Mechanical Design of the Legs of Dolomedes Aquaticus

Home , Arthropod leg, Phrixotrichus

Mechanical design of the legs of Dolomedes aquaticus

Novel approaches to quantify the hydraulic contribution to joint movement and to create a segmented 3D spider model

Stefan Reußenzehn

A thesis submitted for the degree of

Master of Science in Zoology

at the University of Otago, Dunedin New Zealand

June 2010 Abstract

Abstract

Recent findings of integrative studies of locomotion have revealed that the principles of exploiting natural interactions of the moving body and its mechanical coupling with its environment are essential for efficient locomotion. Thus agility depends as much on mechanical design as on neural control. This work investigates specific aspects of mechanical design of spiders relevant to agile locomotion. Like other arthropods, spiders are capable of agile movement, but the anatomical mechanisms underlying this behavior are somewhat unique: instead of leg articulation being solely driven by muscle movement, spiders employ a hydraulic system to extend certain joints exclusively by hemolymph pressure. Thus the mechanical design of their legs is different from that of insects examined in previous studies. This makes spiders particularly interesting for further research in this area. The methods developed in this study provide a quantitative description of the angle-volume characteristics for femur-patella and tibia-metatarsus joints in the nursery web spider Dolomedes aquaticus, a semi aquatic arachnid from New Zealand. I designed an apparatus based on the principle of joint volume shift caused by passive joint movement to measure the displacement of hemolymph as a leg is flexed. Computational image analysis of video recordings from experimental trials was achieved using a custom- made algorithm. I fitted exponential, polynomial, power-law and hyperbolic models to the angle-volume data and used Akaike Information Criterion (AIC) to evaluate how well each model described the hydraulic characteristic of each joint. Based on AIC values the polynomial model had the best fit. Angle-volume characteristics for tibia-metatarsus joints revealed a continuous increase in volume-shift with more posterior position of the individual leg. For femur-patella joints the angle-volume characteristic of the most posterior leg was also the most pronounced. In contrast to the tibia-metatarsus joint the angle-volume characteristic of the anterior third leg showed the least volume-shift while the anterior second leg was almost equal to that of the most posterior leg. Results for standardized angle-volume characteristics suggest that joint volume in D. aquaticus scales according to geometric similarity. However, no consistent pattern for the standardization factor could be identified. In addition to the angle-volume characteristics a 3D model of D. aquaticus was reconstructed. I used modern micro-CT technology to generate a surface rendering dataset of a specimen. This technique provided sufficient accuracy to reproduce the topography of the external geometry. The surface model was segmented using position of joint axes as a reference. Segments were reconstructed manually using simple mesh geometries which were superimposed on the CT surface model.

ii Abstract

The resulting 3D model closely resembled the segmented exoskeleton and provides a platform for the construction of a fully functional biomechanical model of this species which will allow numerical simulations of inverse and forward-dynamics. Mechanical leg design is expected to be a key determinant of gait and locomotor efficiency. This study represents a further step towards an integrative analysis of mechanical leg design and its effect on locomotor dynamics. The findings contribute to an integrative understanding of the unique locomotor strategy employed by spiders. Furthermore, information and data are provided for computational modelling and technical applications in the field of robotics.

Key words arthropod, arachnid, Dolomedes aquaticus, legged locomotion, mechanical design, hydraulic leg joint, 3D model, robotics

iii Acknowledgements

Acknowledgements

I wish to thank Mike Paulin for supervision and for giving me the chance to conduct this very interesting research project. Thank you for supporting me particularly with the reconstruction of the 3D model and for showing me things that can be done with a computer that I didn’t think were possible before.

Yuri Springer has become a great friend during his stay at the Zoology Department and has been so involved in my endeavors to make this thesis a sound scientiﬁc piece of work. Thank you Yuri for your great feedback, encouragement, and for our ice cream breaks in the park!

I am grateful to all the staﬀ and students of the Zoology Department. In particular, Anne Ryan for her skills and patience making the glass capillaries. This work would not have been possible without this hand made piece of the measurement apparatus. To Ken Miller, who has been extremely helpful with ﬁnding the necessary camera equipment and for taking pictures of the specimens. Barry Baxter and Murray McKenzie for building all the parts I needed in a matter of days. Keith Payne for wiring and testing the stepper motor. To the following people who provided very useful bits and pieces for my experiment: Alison Mercer, Jan Littelton, Karen Judge, Mark Lokman, Nicky McHugh, Shelley Cameron, Tania King, and Vivienne McNaughton. To Amy Armstrong for the continuous "spider food" supply and Shinichi Nakagawa for statistical advice and hints on programming in R. Thanks to my small "lab group": Kiri Pullar who shared the lab space with me and helped me a great deal to get the tracking algorithm going. Travis Monk for his great sense of humor. Last but not least, representative for all the friendly faces in the Department, I wish to thank Marc Schallenberg and Sue Heath for their friendly nature - a smile makes working a lot more pleasant:-)

I would also like to express my thanks to Andrew McNaughton (Department of Anatomy and Structural Biology) for showing me how to run the micro-CT scanner and introducing me to the reconstruction software Amira. Furthermore, Phil Christensen (Fastec Imaging, San Diego, CA, USA) for tweaking the high speed camera software which made recordings in "slow motion" possible. Jun Ng and Michael Macknight (ADInstruments, Dunedin, NZ) for introducing me to the PowerLab data acquisition system. Cor Vink (AgResearch, Christchurch, NZ) for providing measurements on leg joints of Tegenaria atrica.

iv Acknowledgements

I owe further thanks to Konstanze Gebauer, Matthew Hamilton, Tina Bayer and Roni Alder for proof reading and comments on the manuscript.

This research has been graciously supported by the Marsden Fund and by the German National Academic Foundation.

A special thanks to my partner Simone, for her loving support and endless patience and last but not least, my son Jaspar and his sibling soon to arrive, for helping me to focus on the really important things in life.

I owe all spiders!

v Contents

Contents

Abstract ii

Acknowledgements iv

List of Figures ix

List of Tables x

List of Abbreviations xi

1 General introduction 1 1.1 Legged locomotion and passive dynamics ...... 1 1.2 Spider anatomy ...... 2 1.3 Nurseryweb spider Dolomedes aquaticus ...... 3 1.4 Computational modelling ...... 4 1.5 Biologically inspired robotics - learning from animals ...... 5 1.6 Objectives of this study and thesis outline ...... 6

2 Acquisition of angle-volume characteristics 8 2.1 Introduction ...... 8 2.1.1 Locomotion and mobility of leg segments ...... 8 2.1.2 Hydraulic system for leg extension ...... 9 2.2 Material and Methods ...... 12 2.2.1 Animal collection and care in the lab ...... 12 2.2.2 Design and setup of measurement apparatus ...... 12 2.2.2.1 Removal and image taking of spider legs ...... 12 2.2.2.2 Leg attachment to stepper motor assembly ...... 13 2.2.2.3 Positioning of dye in glass capillary ...... 14 2.2.3 Apparatus settings ...... 15 2.2.3.1 Eﬀect of time on angle-volume characteristics ...... 15 2.2.3.2 Eﬀect of hydrostatic pressure on angle-volume characteristics ...... 15 2.2.3.3 Direction of joint movement ...... 15 2.2.3.4 Stepper motor setup ...... 16 2.2.3.5 Lighting and camera/video settings ...... 16

vi Contents

2.2.4 Data collection ...... 17 2.2.5 Image analysis ...... 17 2.2.5.1 Calibrating glass capillary ...... 17 2.2.5.2 Tracking displacement of dyed fluid ...... 18 2.2.5.3 Acquiring joint angle and width ...... 21 2.2.5.4 Calculating volume change and effective step width ... 22 2.2.6 Data analysis ...... 22 2.2.6.1 Testing the effect of time on angle-volume characteristics 22 2.2.6.2 Fitting models to data ...... 23 2.2.6.3 Evaluating model fit ...... 24 2.2.6.4 Testing the effect of power exponent value on the standardization factor ...... 24 2.2.6.5 Quantifying effect of joint width on the standardization factor ...... 25 2.2.6.6 Standardizing angle-volume characteristics to mean joint width ...... 26 2.3 Results ...... 28 2.3.1 Preliminary findings ...... 28 2.3.1.1 Effect of time on angle-volume characteristics ...... 28 2.3.1.2 Effect of hydrostatic pressure on angle-volume characteristics ...... 29 2.3.2 Model performance ...... 29 2.3.3 Effect of power exponent on standardization factor ...... 31 2.3.4 Effect of joint width on standardization factor ...... 32 2.3.5 Angle-volume characteristic of leg joints ...... 33 2.4 Discussion ...... 37 2.4.1 Effect of time on angle-volume characteristics ...... 37 2.4.2 Effect of hydrostatic pressure on angle-volume characteristics ... 37 2.4.3 Model performance ...... 38 2.4.4 Effect of power exponent on standardization factor ...... 40 2.4.5 Effect of joint width on standardization factor ...... 40 2.4.6 Angle-volume characteristic of leg joints ...... 41 2.4.6.1 Volume-shift in different leg joints ...... 41 2.4.6.2 Scaling of angle-volume characteristics ...... 45

vii Contents

3 Reconstruction of 3D spider model 47 3.1 Introduction ...... 47 3.1.1 Forward and inverse solutions in movement biomechanics ..... 47 3.1.2 3D imaging using micro-CT ...... 48 3.2 Material and Methods ...... 51 3.2.1 Exoskeleton geometry acquisition ...... 51 3.2.1.1 Preparation of specimen ...... 51 3.2.1.2 Micro-CT scan and numerical reconstruction ...... 51 3.2.1.3 Construction of Isosurface ...... 51 3.2.1.4 Exoskeleton segmentation ...... 52 3.2.1.5 Body segment reconstruction ...... 52 3.3 Results ...... 54 3.3.1 Threshold adjustment ...... 54 3.3.2 Segmented 3D model ...... 54 3.4 Discussion ...... 57

