In situ sensing physiological properties of biological tissues using wireless miniature soft robots

Implanted electronic sensors, compared with conventional medical imaging, allow monitoring of advanced physiological properties of soft biological tissues continuously, such as adhesion, pH, viscoelasticity, and biomarkers for disease diagnosis. However, they are typically invasive, requiring being deployed by surgery, and frequently cause inflammation. Here we propose a minimally invasive method of using wireless miniature soft robots to in situ sense the physiological properties of tissues. By controlling robot-tissue interaction using external magnetic fields, visualized by medical imaging, we can recover tissue properties precisely from the robot shape and magnetic fields. We demonstrate that the robot can traverse tissues with multimodal locomotion and sense the adhesion, pH, and viscoelasticity on porcine and mice gastrointestinal tissues ex vivo, tracked by x-ray or ultrasound imaging. With the unprecedented capability of sensing tissue physiological properties with minimal invasion and high resolution deep inside our body, this technology can potentially enable critical applications in both basic research and clinical practice.

Subsequently, and can be solved by employing the following optimization process: where and are the matrices that give higher weightings to the robot body positions considered more important. The optimization process can be solved with solvers, such as quadratic optimization (48), which can minimize the effect of the detection noise, as shown in fig. S21. Furthermore, we assume the reaction torque at the patch-substrate interface is negligible, as shown in fig. S22. For the whole robot body, we have the force balancing equations where E is the gravity of the bio-adhesive patch. Therefore, with Eqns. (17)(18)(19)(20), we could estimate D7 and D4 .

Supplementary Note 2. Estimating tissue viscoelastic properties.
We use the following viscoelastic constitutive equation to model the soft tissues.
where is the Cauchy stress of the soft material, 2 and 2 are the material's shear modulus and bulk modulus, respectively.
represents the deformation gradient tensor. -= ( ) is the first invariant of the left Cauchy-Green tensor. The quantity 2 is the volumetric Jacobian of the deformation, as defined as 2 = det . Ω 2 is the domain of the soft tissue. is the domain of time. For an incompressible solid, the deformation satisfies 2 = 1. We have the stress and strain relationship given by , where is the strain of the soft materials, is the elasticity tensor, and 2 is the viscosity of the soft material. The normal stress-strain relationship of the soft material is given by
We propose a frequency-sweeping method to estimate 2 and 2 . By representing the system states in the frequency domain, we have where is the frequency and is the imaginary unit. Similarly, the soft robot could also be modeled following the generalized neo Hookean model for magnetic composite materials (49), given by where is the Cauchy stress of the robot, where is the Cauchy stress of the robot soft body, : and : are the material's shear modulus and bulk modulus, respectively. represents the deformation gradient tensor. -: = ( ) is the first invariant of the left Cauchy-Green tensor. The quantity : is the volumetric Jacobian of the deformation, as defined as : = det . Ω : is the domain of the soft tissue. We further have the boundary conditions given by = − , where is the tissue surface normal unit vector. Given a specific robot, we assume that the normal stress of the soft tissue is proportional to the external magnetic field with a scaling factor, which could be calibrated. 4 is a function of the bulk modulus : and the magnetization profile ( ) of the robot and independent from the external magnetic field and tissues. 44 2 can be estimated from the displacement of the tissue at the boundary, 4 2 = 4 : , where 4 : and 4 2 are the robot body displacement and tissue displacement. Based on the Hertzian contact theory (50), the relation between the strain field distribution 44 2 and the robot displacement 4 : can be assumed as the line contact on a half-plane, where is the constant that can be determined by regression, as shown in fig. S19.

Now we have
Notably, the elasticity 2 and the viscosity 2 in the viscoelastic model represent the same physical terms as the storage modulus ] and the loss modulus ′′ as measured by a rheometer. Considering this, we correlate the elasticity 2 with the storage modulus ] as . Equation 30 is rewritten as Here, we define = @ -@ 4 , which was calibrated by the regression shown in Fig. 6D. We correlate with the ratio R 1 . Equation (31) can be expressed as where the coefficient ^ was calibrated by regression, as illustrated in Fig. 6E.

