Papain-induced in vitro disc degeneration model for the study of injectable nucleus pulposus therapy

BACKGROUND CONTEXT Proteolytic enzyme digestion of the intervertebral disc (IVD) offers a method to simulate a condition of disc degeneration for the study of cell-scaffold constructs in the degenerated disc. PURPOSE To characterize an in vitro disc degeneration model (DDM) of different severities of glycosaminoglycans (GAG) and water loss by using papain, and to determine the initial response of the human mesenchymal stem cells (MSCs) introduced into this DDM. STUDY DESIGN Disc degeneration model of a bovine disc explant with an end plate was induced by the injection of papain at various concentrations. Labeled MSCs were later introduced in this model. METHODS Phosphate-buffered saline (PBS control) or papain in various concentrations (3, 15, 30, 60, and 150 U/mL) were injected into the bovine caudal IVD explants. Ten days after the injection, GAG content of the discs was evaluated by dimethylmethylene blue assay and cell viability was determined by live/dead staining together with confocal microscopy. Overall matrix composition was evaluated by histology, and water content was visualized by magnetic resonance imaging. Compressive and torsional stiffness of the DDM were also recorded. In the second part, MSCs were labeled with a fluorescence cell membrane tracker and injected into the nucleus of the DDM or a PBS control. Mesenchymal stem cell viability and distribution were evaluated by confocal microscopy. RESULTS A large drop of GAG and water content of the bovine disc were obtained by injecting >30 U/mL papain. Magnetic resonance imaging showed Grade II, III, and IV disc degeneration by injecting 30, 60, and 150 U/mL papain. A cavity in the center of the disc could facilitate later injection of the nucleus pulposus tissue engineering construct while retaining an intact annulus fibrosus. The remaining disc cell viability was not affected. Mesenchymal stem cells injected into the protease-treated DDM disc showed significantly higher cell viability than when injected into the PBS-injected control disc. CONCLUSIONS By varying the concentration of papain for injection, an increasing amount of GAG and water loss could be induced to simulate the different severities of disc degeneration. MSC suspension introduced into the disc has a very low short-term survival. However, it should be clear that this bovine IVD DDM does not reflect a clinical situation but offers exciting possibilities to test novel tissue engineering protocols.

Validation of targeting the ventrointermediate thalamic nucleus using Q-ball calculation in deep brain stimulation for tremor

Objective: Identification of the ventrointermediate thalamic nucleus (Vim) in modern 3T high-field MRI for image-based targeting in deep brain stimulation (DBS) is still challenging. To evaluate the usefulness and reliability of analyzing the connectivity with the cerebellum using Q-ball-calculation we performed a retrospective analysis. Method: 5 patients who underwent bilateral implantation of electrodes in the Vim for treatment of Essential Tremor between 2011 and 2012 received additional preoperative Q-ball imaging. Targeting was performed according to atlas coordinates and standard MRI. Additionally we performed a retrospective identification of the Vim by analyzing the connectivity of the thalamus with the dentate nucleus. The exact position of the active stimulation contact in the postoperative CT was correlated with the Vim as it was identified by Q-ball calculation. Results: Localization of the Vim by analysis of the connectivity between thalamus and cerebellum was successful in all 5 patients on both sides. The average position of the active contacts was 14.6 mm (SD 1.24) lateral, 5.37 mm (SD 0.094 posterior and 2.21 mm (SD 0.69) cranial of MC. The cranial portion of the dentato-rubro-thalamic tract was localized an average of 3.38 mm (SD 1.57) lateral and 1.5 mm (SD 1.22) posterior of the active contact. Conclusions: Connectivity analysis by Q-ball calculation provided direct visualization of the Vim in all cases. Our preliminary results suggest, that the target determined by connectivity analysis is valid and could possibly be used in addition to or even instead of atlas based targeting. Larger prospective calculations are needed to determine the robustness of this method in providing refined information useful for neurosurgical treatment of tremor.

Minimizing the Threat of a Positive Majority Deficit in Two-tier Voting Systems with Equipopulous Units

The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College.

Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.