4 Discussion 59 4.1 Conclusion ...... 59 4.2 Suggestions for further research ...... 59

References 62

Appendix 74

viii List of Figures

List of Figures

1.2.1 External anatomy of a spider ...... 3 1.3.1 Dolomedes aquaticus ...... 4 2.1.1 Ranges of movement for leg joints in D. aquaticus ...... 9 2.1.2 Hydraulic extension mechanism in hinge joints ...... 10 2.2.1 Autotomy of spider leg ...... 13 2.2.2 Design and setup of measurement apparatus ...... 14 2.2.3 Calibration characteristic ...... 18 2.2.4 Procedure of acquiring angle-volume characteristics ...... 20 2.2.5 Procedure of measuring joint angles ...... 21 2.2.6 Fitted polynomial model ...... 24 2.2.7 Procedure of aquiring the standardizing factor ...... 26 2.3.1 Effect of time on angle-volume characteristics ...... 28 2.3.2 Effect of increasing internal pressure on angle-volume characteristics .. 29 2.3.3 Boxplot for AIC percentiles ...... 30 2.3.4 Effect of joint width on standardizing factor ...... 33 2.3.5 Standardized angle-volume characteristics for femur-patella joints ... 34 2.3.6 Standardized angle-volume characteristics for tibia-metatarsus joints .. 36 2.4.1 Comparison of angle-volume characteristics ...... 42 3.1.1 Principle of computer tomography ...... 49 3.2.1 Segmentation of surface model ...... 52 3.2.2 Reconstruction of 3D segment ...... 53 3.3.1 Comparison of isosurfaces at different threshold settings ...... 54 3.3.2 Visual comparison of wire frame mesh geometries with spider leg .... 55 3.3.3 3D model of D. aquaticus ...... 56 A.1.1 Main display of tracking GUI ...... 74 A.1.2 Effect of custom convolution filter and threshold setting ...... 75 A.2.1 Effect of decreasing internal pressure on angle-volume characteristics .. 85 A.2.2 Angle-volume characteristics for femur-patella joints ...... 86 A.2.3 Angle-volume characteristics for tibia-metatarsus joints ...... 87

ix List of Tables

List of Tables

2.3.1 Visualization of selected models according to lowest AIC-value ..... 31 2.3.2 Standard deviations of standardized angle-volume characteristics .... 32 3.3.1 Number of vertices and faces for master segments ...... 55 A.2.1 Joint width ...... 88

x List of Abbreviations

List of Abbreviations

3D three dimensional AIC Akaike Information Criterion ANCOVA Analysis of covariance ANOVA Analysis of variance Cox Coxa CT Computer tomography ∆P Pressure drop ∆t Change in time ∆V Change of volume η Dynamic viscosity exp Exponential Fem Femur hyp Hyperbolic ID Inner diameter l Length L1 Leftleg1 L2 Leftleg2 L3 Leftleg3 L4 Leftleg4

lg Given joint width

ls Standardized joint width M Torque mdn Median Met Metatarsus mjw Mean joint width OD Outer diameter P Pressure Pat Patella π Pi pol Polynomial pow Power r Radius

xi List of Abbreviations

R1 Right leg 1 R2 Right leg 2 R3 Right leg 3 R4 Right leg 4 sfac Standardization factor S1 Spider 1 S2 Spider 2 S3 Spider 3 SE Standard error Tar Tarsus θ Joint angle Tib Tibia Tro Trochanter V Joint volume ϕ˙ Angular velocity V˙ Volumetric ﬂow

Vg Given joint volume

Vs Standardized joint volume

xii General introduction 1.1 Legged locomotion and passive dynamics

1 General introduction

1.1 Legged locomotion and passive dynamics

It has become clear that mechanical design of the body is a key factor in trajectory formation for agile legged locomotion. This was ﬁrst suggested almost 100 years ago by Thompson (1917), but was overshadowed and largely forgotten after the appearance of servo-control theory and its successful applications in robotics in the middle of the twentieth century. Servo-control models imply that the nervous system generates movements by using muscles to force limbs along desired trajectories (Wiener, 1965).

Recent studies have suggested that the principles of exploiting the natural interaction between the moving body and its mechanical coupling with its environment are key factors in locomotion (Dickinson et al., 2000; Biewener, 2003). Throughout a step cycle, energy is mostly dissipated because of friction, drag and impact. In order to minimize the cost of locomotion and recapture energy, continuous interaction occurs between the nervous system, the moving body and the environment. Thus periodic leg motion appears to be essentially due to mechanical design, tuned and stabilized by the nervous system. The function of the brain is to exploit, rather than to override, the natural dynamics of the organism and its interactions with the environment (Chiel and Beer, 1997; Iwasaki and Zheng, 2006).

It is possible to build mechanical walking machines that have no sensors, actuators, or controllers that walk purely by exchange of kinetic and potential energy and are stabilized by dissipating impacts. This is called passive dynamic locomotion (Ruina, 2006). Seminal work on this subject was published by McGeer (1990a,b, 1992), who showed how bipedal walking can emerge from mechanical design without the need for actuation or control. McGeer’s computational and mechanical models showed how a cyclic exchange of kinetic and potential energy in a mechanical structure can generate gaits for legged locomotion. This idea has been used to develop eﬃcient walking robots (Collins et al., 2005).

In vertebrates, passive dynamic mechanisms involving cyclic exchange of kinetic, gravitational, and elastic energy are important for gait generation, eﬃciency, and agility of legged locomotion (Alexander and Vernon, 1975; Dimery et al., 1986; Biewener, 1998). Such mechanisms would seem to be less important for legged arthropod locomotion than for vertebrates since frictional and drag forces become relatively larger than gravitational

1 General introduction 1.2 Spider anatomy and inertial forces at smaller scales. However, it has been shown that cyclic exchange of kinetic, gravitational and elastic energy is important for gait generation and stability of legged locomotion in insects, and that mechanical design is an important determinant of this pattern of exchange (Full et al., 1998; Frazier et al., 1999). This is not to suggest that neurons and muscles are irrelevant to understanding motor agility in these organisms, but rather that they play a diﬀerent role than mid-twentieth century control theorists would have had us believe. Movement is not a product of the brain alone, but is fundamentally integrated with the mechanical design of the organism (Dickinson et al., 2000; Blickhan et al., 2003).

A unique strategy in legged locomotion is employed by spiders and other members of the class Arachnida. While limb movement in vertebrates and insects is exclusively due to muscular activity, spiders employ a hydraulic system to extend certain joints exclusively by hemolymph pressure during locomotion (Parry and Brown, 1959a,b; Shultz, 1991; Karner, 1999). This unique mechanical design oﬀers a previously unexplored focus for studies of the principles of agile locomotion.

1.2 Spider anatomy

Spiders are predatory arthropods in the order Araneae that have a body consisting of an exoskeleton separated into two parts (Fig. 1.2.1). The anterior section, called the cephalothorax or prosoma, is covered by a carapace and consists of a combined head and thorax. Most of its ventral surface is covered by a large plate called the sternum. The cephalothorax contains the brain and the eyes as well as the mouthparts and the stomach. It is also important for feeding and locomotion since all the appendages are attached to it. The posterior section, called the abdomen, contains the heart, respiratory and reproductive systems, and the spinnerets and silk producing glands. Four pairs of legs are attached between the sternum and the carapace. Each leg consists of seven segments called podomeres: Coxa, Trochanter, Femur, Patella, Tibia, Metatarsus and Tarsus (proximal to distal, Forster and Forster, 1999; Hillyard, 2007).

2 General introduction 1.3 Nurseryweb spider Dolomedes aquaticus

Cox. Tro. Fem. Pat. R4 Tib. Met. L1 Tar.

R2 R1

Figure 1.2.1: Perspective view of a spider showing external anatomy. The body of a spider is divided into two segments. The front section of the spider consists of a combined head and thorax called cephalothorax or prosoma. The rear section is the abdomen. Cox: Coxa, Tro: Trochanter, Fem: Femur, Pat: Patella, Tib: Tibia, Met: Metatarsus and Tar: Tarsus. Leg 1L: ﬁst leg on the left side, R4: fourth leg on the right side, etc.

1.3 Nurseryweb spider Dolomedes aquaticus

In the present study I investigated joints in the nurseryweb spider Dolomedes aquaticus Goyen (Araneae, Lycosoidea, Pisauridae, Fig. 1.3.1). Dolomedes is a common genus of large, vigorous spiders in New Zealand. D. aquaticus usually lives on stones, plants, or pieces of wood near streams and rivers. It can run very rapidly on land and on the water surface (Goyen, 1887; Forster and Forster, 1973). This species uses silk to construct nurserywebs but does not build snares to hunt. Instead it captures its prey by seizing it directly with its fangs (Forster and Forster, 1999). Other free living spiders which are not adapted to live near water (e.g. wolf spiders, Lycosidae) also apply similar strategies (Rovener, 1980). Agility and hence movability of legs is especially important for vagrant spiders that hunt their prey instead of capturing it in a web or burrow. Ward and Humphreys (1981) concluded that the well-developed walking ability of wolf spiders is indicated by the fact that their fourth leg pair is the longest. The fourth leg

3 General introduction 1.4 Computational modelling

10mm Figure 1.3.1: A female Dolomedes aquaticus feeding on Teleogryllus commodus. pair in D. aquaticus is also the longest (Reußenzehn and Paulin, in prep.) suggesting that Dolomedes’ locomotor system is also well developed and not speciﬁcally evolved for movement on or near water. In addition, Ehlers (1939) pointed out that locomotion on water generally does not require anatomical adaptation.

Williams (1979) showed that D. aquaticus detects prey by touch, vibration and air- borne sound and stated that even though D. aquaticus often waits passively for a prey organism, it is capable of performing very agile movements. In addition dashes of up to 40 cm across the water and very rapid leaps to capture ﬂying insects have been reported by Williams. D. aquaticus’ remarkable performance in diﬀerent terrains makes it particularly interesting for locomotion analysis.

1.4 Computational modelling

Previous studies of D. aquaticus provided quantitative models for joint limits and the forces required to move the joints towards them (Reußenzehn and Paulin, in prep). Those models are required for ongoing research into spider locomotor kinematics and dynamical modelling (Pullar and Paulin, in prep.).

Advances in computer technology have greatly enhanced the power to quantify and analyze locomotor mechanics using computational modelling. Computer simulations of legged locomotion permit the dynamics and kinematics of movement of different animals to be precisely analyzed. They also enable comparisons between the efficiency of different locomotive apparatuses and their mechanical designs. Simulation of rigid body construc- tions like the compass gait walker and the rimless wheel already provide insights into the efficiency of passive walking systems (Coleman et al., 1997). Even though arthropods

4 General introduction 1.5 Biologically inspired robotics - learning from animals and vertebrates use completely diﬀerent mechanical designs(Biewener, 2003), computational modelling can reveal similarities of locomotive principles.

Spiders have a rigid exoskeleton with relatively simple joint articulations. Vertebrates have non-rigid masses attached to a complex skeleton with many degrees of freedom, and a body surface that moves in a complex way relative to the skeleton. This means that the gait of a spider is in principle easier to track and to numerically simulate than that of a vertebrate.

