsing scheme on the induced pressures and temperatures in our model. Based on our previous in vitro experiments, we determined that ultrasound at 1 MHz at 5 W/cm² applied directly from the anterior of the patient on the abdomen delivers the optimal pressure to the pancreas for inducing therapeutic effects to combat T2DM. Further, we have identified pulsing schemes which are expected to allow ultrasound to be delivered without causing deleterious amounts of heating to the pancreas or any other surrounding anatomy. Though the limits of the pulsing scheme will be dictated by the individual body type of each patient given that fat absorbs more acoustic energy than most other tissues in the body, active cooling due to blood flow (which was not simulated here) or skin surface cooling during therapy means that for most patients there should be an ultrasound application scheme which allows for a realistic therapeutic regimen.