Supplementary Note 3. Calculating the signal-to-noise ratio.
The signal for estimating the material stiffness is based on the material strain, so the signal-tonoise ratio (SNR) is defined as where ̅ denotes the average of the strain values, while represents the standard deviation of the strain values. For ultrasound elastography, ̅ and are the average and standard deviation of the strain within the sampling window, respectively (38).
The SNR of our proposed method was calculated with the following steps. First, the robot attached to the porcine stomach ( fig. S23A) was placed under the X-ray imaging device (XPERT 80, KUBTEC, Stratford CT) with no magnetic field applied ( fig. S23B (i)), after which the robot body shape was extracted using the image processing algorithm in "Robot shape tracking and analysis" Section in Materials and Methods, as shown in fig. S23B (ii). Then, the tissue was deformed by the robot with a static magnetic field applied ( fig. S23C (i) is the estimated tissue strain at time h , and is number of frames in the captured video. Further, the standard deviation was calculated with The calculated SNR of our method was 39.827, with ̅ = 0.162 and σ = 0.004.        can be used to characterize the rotation angle for calculating the robot body displacement in the robot coordinate system ("Correction of the robot curve misalignment for viscoelasticity sensing" Section in Materials and Methods).       The length and width of the robots were measured using a caliper and the thickness of the robots was measured using a 3D laser scanning confocal microscope (VK-X260K, KEYENCE). The remanent magnetization was measured using the vibrating sample magnetometer (EZ7 VSM, MicroSense LLC). B. The deviation in the dimensions of the adhesive patches of 5 fabricated viscoelasticity sensing robots. The length and width were measured using a caliper and the thickness was measured using a 3D laser scanning confocal microscope. C. The schematic of the adhesive patch of a pH sensing robot with the surface profile as measured using a 3D laser scanning confocal microscope. D. The deviation in the dimensions of the adhesive patches of 5 fabricated pH sensing robots.    sensing under X-ray imaging. The robot and porcine small intestine tissue were placed inside a 3D printed human intestine phantom (Elastic 50A, Formlabs Inc., density 1 g/cm 3 , the same as the tissues) as illustrated in (iii). Two magnets (Product number: 3800, EarthMag GmbH, Dortmund, Germany) were fixed at the two ends of a PMMA disk of 10 cm in diameter with the opposite magnetic field directions. The disk was connected to a step motor (NEMA17-01, Neukirchen-Vluyn, Germany) which was mounted on a linear motorized stage (LTS300/M, Thorlabs Inc., Newton, NJ, USA). B. The schematic (i) and the practical image (ii) of the experimental setup for viscoelasticity sensing under X-ray imaging. The robot and porcine stomach tissue were placed inside a 3D printed human intestine phantom (Elastic 50A, Formlabs Inc., density 1 g/cm 3 , the same as the tissues) as illustrated in (iii). A magnet (Product number: 3982, EarthMag GmbH, Dortmund, Germany) was connected to a DC motor (242478, Maxon Co., Switzerland) which was mounted on a linear motorized stage (LTS300/M, Thorlabs Inc., Newton, NJ, USA) as shown in (i).

Supplementary Movies Movie S1. Robot locomotion and deployment on tissues.
This video shows the process of deploying the robot to the tissue with the climbing locomotion, sensing the tissue adhesion and viscoelasticity with static and dynamic shape change, and retrieving the robot from the tissue surfaces ex vivo. The robot locomotion and sensing function are controlled by varying the external magnetic field.

Movie S2. Robot sensing adhesion on synthetic materials and tissues.
This video demonstrates the mechanism of sensing adhesion using the robot static body shape, the test results on synthetic materials of different types and curvatures, and the ability to sense pH on tissue surfaces by integrating the pH-responsive adhesive patch.

Movie S3. Robot sensing viscoelasticity on synthetic materials and tissues.
This video presents the mechanism for sensing material viscoelasticity with the robot dynamic body shape and the test results on different synthetic materials and ex vivo tissues. The generated displacement and strain field by tracking the fluorescent particles dispersed in the material are also shown to visualize the material deformation. Additionally, the video also shows a proof-of-concept demonstration of sensing stiffer artificial disease spots using the robot dynamic body shape.

Movie S4. Robot sensing pH of TNK1-expression disease models of mice ex vivo.
This video shows the X-ray imaging quality for sensing tissue adhesion ex vivo. This video also shows the results of sensing adhesion on mice stomach tissues with and without a TNK1expression disease ex vivo.

Movie S5. Robot sensing viscoelasticity of TNK1-expression disease models of mice ex vivo.
This video illustrates the X-ray and ultrasound imaging effect for sensing tissue viscoelasticity and the viscoelasticity sensing results on ex vivo mice stomach tissues with and without a TNK1-expression disease.