Gasparetto et al. (2008) developed a rigid-body linkage model of a spider and repro- duced kinematics of spider movement computationally, but did not model the dynamic mechanisms - active or passive - which give rise to the movement patterns of real spiders. Hence, investigation of the mechanical design of spiders provides a novel and insightful ﬁeld for further research using computational modelling. Simulation of spider dynamics based on parameters measured in D. aquaticus in this and previous studies (Reußenzehn and Paulin, in prep, Pullar and Paulin, in prep.) will advance current understanding of the mechanics of legged locomotion in this and other systems. This may ultimately lead to technical applications in the rapidly advancing ﬁeld of robotics.

1.5 Biologically inspired robotics - learning from animals

Multi-legged locomotion has been successfully implemented in several robots mimicking arthropods. For example, Spenneberger and Kirchner (2002) developed an eight-legged robotic "scorpion" and Lewinger et al. (2005) created a hexapod robot whose design was inspired by leaf-cutter ants. These robots were capable of navigating across uneven terrain and over/around diﬀerent obstacles. Due to the lack of elastic elements such as springs, however, no elastic energy was recycled during leg motion. Thus locomotion required continuous power output from electric motors. The robots were always in a quasi-stable position and dissipated energy at all times during a step cycle. Kim et al. (2006) built a comparatively swift bio-inspired hexapod executing bouncy locomotion. Nevertheless their walking machine, as well as all other robots, are still far less eﬃcient and agile compared to their biological archetypes.

A few previous investigations of spider hydraulics resulted in spider-inspired technical applications. Bohmann and Blickhan (1998), Zentner et al. (2000) and Zentner and Mol- nar (2001) presented a preliminary design concept for a hydraulic device using a spider leg as a model. Schwörer et al. (1998) and Menon and Lira (2006) presented prototypes

5 General introduction 1.6 Objectives of this study and thesis outline of hydraulic ﬂexible joints for possible medical or robotic applications. However, to date no functional spider-robots have been reported in the peer-reviewed literature.

1.6 Objectives of this study and thesis outline

An understanding of the mechanical design of legs is essential for understanding locomotive behavior in animals (as outlined in section 1.1). Due to their special semi-hydraulic mechanical design, spiders provide a unique opportunity for studying the importance of hydraulic mechanisms for agile movement in animals. Large spiders like D. aquaticus are heavy and fast enough for inertia and elasticity to have a significant effect on locomotor dynamics. Therefore, mechanical leg design is expected to be a key determinant of gait and locomotor efficiency. The fact that D. aquaticus can perform agile movement on land and water makes this species particularly interesting. Apart from an investigation of leg joint compliances in D. aquaticus (Reußenzehn and Paulin, in prep) there are currently only a few studies on other terrestrial spiders reported in the scientific literature that investigate the mechanical design of spiders from this perspective (Weihmann and Blickhan, 2006; Weihmann et al., 2010; Siebert et al., 2010).

Objectives of this study:

A: Acquire the angle-volume characteristics for femur-patella and tibia-metatarsus leg joints in D. aquaticus

• Build an apparatus to measure the change in hemolymph volume during joint movement • Establish a computational method for image analysis • Identify a mathematical model to describe the angle-volume relationship • Analyze the effect of time between leg autotomy and experimental measurement of angle-volume characteristics • Quantify the influence of hydrostatic pressure on angle-volume characteristics • Investigate scaling of leg joints and change in hemolymph volume in D. aquaticus • Assess differences between the change in hemolymph volume for standardized angle-volume characteristics of joints at different leg positions

6 General introduction 1.6 Objectives of this study and thesis outline

B: Reconstruct 3D model of D. aquaticus

• Use micro-CT technology to generate surface rendering dataset • Create segmented 3D model by approximated simple mesh geometries

Thesis outline: Chapter 2 describes an experiment focused on the mechanical design of hydraulic leg extension in D. aquaticus. The objective of the experiment was to acquire the angle- volume characteristics for femur-patella and tibia-metatarsus leg joints in this species. The experimental procedure used was a newly developed version of a technique reported in previous studies (Parry and Brown, 1959a; Karner, 1999): As joint movement induces a volume change in the femur-patella and tibia-metatarsus joints, I used a custom made apparatus to measure volume shift of hemolymph across the full range of movement of these two joints. Thus, I established a reproducible and automated method to acquire the angle-volume characteristics of leg joints in spiders using a custom-made algorithm for computational image analysis. Results of this experiment provide novel information about the importance of hydraulic extension across diﬀerent leg pairs.

Chapter 3 describes the procedure used to create a 3D model of D. aquaticus using micro-CT technology. The aim of the modelling exercise was to reconstruct the external geometry of a specimen to acquire physical parameters needed for biomechanical simulations. The established model provides a platform for a fully functional biomechanical model of this species which will allow numerical simulations of inverse and forward-dynamics.

Chapter 4, a concluding discussion, includes a synthesis and interpretation of ﬁndings from the experiment and 3D modelling exercise. I identify the importance of my ﬁndings for computational modelling and possible robotic applications and end with suggestions for further research.

7 Acquisition of angle-volume characteristics 2.1 Introduction

2 Experimental investigation of angle-volume characteristics of femur-patella and tibia-metatarsus leg joints

2.1 Introduction

2.1.1 Locomotion and mobility of leg segments

Scientific interest in locomotion principles of spiders has a history of more than 100 years (e.g. Gaubert, 1892; Dixon, 1893). Ehlers (1939) was the first to present an extensive comparative study of variation in the kinematics of locomotion among a wide variety of different wandering spiders. In contrast to these spiders, which use their legs to move on the ground, web-spinning spiders have evolved unique behaviors associated with suspensory locomotion (Moya-Laraño et al., 2008). In spite of the wide variation in predatory strategies, each of which requires unique locomotor demands, all spiders share a common evolutionary strategy of leg design (Fichter and Fichter, 1988). Each leg has seven leg segments or podomeres: Coxa, Trochanter, Femur, Patella, Tibia, Metatarsus and Tarsus (proximal to distal). The podomers are thin-walled, stiff cylinders that are connected by elastic cuticular joint membranes. Spiders have fast moving limbs with a wide range of motion and as a result the legs experience inertia during locomotion. In order to minimize inertial forces, the legs are slender and most of the mass is located proximally. Thus most of the muscles responsible for motion of the proximal podomeres are located within the prosoma (Blickhan and Barth, 1985; Foelix, 1996). Movement of each podomere is affected by the geometry and compliance of the joints it shares with adjacent leg segments (Fig. 2.1.1). Joints with several degrees of freedom are located proximally. The sternum-coxa joint is similar to a ball and socket joint, but constrained so that antero-posterior movement causes the coxa to rotate about its long axis Frank, 1957; Reußenzehn and Paulin, in prep.). Dicondylous or hinge joints are found in the trochanter-femur and the femur-patella joint. These can only move in the dorso-ventral plane and hence do not need muscles for stabilization in the antero- posterior plane (Blickhan and Barth, 1985; Foelix, 1996; Siebert et al., 2010). All other joints are capable of both dorso-ventral and antero-posterior movement (Dillon, 1952; Clark, 1984, 1986; Foelix, 1996; Sens, 1996).

8 Acquisition of angle-volume characteristics 2.1 Introduction

115° a 50° 115° 141° 132° 71° Figure 2.1.1: Ranges of movement for leg joints in D. aquaticus in degrees. Anterior 112° (a) and dorsal view (b) of second right leg. Arrows indicate the furthest movement which can be made by the podomeres around their joint axes (indicated by circles) relative to Tar. Met. Tib. Pat. Fem. Tro. Cox. Ste. the reference axis (dashed lines) of the proximal podomere. Dot-and-dashed line: antero- b posterior axis of the ventral midline, dotted 135° line: contour of sternum and right coxae. 20° 76° 76° Ste: Sternum, Cox: Coxa, Tro: Trochanter,

144° Fem: Femur, Pat: Patella, Tib: Tibia, 5mm 89° Met: Metatarsus, Tar: Tarsus (modiﬁed after Reußenzehn and Paulin, in prep.).

2.1.2 Hydraulic system for leg extension

Most joints in spider legs have flexor and extensor muscles. The two exceptions are the femur-patella joint and the tibia-metatarsus joint (Dillon, 1952; Frank, 1957; Whitehead and Rempel, 1959). These two joints deviate from the characteristic antagonistic muscle design. Shultz (1989) states that Blanchard (1851-1864) was the first to note the absence of extensors in spiders. Although Gaubert (1892) was the first to propose a hydraulic extensor mechanism by hemolymph pressure while still believing in the exis- tence of extensor muscles for these joints, the full significance of this hypothesis would not be appreciated for about half a century. Petrunkevitch (1909), who concluded that extension was entirely due to elastic recoil of the interarticular joint membrane, did not recognize Gaubert’s proposal. Eventually, Ellis (1944) showed that leg extension is accompanied by a change in hemolymph volume or internal fluid pressure. Parry and Brown (1959a) were the first to provide quantitative experimental evidence to support this hypothesis.

In spiders, the femur-patella joint and the tibia-metatarsus joint are hinge joints with a dorsal pivot. The flexor muscles are therefore confined to the ventral side and can only induce flexion of these joints. As a result they need to work against the extension forces generated by hemolymph pressure (Stewart and Martin, 1974). During extension, hemolymph from the pressurized prosoma is pumped into the joints causing the

9 Acquisition of angle-volume characteristics 2.1 Introduction

a b

Figure 2.1.2: Femur-patella joint as exemplary design for hydraulic extension mechanism in hinge joints of spiders. a: Femur-patella joint of D. aquaticus. b: Schematic diagram of spider hinge joint showing mechanical design of articular membrane. Hemolymph pressure acting on exoskeleton (green arrows) and articular membrane (blue arrows). Resulting torques are depicted by red arrows with dashed line. Segment boundaries are indicated by dotted lines. (modified after Zentner, 2003). joint volume to increase (Wilson, 1970; Wilson and Bullock, 1973; Anderson and Prest- wich, 1975; Prestwich, 1988; Paul et al., 1989; Shultz, 1991). Blickhan and Barth (1985) showed that the in- and outflow of hemolymph to the torque generating joint region occurs through channels called lacunae. The authors also found that the articular membrane of a hinge joint inflates when hemolymph flows into the joint, generating extension torques which alter the joint angle (Fig. 2.1.2). The volume of hydraulic joints and the angular movement of those joints are thus mechanically linked (Parry and Brown, 1959a; Blickhan and Barth, 1985; Karner, 1999).

Karner (1999) argued that analysing angular rotation of certain joints allows deduction of information about the corresponding joint volume if the angle-volume characteristics of the joints are known. The author concluded that the volume shift created by the pressure-generating apparatus can be inferred from the sum of volume changes in the hydraulic joints. If the system contains multiple volume-shifting units the pressure generating actuators and the torque transmitting elements can only be distinguished if the status of each unit is known.

An attempt to quantify angle-volume characteristics for femur-patella and tibia-metatarsus joints has been made previously (Parry and Brown, 1959a; Karner, 1999). How- ever, Parry and Brown (1959a) obtained only seven measurements by increasing the joint angel of one leg manually and recorded the occurring change in hemolymph volume once every 20◦. Karner (1999) examined only joints of the fourth leg pair. For that the author also changed joint angles manually but achieved a higher resolution (≈ 1◦)

10 Acquisition of angle-volume characteristics 2.1 Introduction by manually-analyzed camera recordings. The present study addresses these shortcomings by establishing a more eﬃcient automated method for joint ﬂexion on a sub-degree angular resolution and a computational image analysis. This approach allowed the examination of all leg pairs from multiple spiders.

11 Acquisition of angle-volume characteristics 2.2 Material and Methods

2.2 Material and Methods

2.2.1 Animal collection and care in the lab

Adult female D. aquaticus were collected from stream banks and riverbeds throughout the Otago region of New Zealand’s South Island. Animals were brought into the lab where they were kept individually in plastic containers (length: 25 cm, width: 15 cm, height: 10 cm) with air holes in the lid. Half of the bottom of each container was covered with moist paper towels. A piece of bark and a plastic container (diameter: 5 cm, height: 1 cm) ﬁlled with untreated spring water were placed in the uncovered area. The spiders were kept under natural light conditions, but out of direct sunlight.

The containers were cleaned and fresh water and food was provided once a week. Crickets (Teleogryllus commodus) and locusts (Locusta migratoria) (Biosuppliers Live Insects) were the main food oﬀered, but wild-caught blowﬂies (Calliphora) were used as well.

2.2.2 Design and setup of measurement apparatus

To quantify the amount of hemolymph required to move the femur-patella and the tibia- metatarsus joints across a range of flexion angles I designed an apparatus based on the principle of joint volume shift caused by passive joint movement (Parry and Brown, 1959a). Following self-amputation I connected a removed spider leg to tubing filled with liquid to which a constant hydrostatic pressure was applied. Flexion of the examined joint caused a decrease in joint volume that resulted in fluid being pushed out of the leg and into the tubing. I measured the displacement of liquid as the leg was flexed.

2.2.2.1 Removal and image taking of spider legs

Since joints could not be analysed in-vivo, observations were made on freshly self- amputated legs separated by autotomy (Parry, 1957). In each case the spider to be examined was held by the cephalothorax using rubber coated forceps. The femur of the leg to be removed was ﬁxed in a sling (rubber band) as close as possible to the trochanter-femur joint (Fig. 2.2.1). The spider was then released from the forceps and teased by having air gently blown at it until it eventually self-amputated the ﬁxed leg at the coxa-trochanter joint. Photographs of the femur-patella and tibia-metatarsus joints

12 Acquisition of angle-volume characteristics 2.2 Material and Methods

a b

Figure 2.2.1: Autotomy of spider leg. a: The spider was held by rubber coated forceps while the leg was ﬁxed in a sling (rubber band). Releasing the spider from the forceps and gently blowing air at it resulted in self-amputation of the leg. b: Acquired spider leg after self-amputation. as well as the whole leg were taken with a digital camera Cyber-shot (Sony USA Foun- dation Inc., New York, NY, USA) mounted onto a stereo microscope (SZ11; Olympus, Tokyo, Japan) with an attached Olympus Photomicrographic PM-10AD system. Ref- erence length for subsequent measurement of joint width was provided by 2 mm graph paper under the specimen.

2.2.2.2 Leg attachment to stepper motor assembly

Cyanoacrylate gel adhesive (Selleys Pty Ltd, Padstow, NSW, Australia) was used to fix the trochanter and approximately half of the femur into a customized syringe tip. Three layers of silk thread saturated with cyanoacrylate adhesive (Holdfast Manufacturing Ltd, Hamilton, New Zealand) were applied to seal the leg. The syringe tip was filled with Ringer’s solution. The composition of the solution is described in Schartau and Leiderscher (1983). The syringe tip was filled from bottom to top with a MicroFil needle (34 gauge) inserted all the way to the bottom. This procedure was applied to prevent air bubbles from forming in the system. The syringe tip with the sealed leg was attached to a needle (18 gauge) connected to polyethylene tubing (OD 0.96mm, ID 0.58 mm, Critchley Electrical Products, Silverwater, NSW, Australia) filled with solution.

To examine the tibia-metatarsus joint the femur-patella joint was extended and immobilized. This was accomplished by ﬁxing the femur and tibia to a steel pin with silk thread and cyanoacrylate gel adhesive.

The 18 gauge needle holding the leg was fastened with a specimen clamp so that the joint axis of the leg aligned with the center axis of a servo-controlled stepper motor (Type:

13 Acquisition of angle-volume characteristics 2.2 Material and Methods

10µl spiderleg positioning 3ml syringes clamp

valve glasscapillary

pressure adjustablestop source

Figure 2.2.2: Design and setup of measurement apparatus for measuring volume shift during passive joint movement. Rotation of femur-patella leg joint (arrow with dotted line) results in movement of dyed fluid (arrow with dashed line) in the glass capillary. Syringes are used to position fluid in capillary before measurement. Internal fluid pressure (6.8 kPa) is provided by a fluid filled vertical glass cylinder. Dot-and-dashed lines indicate polyethylene tubing. Names of podomeres are shown in Fig. 2.1.1.

17HS4002-56M, Spark Fun Electronics, Boulder, CO, USA, Fig. 2.2.2). Alignment was checked with an OPMI 99 operational microscope (Zeiss, Jena, Germany). Angular resolution of 0.225◦ per step was achieved through a stepper motor driver (EasyDriver V3, Spark Fun Electronics, Boulder, CO, USA) controlled by a PowerLab8/30 interface unit and LabChart6 software (ADInstruments, Dunedin, NZ).

2.2.2.3 Positioning of dye in glass capillary

The custom-made borosilicate glass capillary (OD ≈ 0.4 mm, ID ≈ 0.2 mm, Duran, Schott, Mainz, Germany) was ﬁlled with water dyed with bromophenol blue using the 3 ml positioning syringe. The apparatus was then connected to a vertical glass cylinder ﬁlled with water, increasing the internal pressure to 6.8 kPa.

Once the ﬂuid pressure fully extended the joint, the dye was positioned in the capillary with a 10 µl Hamilton microsyringe. Using a micromanipulator, an adjustable stop was placed against the distal leg segment to prevent rotational movement.

14 Acquisition of angle-volume characteristics 2.2 Material and Methods

2.2.3 Apparatus settings

Before conducting measurements the whole system was flushed with 10 ml (8%) luke- warm detergent solution (Cussons Pty Ltd, Australia) and rinsed with 40 ml filtered de-ionized water (milli-Q water). This prevented a stick-slip effect from occurring in the glass capillary and interfering with movement of the dye. Between experimental trials the system was flushed with de-ionized water and then air dried to prevent deposition of Ringer’s solution on the inner walls of tubing and glass capillary.

2.2.3.1 Eﬀect of time on angle-volume characteristics

To examine whether the relationship between joint volume and joint ﬂexion changed as a function of the duration of time between leg autotomy and experimental measurement a preliminary experiment was conducted. I measured the volume-shift of a single femur- patella joint with the internal pressure set to 6.8 kPa. Trials were conducted in approx. 4 minute intervals over an extended period of 36 - 72 minutes after autotomy.

2.2.3.2 Eﬀect of hydrostatic pressure on angle-volume characteristics

In order to quantify the effect of different hydrostatic pressures on the angle-volume characteristic, two femur-patella joints were examined prior to the main experiment. The joint was flexed repeatedly while the internal pressure was increased and decreased in a stepwise manner between 3.9 and 19.6 kPa, respectively.

For subsequent trials during data collection for all joints the internal pressure was set to 6.8 kPa. Wilson (1970) concluded that a pressure of 50 mmHg (≈ 6.7 kPa) is suﬃ- cient for leg extension during locomotion. Stewart and Martin (1974) reported walking pressures of 40 - 60 mmHg (≈ 5.3 − 8.0 kPa) in Dugesiella hentzi (tarantula) and Ander- son and Prestwich (1975) measured ﬂuid pressure of 4 − 6.7 kPa in the legs of Filistata hibernalis (Hentz) during locomotion.

2.2.3.3 Direction of joint movement

Joints were ﬂexed rather than extended for measuring angle-dependent volume shift to minimize measurement errors due to hysteresis behavior. Preliminary experiments revealed a hysteresis while the joints were extended. Karner (1999) attributed this eﬀect

15 Acquisition of angle-volume characteristics 2.2 Material and Methods to low-pressure caused by the flow resistance in the glass capillary thus causing the joint membrane to collapse. During flexion of the joint the volume decreases and fluid is pushed out of the leg. Thus the joint membrane remains turgid the whole time.

2.2.3.4 Stepper motor setup

The stepper motor was programmed to flex the joint at a constant speed of 11.25◦s−1, which corresponds to a step rate of 50 s−1, until the maximum flexion angle was reached. This rate was the slowest possible because limitation of camera firmware created synchronization problems below 50 Hz.

2.2.3.5 Lighting and camera/video settings

The capillary was lighted from above using two 10 x 10 arrays of ultra bright LEDs (SCL Limited, Dunedin, NZ). In order to achieve a more uniform light intensity layers of frosted glass and paper were used to scatter the light from the LEDs. Fluid movement was recorded using a Troubleshooter 1000HR video camera (50fps, 1x shutter speed, 640x480 pixels, Fastec Imaging, San Diego, CA, USA). The camera was operated in synchronization-mode using the camera software FastControl, v. 1.2.0.0 (Fastec Imaging, San Diego, CA, USA). One frame was recorded for each motor step. After each trial, data were transferred from the camera to the computer and converted into HD resolution *.avi ﬁles using the camera software FastDownload, v. 1.4.0.0 (Fastec Imaging, San Diego, CA, USA). Corresponding joint movement was recorded by the use of a CCD color camera (Panasonic GP-AD22TA with camera-head GP-KS162HDE) connected to a stereo microscope (SZ60; Olympus, Tokyo, Japan). The camera output signal was converted using a camera control unit (Panasonic GP-KS162) and a Dazzle Hollywood DV-Bridge, v. 3.50 (Dazzle Inc., Fremont, CA, USA). Movies were captured as *.avi ﬁles using WinDV, v. 1.2.3.0 (http://windv.mourek.cz/).

16 Acquisition of angle-volume characteristics 2.2 Material and Methods

2.2.4 Data collection

All eight legs of three adult female D. aquaticus (Body weight, length: S1: 1.0 g, 21 mm; S2: 1.2 g, 22 mm; S3: 1.1 g, 22 mm) were used to acquire angle-volume characteristics for the femur-patella and tibia-metatarsus joints. All spiders appeared to be healthy and walking normally prior to the start of the experiment.

For each leg the change in hemolymph volume during ﬂexion was recorded three times for the femur-patella joint. After the femur-patella joint was extended and immobilized volume change was recorded three times for the tibia-metatarsus joint.

Femur-patella joints were ﬂexed over a range of approx. 100◦. To prevent mechanical damage of the joints the stepper motor range was set so it ended approx. 20◦ before the anatomical ventral hinge stop of about 45◦ (Reußenzehn and Paulin, in prep). Tibia- metatarsus joints were ﬂexed over a range of approx. 70◦. For this joint the stepper motor range was set to end approx. 20◦ before the anatomical ventral hinge stop of approx. 85◦. Examination took place at 20.0 ◦C ± 0.11 SE.

2.2.5 Image analysis

2.2.5.1 Calibrating glass capillary

In order to convert fluid displacement in the glass capillary to volume shift the glass capillary was calibrated with the 10 µl Hamilton microsyringe. The capillary was filled with dyed fluid in 0.1 µl increments. For each fluid position one frame was captured with the Troubleshooter 1000HR video camera. This procedure was repeated three times at 20.0 ◦C and recorded HD resolution *.avi files were analyzed using MATLAB (The MathWorks Inc., Natick, MA, USA) as described below in section 2.2.5.2. The characteristic for the fluid displacement in the glass capillary showed a strong linear relationship 2 (Radj =0.999, F1,67 = 73230, P < 0.0001) indicating a constant inner diameter over the total length (Fig. 2.2.3). Thus, the slope of the regression line, 36.6422 mm µl−1, was used as a calibration factor to convert derived fluid position to volume shift.

17 Acquisition of angle-volume characteristics 2.2 Material and Methods

trail 1 trail 2 trail 3 Displacement (mm)

0 20 40 60 80 Figure 2.2.3: Calibration characteristics of glass capillary used for volume shift experi- 0.0 0.5 1.0 1.5 2.0 ment. Linear regression equation: − 2 Volume shift (µl) y = 36.64x 0.514 (Radj = 0.999)

2.2.5.2 Tracking displacement of dyed ﬂuid

Gray-scaled video files showing fluid movement in the glass capillary were loaded into MATLAB. The video stream was treated as a sequence of images where each frame was represented by a single m-by-n matrix with m pixels (columns) and n pixels (rows). The brightness of each pixel was represented by a value corresponding to how bright the intensity of the pixel was; 0 corresponds to black and 255 to white. A custom convolution filter was applied to homogenize the lighting of the glass capillary and enhance edge contrast of the image.

Convolution is a per-pixel operation where the calculation performed at each pixel is a weighted sum of gray levels from a neighborhood surrounding a pixel. Every pixel in the input image is evaluated with its neighbors by multiplying each pixel by its corresponding value in the convolution kernel. The sum of these multiplications becomes the new intensity of the pixel that is directly under the center of the kernel and hence produced the output pixel value (Baxes, 1994, pp. 86; Eﬀord, 2000, pp. 134). Kernel multiplication was performed using the conv2 function of MATLAB and a 3x3 kernel matrix, [0 1 0; 1 1 1; 0 1 0].

Pixels below a manually set threshold level were set to 0, turning the area around the dyed fluid black. A custom made tracking algorithm was used to find the end position of the dyed fluid (non-black pixel) in the cropped image. This was repeated for all images and the position of each end position pixel was stored. Accuracy of tracking was

18 Acquisition of angle-volume characteristics 2.2 Material and Methods monitored by displaying the tracked position in the analyzed image during tracking and finally by plotting the obtained matrix for the whole video stream to check for errors. To provide a reference length the number of pixels for a 20 mm arrow displayed in the recorded area was determined using the "gtrack" function of MATLAB written by Jose F. Pina 1 which tracks the mouse and returns the coordinates. Tracking data for each leg joint were saved as *.mat files, a MATLAB file format to store matrices and variables.

Figure 2.2.4 shows an example of the procedure to acquire the angle-volume characteristic for a femur-patella joint. To facilitate effective processing of the video data a graphical user interface (GUI) for MATLAB was developed. See Fig. A.1.1 and A.1.2 (pp. 74) for key components of the GUI and the effect of the custom convolution filter and threshold setting.

1(http://www.mathworks.com/matlabcentral/ﬁleexchange/loadFile.do?objectId=15099)

19 Acquisition of angle-volume characteristics 2.2 Material and Methods

Q Q

Figure 2.2.4: Procedure of acquiring angle-volume characteristics for femur-patella joint (first right leg of spider one, trial one). Left side: start position, extended joint. Right side: end position, flexed joint. a: Spider leg mounted to stepper motor, b: Video frame of glass capillary with superimposed tracked position of dyed fluid (red symbol), c: Volume plotted against joint angle, circles indicate start and end position, respectively.

20 Acquisition of angle-volume characteristics 2.2 Material and Methods

2.2.5.3 Acquiring joint angle and width

To link displacement data, and subsequently volume data, to the joint properties of the corresponding leg I acquired joint angle and width from images. Video files showing joint movement during flexion by the stepper motor were imported into VirtualDub (v. 1.8.8, http://www.virtualdub.org). Frames showing maximum flexion and extension angles were exported as png-images and analyzed using the "Angle Tool" of ImageJ (v. 1.42q, http://rsb.info.nih.gov/ĳ/).

In order to determine the angle of the tibia-metatarsus joint the axes of adjacent joints was used as a reference. This method could not be applied for the femur-patella joint since the trochanter and parts of the femur needed to be glued into the customized syringe tip. Thus a direct visual determination of the trochanter-femur joint axis was not possible. To obtain this value I measured the quasi-femur-trachanter joint angle using the joint axis of the adjacent patella-tibia joint and the edge of the silk layers sealing the femur as a reference. This provided the range of movement of the joint while ﬂexed by the stepper motor. In order to determine the actual joint angle the lines drawn with the "Angle Tool" were imprinted on images showing maximum extension angle. I then superimposed a semitransparent image of the corresponding spider leg onto the previously saved images and rotated and scaled them so that the femura matched (Fig. 2.2.5). Hence, the actual femur-patella joint angle in relation to adjacent joint axes was determined by subtracting the derived correction angle from the previously acquired quasi maximum ﬂexion and extension angles. These steps ensured that the derived

a b

Q Q a

Figure 2.2.5: Procedure of measuring joint angles exempliﬁed for ﬁrst right leg of spider one. a: For the femur-patella joint a semitransparent image of the spider leg was superimposed on a corresponding image showing maximum extension angle of this leg during the experiment. Θ: actual femur-patella joint angle, α + Θ: previously measured extension angle, α: correction angle. Joint axis indicated by circles. b: For tibia-metatarsus joint the actual joint angle Θ could be obtained directly from the image taken during the experiment.

21 Acquisition of angle-volume characteristics 2.2 Material and Methods joint volume, acquired by subsequent analysis, corresponded to the actual femur-patella joint.

Photographs showing the width of the femur-patella and tibia-metatarsus joints were analyzed using the "Straight line selection Tool" of ImageJ. I acquired joint width in number of pixels and used the number of pixels for the reference length (2 mm) to calculated joint width in millimeters.

2.2.5.4 Calculating volume change and eﬀective step width

In order to convert the acquired ﬂuid displacement to meaningful volume information, tracking data for each trial were read into MATLAB and pixel position was converted to volume change using the number of pixels of the reference length and the calibration factor of the glass capillary.

Since data acquisition for change of joint angle (motor step) and change of joint volume (video frame) was synchronized, each joint volume could be allocated to a joint angle. However, a slight displacement of the joint axis versus the axis of the motor’s drive shaft during flexion caused the joint to flex less than the actual range of movement of the motor. Displacement appeared to be linearly related to rotation, thus the effective step width for each joint was calculated by the range of movement derived from images divided by the number of steps. Effective step width was used for further calculations.

2.2.6 Data analysis

2.2.6.1 Testing the eﬀect of time on angle-volume characteristics

Linear regression was carried out in R (R Development Core Team, 2008) to test for correlation between measured joint volume at 120◦ and duration of time between leg autotomy and experimental measurement. Joint volume at 120◦ / 140◦ for femur-patella / tibia-metatarsus joints was chosen to represent angle-volume characteristic because a) the maximum joint angle (180◦ / 200◦) is based on the estimate of the mathematical model and not on acquired raw data and b) 120◦ / 140◦ represents approximately the middle of the actual range of movement measured during trials (comp. Fig. 2.2.6, p. 24).

22 Acquisition of angle-volume characteristics 2.2 Material and Methods

2.2.6.2 Fitting models to data

Volume shift was plotted against joint angle and four different models were fitted to data of all three trials for each joint in order to find a mathematical model to describe the dependency of joint volume on joint angle (V(θ)).

First, a polynomial model of the form

2 V(θ) = a θ + b θ + c (2.2.1) was ﬁtted. This model has a simple mathematical form and was used by Karner (1999) to describe the relationship between angle and volume.

Second, a power-law model of the form

k V(θ) = a + b (θ − c) (2.2.2) was ﬁtted. It was previously reported that movement of spider joints exhibits power-law dynamics (Blickhan, 1986) and mechanical systems often obey power law relationships because of dimensional constraints (Barenblatt, 2003).

Third, a hyperbolic model of the form

b V = a + (2.2.3) (θ) (θ − c) was ﬁtted. This model, a special case of the power law model with k= −1, was chosen because it performed better than the power law model in describing joint compliances in D. aquaticus in a previous analysis (Reußenzehn and Paulin, in prep.).

Finally, an exponential model of the form

− θ−c d V(θ) = a + b e (2.2.4) was ﬁtted. This model was chosen because it seems to have a simple mathematical form with the required property that joint volume increases up to a limiting volume.

An example of a fitted polynomial model is shown in Fig. 2.2.6. Model parameters were fitted using the lsqcurvefit function of MATLAB Optimization Toolbox to minimize the residual error variance.

23 Acquisition of angle-volume characteristics 2.2 Material and Methods

Figure 2.2.6: Fitted polynomial model: Vol- ume plotted against joint angle for data of three trials (1:blue, 2: green, 3: red) for

Jointvolume( l) the femur-patella joint (ﬁrst right leg of spider one). Solid line: polynomial model determined by equation 2.2.1, ﬁtted using the method of least squares error. Joint volume JointangleQ ( ° ) set to zero at 40◦.

The angle-volume characteristic was standardized by setting joint volume to zero at 40◦ joint angle for femur-patella joints. This volume zero point was chosen by Karner (1999) because measured joint angels for maximum ﬂexion of this joint were always greater. The same was true for all measurements in this study and previously estimated maximum ﬂexion angles for these joints in D. aquaticus (Reußenzehn and Paulin, in prep.). The volume zero point for tibia-metatarsus joints was set to 80◦ based on the same rationale.

2.2.6.3 Evaluating model ﬁt

The best-fit model was identified using Akaike’s Information Criterion (AIC) that im- poses penalties for additional fitting parameters (Akaike, 1973). AIC is defined as:

n 2 (Yi − Yˆi) i AIC = n · log X=1 +2k (2.2.5) n ! where n is the number of angle-volume data points measured per joint, k is the number ˆ of model parameters, and Yi and Yi denote observed data and predicted joint volume by the model, respectively (Burnham and Anderson, 2002).

2.2.6.4 Testing the eﬀect of power exponent value on the standardization factor

In order to compare angle-volume characteristics of joints from different legs, characteristics had to be standardized to the same joint width. Karner (1999) found that dimensions in Cupiennius salei scaled isometrically confirming earlier findings by Prange

24 Acquisition of angle-volume characteristics 2.2 Material and Methods

(1977) for the spider Lycosa lenta. The author also showed that volume shift scales according to geometric similarity in C. salei. Since the volume of geometrically similar objects depends on the third power of its linear dimension the author standardized by using a cubic relationship (n = 3) for the joint width in equation

n −n Vs = Vg(lg , ls ) (2.2.6)

where Vs is the standardized joint volume, Vg is the given joint volume, lg is the joint width of the corresponding joint, ls is the standardized joint width and n is the power exponent value used for standardization.

To test for this relationship diﬀerent power exponents (n = 1, 2, 3, 8/3) were used to n −n calculate the standardizing factor (sfac, lg /ls ) in equation 2.2.6, where ls is the mean joint width for all joints of same type of all three spiders. Exponent n = 1 assumes a linear relationship between joint width and volume, whereas n = 2 and n = 3 assume a quadratic or cubic relationship, respectively. Scaling based on elastic similarity is ex- pressed by n = 8/3 where leg lengths increases as the 2/3 power of diameter (joint width) and weight (volume) increases to the 4th power of length (McMahon, 1973; Alexander, 1988, pp. 116). Since the best power exponent for standardization minimizes variance between standardized angle-volume characteristics I calculated standard deviations of standardized characteristics at 120◦ (140◦ for tibia-metatarsus joints) for each spider using all eight legs respectively (compare section 2.2.6.1, p. 22 for selection of joint angles).

2.2.6.5 Quantifying eﬀect of joint width on the standardization factor

A mean characteristic V(θ)av was ﬁtted to the data of all characteristics for all joints of the same type of the three spiders. This characteristic was then scaled to characteristics of each joint V(θ)i by multiplying it with a standardizing factor sfac, using equation ◦ V(θ)i = V(θ)av · sfac, so that joint volume of both characteristics matched closely at 120 (Fig. 2.2.7, compare section 2.2.6.1, p. 22 for selection of joint angles).

Standardizing factor (sfac) was plotted against joint width for each spider and linear regression models were ﬁtted to these data in R. To justify pooling of the data, one- way analysis of covariance (ANCOVA) was carried out to test for diﬀerences in the ratio between standardizing factor and joint width of the three spiders. In this analysis, spider number was a categorical variable, joint width a covariate and standardizing

25 Acquisition of angle-volume characteristics 2.2 Material and Methods

3.5 3.5 a b 3 3 L2 l) l)

µ 2.5 mean µ 2.5 mean 1.1334 L1 2 2 1.5 1.5 0.9217 1 1 Joint volume ( Joint volume ( 0.5 0.5 0 0 40 60 80 100 120 140 160 180 40 60 80 100 120 140 160 180 Joint angle Θ (°) Joint angle Θ (°)

Figure 2.2.7: Procedure of aquiring the standardizing factor for each angle-volume characteristic. a: Mean characteristic (blue) was determined by fitting a polynomial model to raw data of all characteristics of all femur-patella joints from three spiders. b: Two examples of scaling the mean characteristic by multiplying it with a standardizing factor (red) to match the corresponding characterisic (black) e.g. Spider one, first and second left leg: L1, L2. Red dashed line: scaled mean characteristic. factor was the dependent variable. Regression slopes were compared across the three spiders by testing the spider group by covariate interaction term (Quinn and Keough, 2002, pp. 352). For this comparison, the level of significance (α) was specified to 0.10 in order to take Type II errors into account. Type II errors account for the risk that an invalid null hypothesis is retained (Sachs, 1984, pp. 117). Analysis was carried out using statistical software R (R Development Core Team, 2008).

2.2.6.6 Standardizing angle-volume characteristics to mean joint width

The angle-volume characteristics for each joint were standardized to mean joint width using equation 2.2.6, p. 25 with n = 3 as the power exponent (compare Discussion section 2.4.4, p. 40 for use of cubic relationship).

In order to determine the average angle-volume characteristic for joints at a certain leg position (1st,2nd,3rd,or4th leg pair) I standardized each joint’s characteristic according to its leg position. The standardized joint width (ls) for each leg position was determined by the mean width of all joints from the same leg position (e.g. femur-patella joint width of all six front legs, no difference was made between left and right). Model parameters for average angle-volume characteristics for each leg position were fitted to data for the six corresponding joints using the "lsqcurvefit" function of MATLAB.

26 Acquisition of angle-volume characteristics 2.2 Material and Methods

To determine if these average angle-volume characteristics for joints at a certain leg position differed among different legs I standardized all joints’ characteristics to the same joint width. This width was determined by the mean width of all joints (e.g. mean width of all femur-patella joints of all legs from all spiders). Model parameters for average angle-volume characteristics for each leg position were fitted in MATLAB using data for the six corresponding joints.

One factor analysis of variance (ANOVA) and Tukey’s Post Hoc Test were carried out to test for differences between mean angle-volume characteristics of joints from different legs. For this, joint volume at 120◦ (140◦ for tibia-metatarsus joints) was taken as a measure for each joint’s characteristic. Level of significance (α) was specified to 0.05.

27 Acquisition of angle-volume characteristics 2.3 Results

2.3 Results

Application of hydrostatic pressure (6.8 kPa) extended the femur-patella joints to 163.9◦ ± 2.0 SE and the tibia-metatarsus joints to 178.3◦ ± 1.7 SE. Femur-patella joints were ﬂexed over a range of approx. 100◦ to 64.9◦ ± 1.1 SE while tibia-metatarsus joints were ﬂexed by approx. 70◦ to 108.5◦ ± 0.8 SE. For femur-patella joints, examination was completed on average within 38 min ± 1.7 SE after autotomy and 55 min ± 1.8 SE for tibia-metatarsus joints.

2.3.1 Preliminary ﬁndings

2.3.1.1 Eﬀect of time on angle-volume characteristics

Linear regression revealed no signiﬁcant relationship between angle-volume characteristics and the duration of time between leg autotomy and experimental measurement 2 over the test period of 36 - 72 minutes (Radj =0.03, F1,10 =1.369, P < 0.269, Fig. 2.3.1). Joint volume at 120◦ was chosen to depict the eﬀect (compare section 2.2.6.1, p. 22 for selection of joint angle).

a b

Jointvolume( l)

Jointvolumeat120 ( l)

JointangleQ ( ° )

Figure 2.3.1: Eﬀect of time after autotomy on angle-volume characteristics. a: Angle-volume characteristics for femur-patella joint of the second right leg, internal pressure 6.8 kPa . Trial number position corresponds to joint volume at 120◦ (dashed line). b: Joint volume at 120◦ 2 plotted against time. Linear regression equation: y = 0.00131x + 1.678 (Radj = 0.03).

28 Acquisition of angle-volume characteristics 2.3 Results

a b

Jointvolume( l)

Jointvolumeat120 ( l)

JointangleQ ( ° )

Figure 2.3.2: Eﬀect of increasing internal pressure on angle-volume characteristics. a: Angle- volume characteristics for femur-patella joint of third right leg. Pressure was increased from trial to trial. Trial number position corresponds to joint volume at 120◦ (dashed line). b: Joint volume at 120◦ plotted against pressure for each trial. Numbers indicate trial numbers.

2.3.1.2 Eﬀect of hydrostatic pressure on angle-volume characteristics

The angle-volume characteristics for the femur-patella joint showed an increase in joint volume with increasing hydrostatic pressure between trials (Fig. 2.3.2). Joint volume at 120◦ was chosen to depict the eﬀect of diﬀerent pressures (compare section 2.2.6.1, p. 22 for selection of joint angle).

Joint volume increased from 1.82 µl at 3.9kPa to 1.98 µl at 19.6 kPa. Joint volume appeared to increase linearly with increasing pressure in the lower range up to 9.8 kPa. However, this trend did not persist once that threshold had been exceeded and change of joint volume between trials decreased. Joint volume at 120◦ deviated on average by ± 0.055 µl between trials. The same general trend was found for the second joint while decreasing the pressure between trials. Due to a corrupted ﬁle and a measurement artefact (compare Fig. A.2.1, p. 85) data were not included in further analyses.

2.3.2 Model performance

For femur-patella joints, the median (mdn) of AICs analyses for the four models tested ranged from -12970 to -10921 (Fig. 2.3.3a). The exponential model showed the best over-

29 Acquisition of angle-volume characteristics 2.3 Results

a b AIC values AIC values −11000 −9000 −7000 −16000 −12000 −8000 exp pol pow hyp exp pol pow hyp Model Model

Figure 2.3.3: Box plot for Akaike’s information criterion (AIC) percentiles as goodness-of-fit for assessing the performance of four models for all joints. a: Femur-patella joints. b: Tibia- metatarsus joints. exp: exponential model, pol: polynomial model, pow: power model, and hyp: hyperbolic model. all performance (mdn: -12970) followed by the polynomial model (mdn: -12773), the power model (mdn: -11975), and the hyperbolic model (mdn: -10921). Consideration of AIC-values on a case-by-case basis revealed that out of 24 cases the exponential and the polynomial model were both selected in 11 cases, whereas power and hyperbolic model were only selected in 1 case each (Table 2.3.1). Thus, Akaike’s criterion selected the exponential and the polynomial model in 48% of all cases, respectively. Qualitatively there was no pattern or any tendency for the exponential or polynomial model to fit better on particular legs, or for particular spiders (Table 2.3.1). A paired-sample t-test showed that the AICs for the fitted exponential model were significantly smaller than the corresponding AICs for fitted polynomial models (t-statistic = 2.6447, P = 0.0145, df = 23). For tibia-metatarsus joints median AICs ranged from -9615 to -10921 (Fig. 2.3.3b). The exponential model showed the best overall performance (mdn: -9615) followed by the polynomial model (mdn: -9580), the power model (mdn: -9369), and the hyperbolic model (mdn: -9303). Consideration of AIC-values on a case-by-case basis indicated that out of 24 cases the polynomial model was selected in 16 cases, the exponential model in 7 cases and the power model in 1 case. The hyperbolic model was never selected (Table 2.3.1). Thus, AIC selected the polynomial model in 67% of all cases and the exponential model in 29% of all cases. A paired-sample t-test showed that the AICs for the fitted

30 Acquisition of angle-volume characteristics 2.3 Results exponential model were not signiﬁcantly smaller than the corresponding AICs for ﬁtted polynomial models (t-statistic = -1.5621, P = 0.1319, df = 23). Due to the performance of the polynomial model on a case-by-case basis and on parsimony grounds (one parameter less than the exponential model) I selected this model as the one providing the best description of angle-volume characteristics for further calculations and comparisons of femur-patella and tibia-metatarsus joints.

Table 2.3.1: Visualization of selected models according to lowest AIC-value across all measured joints for each spider (S1, S2, S3). L1: ﬁrst left leg, R2: second right leg, etc., exp: exponential model, pol: polynomial model, pow: power model, and hyp: hyperbolic model.

femur-patella tibia-metatarsus L1 L2 L3 L4 R1 R2 R3 R4 L1 L2 L3 L4 R1 R2 R3 R4

S1 exp exp pol pol exp pol pol exp pol pol pol pol exp pol pol pol

S2 exp exp pol exp pol pol pow pol pol exp exp exp pol pol pol pol

S3 exp pol exp hyp pol exp pol exp pow pol exp exp pol pol pol exp

2.3.3 Eﬀect of power exponent on standardization factor

For femur-patella joints, the standard deviation of standardized angle-volume characteristic was smallest for power exponent n = 3 in spider one, n = 2 in spider two and n = 1 in spider three (Table 2.3.2). In contrast, standard deviations of standardized angle-volume characteristics for tibia-metatarsus joints were smallest for n = 3 for spider one and three. For spider two n = 8/3 resulted in the smallest deviation. Hence no consistent pattern for the lowest value could be found for best power exponent among the three spiders in either of the two joints.

31 Acquisition of angle-volume characteristics 2.3 Results

Table 2.3.2: Standard deviations of standardized angle-volume characteristics for femur-patella (at 120◦) and tibia-metatarsus joints (at 140◦) for each spider (S1, S2, S3) using all eight joints respectively. Minimum within each set indicated by underscore. Characteristics were standardized using equation 2.2.6, p. 25.

femur-patella tibia-metatarsus S1 S2 S3 S1 S2 S3

n=1 0.1665 0.1557 0.1144 0.1497 0.1031 0.1442 n=2 0.1273 0.1272 0.1274 0.1207 0.0739 0.1155 8 n = 3 0.1147 0.1545 0.1610 0.1041 0.0695 0.1024 n=3 0.1140 0.1783 0.1823 0.0966 0.0735 0.0990

2.3.4 Eﬀect of joint width on standardization factor

There was a significant positive relationship between joint width and standardization factor for femur-patella joints with a good fit of the data for spiders one and two 2 2 (S1: Radj =0.87, F1,6 = 46.93, P < 0.001; S2: Radj =0.84, F1,6 = 38.42, P < 0.001; Fig. 2 2.3.4a). There was not a significant relationship for spider three (Radj =0.19, F1,6 =2.6, P < 0.15). A significant positive relationship was observed for tibia-metatarsus joints 2 2 in all spiders (S1: Radj =0.74, F1,6 = 21.4, P=0.0036; S2: Radj =0.72, F1,6 = 19, 2 P=0.0048; S3: Radj =0.63, F1,6 = 12.98, P=0.011; Fig. 2.3.4b). The ratio between scaling factor and joint width is indicated by the slope angle of the linear regression trend line. All spiders differed significantly at the α = 0.10 level regardless of joint type (femur-patella joints: F2,18 =3.42, P=0.055, tibia-metatarsus joints:

F2,18 =3.86, P=0.040). Because statistical differences between slopes did not permit pooling of data for all spiders into a single analysis, a general (non-spider-specific) relationship between joint width and standardization factor could not be analyzed. Graphi- cal exploration of residuals indicated a rather non-linear relationship between joint width and standardization factor. However, given noise in the data no clear pattern could be discerned and no further attempt was made to fit higher degree models.

32 Acquisition of angle-volume characteristics 2.3 Results

a b

Standardization factor S1 Standardization factor S1 S2 S2 S3 S3 0.7 0.8 0.9 1.0 1.1 0.6 0.8 1.0 1.2 1.4 1.6 1.8

−0.1 −0.05 0 0.05 0.1 −0.1 −0.05 0 0.05 0.1 Centred joint width (mm) Centred joint width (mm)

Figure 2.3.4: Effect of joint width on standardizing factor for all examined joints of spiders S1, S2, and S3. a: Femur-patella joints, linear regression equations are: S1: y = 2.607x+1.030 (SE 2 of regression coefficients: 0.381, 0.015; Radj = 0.87), S2: y = 1.398x+0.860 (SE of regression co- 2 efficients: 0.226, 0.019; Radj = 0.84), S3: y = 0.908x+1.090 (SE of regression coefficients: 0.557, 2 0.032; Radj = 0.19), n = 8 per spider. Graph centered around mean joint width (1.275 mm) of all joints. b: Tibia-metatarsus joints, linear regression equations are: S1: y = 7.812x + 0.636 2 (SE of regression coefficients: 1.689, 0.112; Radj = 0.74), S2: y = 2.791x + 1.001 (SE of re- 2 gression coefficients: 0.640, 0.056; Radj = 0.72), S3: y = 4.585x + 1.132 (SE of regression 2 coefficients: 1.273, 0.080; Radj = 0.63), n = 8 per spider. Graph centered around mean joint width (0.877 mm) of all joints.

2.3.5 Angle-volume characteristic of leg joints

The angle-volume characteristic for all leg joints measured showed a non-linear relationship between increasing angle and increasing volume. The change in joint volume decreased with increasing joint angle causing the characteristics to level out towards maximum extension. Angle-volume characteristics for both types of leg joints of each spider were similar amongst the three spiders (Fig. A.2.2 and A.2.3, pp. 86). Femur- patella joints of the ﬁrst and third leg pair showed slightly lower characteristics than those of the second and third. Over the whole range of movement (40◦ - 180◦) the joint volume changed by approx. 2 - 3 µl among all legs.

For tibia-metatarsus joints, the characteristic was greater in more posterior legs. The change between the ﬁrst three leg joints was only marginal whereas the angle-volume

33 Acquisition of angle-volume characteristics 2.3 Results characteristic of joints for the forth legs showed a much greater volume change. Over the whole range of movement (80◦ - 200◦) the joint volume changed by approx. 0.5 µl for the joints of the ﬁrst three legs and by approx. 1.25 µl for joints of the forth leg. Corresponding widths of both types of joints reﬂected a similar relationship as angle- volume characteristics (table A.2.1, p. 88).

Standardized mean angle-volume characteristics for femur-patella joints (Fig. 2.3.5a) revealed that joints of the fourth leg, with a mean joint width (mjw) of 1.329 mm, showed the greatest volume change (2.7 µl) over the whole range of movement. Joints of the second leg (mjw:1.297 mm) showed a volume change of 2.65 µl while those of the

3 a b

2.5

1.5

Jointvolume( l) 1

1st leg 2nd leg 0.5 3rd leg 4th leg 0 40 60 80 100 120 140 160 180 40 60 80 100 120 140 160 180 JointangleQ ( ° ) JointangleQ ( ° )

Figure 2.3.5: Standardized mean angle-volume characteristics for femur-patella joints determined by a polynomial model. Joint volume was set to zero at 40◦. (a): Each angle- volume characteristic was standardized to corresponding mean joint width for each leg position (1: 1.262 mm, 2: 1.297 mm, 3: 1.213 mm, 4: 1.329 mm). (b): Angle-volume characteristics were standardized to mean joint width of all joints (1.275 mm). Standard error of mean indicated by thin line of same type for each standardized mean (n = 6). Angle-volume characteristic for each joint can be found in Fig. A.2.2.

34 Acquisition of angle-volume characteristics 2.3 Results

ﬁrst leg (mjw: 1.262 mm) showed a change of 2.4 µl and the third leg (mjw: 1.213 mm) resulted in only 2.2 µl over the whole range of movement. However, single factor analysis of variance based on joint volume at 120◦ showed no diﬀerence between mean standardized angle-volume characteristics of all legs (F3,20 =2.41, P=0.0968). Angle-volume characteristics shown in Fig. 2.3.5b were standardized to mean joint width of all joints

(1.275 mm) and did not diﬀer signiﬁcantly (F3,20 =0.21, P=0.8886) either.

For tibia-metatarsus joints, standardized mean angle-volume characteristics (Fig. 2.3.6a) indicated that joints of the fourth leg (mjw: 0.962 mm) showed the greatest volume change (1.1 µl). The same was true for the femur-patella joints. However, the second largest volume change (0.75 µl) occurred in joints of the third leg (mjw: 0.882 mm). This stands in contrast to femur-patella joints for which the third leg showed the smallest volume change. Joints of the second leg (mjw: 0.846 mm) showed a volume change of 0.6 µl while volume change for joints of the first leg (mjw: 0.846 mm) resulted in only 0.5 µl over the whole range of movement. Single factor analyzes of variance based on joint volume at 140◦ showed highly significant differences between standardized angle- volume characteristics of all legs (F3,20 = 20.51, P < 0.0001). The limits of the 95% confidence interval, resulting from Tukey’s Post Hoc Test, did not include zero for pair- wise combinations including the fourth leg. Thus, for α = 0.05, a significant difference between leg four and all remaining legs was detected. There was no statistical difference between leg one, two, and three. Angle-volume characteristics, which were standardized to mean joint width of all joints (0.877 mm), did not differ significantly (F3,20 =1.96, P=0.1531) among all leg positions (Fig. 2.3.6b).

35 Acquisition of angle-volume characteristics 2.3 Results

1.2 a b

0.8

0.6

Jointvolume( l) 0.4 1st leg 2nd leg 0.2 3rd leg 4th leg 0 80 100 120 140 160 180 200 80 100 120 140 160 180 200 JointangleQ ( ° ) JointangleQ ( ° )

Figure 2.3.6: Standardized mean angle-volume characteristics for tibia-metatarsus joints determined by a polynomial model. Joint volume was set to zero at 80◦. (a): Each angle- volume characteristic was standardized to corresponding mean joint width for each leg position (1: 0.817 mm, 2: 0.846 mm, 3: 0.882 mm, 4: 0.962 mm). (b): Angle-volume characteristics were standardized to mean joint width of all joints (0.877 mm). Standard error of mean indicated by thin line of same type for each standardized mean (n = 6). Angle-volume characteristic for each joint can be found in Fig. A.2.3.

36 Acquisition of angle-volume characteristics 2.4 Discussion

2.4 Discussion

2.4.1 Eﬀect of time on angle-volume characteristics

As dead body parts were used for examination, incipient desiccation and rigor mortis resulted in stiffening of the joint membranes. That effect would have altered properties of the articular membrane causing changes in hemolymph volume-shift of the examined joint. However, the effect could be excluded for the period of the observation as no significant correlation between joint volume and time between leg autotomy and experimental measurement occurred in the observed femur-patella joint.

Since the femur-patella joint membrane provides a larger surface than that of the tibia- metatarsus joint (S. Reußenzehn, pers. obs.) it was assumed that the latter experienced less of a desiccation eﬀect and therefore retained its natural characteristic longer than the examined joint.

2.4.2 Eﬀect of hydrostatic pressure on angle-volume characteristics

The examination of one femur-patella joint revealed a positive relationship between joint volume and internal fluid pressure. Joint volume varied by approx. 9% between trials with lowest and highest pressure applied respectively. While joint volume seemed to increase linearly, during stepwise pressure increase up to 9.8 kPa, the change of joint volume between trials appeared to decrease once that threshold was exceeded. This indicates a non-linear relationship where the increase might eventually level out. Parry and Brown (1959a) analyzed pressure effects on changes in joint volume in the spider Tegenaria atrica. Their data suggested that the correlation between increasing pressure and increasing change in joint volume appears to be mostly linear even though much higher pressure was applied (≈ 27 − 67 kPa).2 However, the authors applied only four different pressures and the difference between characteristics for the lowest and second lowest pressures appears smaller than the differences between characteristics of higher pressures for the femur-patella joint, suggesting some degree of non-linearity. Elastic properties of the joint membranes have been reported for C. salei (Blickhan and Barth, 1985) and D. aquaticus (Reußenzehn and Paulin, in prep.). Therefore, the non-linear pressure dependency might be explained by the fact that the flexible joint membranes

2Wilson (1970) attributed the high pressure recorded for Taganaira by Parry and Brown (1959a) to the experimental treatment causing an escape reaction in the spider.

37 Acquisition of angle-volume characteristics 2.4 Discussion can only stretch up to a certain limit and that increasing stiffness during expansion results in reduced increase of joint volume with rising pressure. Karner (1999) acquired angle-volume characteristics for the fourth leg of C. salei but did not test for the effect of different internal pressures on angle-volume characteristics and did not report any specific pressure settings. He argued, based on Parry and Brown’s (1959a) findings, that the slope of the angle-volume characteristic is not pressure dependent. While data from Parry and Brown (1959a) seem to support that assumption it must be remembered that the authors did not standardize their characteristics by setting joint volume to zero. Observations of femur-patella joints in D. aquaticus showed that for maximum flexion of the joint the articular membrane folds completely and gets almost entirely encapsulated by the adjacent leg segments (S. Reußenzehn, pers. obs.). This supports the adoption of a pressure independent minimum joint volume. Thus, assuming a zero joint volume and a pressure dependent maximum volume, the slopes of the angle-volume characteristics should increase with increasing pressure. Deriving the polynomials that describe the angle-volume characteristics for different pressures confirmed this assumption for slopes at 120◦.

Results from earlier studies involving different spider species showed that the fluid pressure in the legs varied between approximately 5 − 8 kPa during locomotion (Wilson, 1970; Stewart and Martin, 1974; Anderson and Prestwich, 1975). Due to these findings it seemed reasonable to adopt a set pressure of 6.8 kPa approx. in the middle of that range. The results of the preliminary experiment with different pressures showed that within the pressure range taken from the literature (5 − 8 kPa) the joint volume varied by only ± 0.037 µl. Compared to that of the trial at 6.8 kPa this accounted for only ± 1.9% of the change in joint volume.

2.4.3 Model performance

Quantitative models of joint compliances and the forces required to move the joints towards their limits are required for ongoing research into spider locomotor kinematics and dynamical modelling (Pullar and Paulin, in prep.). For this, simple models are sought that can approximate the mechanical compliance and provide reproducible estimates of the range of motion at each joint. This study contributes to that eﬀort by providing a quantitative description of the angle-volume characteristics of the hydraulically extended femur-patella and tibia-metatarsus joints.

38 Acquisition of angle-volume characteristics 2.4 Discussion

Models were chosen on parsimony and mathematical grounds to quantify the non-linear characteristic. The polynomial and the hyperbolic model have three parameters to describe the angle-volume characteristic mathematically while the power law and the exponential model have four parameters. Hence the latter two models are more flexible in fitting to data. All four models allowed a reasonable approximation of the characteristic. According to AIC percentiles as goodness-of-fit for the overall performance the exponential model showed to be a slightly better fit than the polynomial model in femur- patella joints. The power model fitted less well and the hyperbolic model showed the worst fit. Differences were not as distinctive for tibia-metatarsus joints. Even though the exponential model showed the best performance overall the difference between it and the polynomial model was almost negligible. The power and hyperbolic model showed slightly worse fit. Looking at AIC results on a case-by-case basis confirmed that the fitted power law model and the hyperbolic model as its special case fitted significantly worse than the other two models regardless of joint type. The power law model and the hyperbolic model fit best only in 1 out of 24 cases (approx. 4%), respectively for femur-patella joints. The power law was best for 1 case while the hyperbolic model never fitted best for tibia-metatarsus joints. Therefore, the power law and the hyperbolic model were eliminated as candidates for both joints. AIC analyses for each case showed that the remaining polynomial and exponential models were selected in 11 cases out of 24, respectively, for femur-patella joints. However, the polynomial model outper- formed the exponential model by fitting best in 16 cases (67%) versus 7 cases (29%) for tibia-metatarsus joints.

A goal of this study was to ﬁnd a simple and computationally eﬃcient way to model angle-volume characteristic during spider locomotion. Due to the performance of the polynomial model on a case-by-case basis and on parsimony grounds (one parameter less than the exponential model) it appeared reasonable to select a polynomial model as the best description of angle-volume characteristic for every joint. The fact that the polynomial model showed the least variance for femur-patella joints (54% of exponential model) contributed to this decision. Thus statistical support for better overall performance of the exponential model was not considered strong enough to select it exclusively to describe the angle-volume characteristics for femur-patella joints.

39 Acquisition of angle-volume characteristics 2.4 Discussion

2.4.4 Eﬀect of power exponent on standardization factor

The examination of different power exponents used to calculate the standardizing factor n −n sfac (lg /ls ) in equation 2.2.6, p. 25, revealed no consistent pattern for best power exponent among the three spiders in either of the two joints. Exponent n = 3 (i.e. maintaining geometric similarity) showed the smallest variance in two spiders for tibia-metatarsus joints and for femur-patella joints in one spider. Exponent n = 8/3 (i.e. maintaining elastic/buckling similarity) was smallest only once for tibia-metatarsus joints. Hence the indirect testing method used in this study could only partly confirm isometric scaling in D. aquaticus even though this relationship was reported in previous studies for other spider species by Prange (1977) and Karner (1999). These authors found isometric scaling by measuring the length and width of leg segments in the spiders L. lenta and C. salei respectively. The scaling of the external dimensions supports geometric similarities instead of buckling similarities in these species. Prange (1977) showed that the wall thickness of the leg segments scaled isometrically with segment length as well. A previous study of external dimensions of D. aquaticus found rather similar ratios of length of leg segments across different leg positions (Reußenzehn and Paulin, in prep.). Further experimental research is needed to determine whether scaling of width versus length is also isometric in D. aquaticus.

Given that the previously examined species mentioned above belong to families of vagrant spiders as well, a mechanical leg design similar to that of D. aquaticus might be expected. A closely-related mechanical design in terms of the limbs’ movability has already been found for D. aquaticus and C. salei (Reußenzehn and Paulin, in prep.). Further, Brüssel (1987) notes that C. salei and Dolomedes species were both able to stand steadily on mercury even though the low viscosity of the substrate did not allow for horizontal forces. Due to the similarities between the two species and the fact that Karner (1999) showed that volume shift scaled according to geometric similarity in C. salei, it seemed reasonable to assume geometric similarity (isometric scaling, n = 3) for standardization of femur-patella and tibia-metatarsus joints in D. aquaticus.

2.4.5 Eﬀect of joint width on standardization factor

In order to ﬁnd simple scaling relationships for further computational models I investigated whether scaling of joints could be approximated by scaling a standardized joint (i.e. template). I examined the scaling behavior of femur-patella and tibia-metatarsus

40 Acquisition of angle-volume characteristics 2.4 Discussion joints subject to the position of the leg they belonged to. The standardizing factor sfac plotted against joint width was used as an indirect measure of scaling behavior (Fig. 2.3.4). Linear regression revealed a significant trend for the relationship between joint width and scaling factor in all spiders apart from the femur-patella joint in spider three. Given noise in the data, however, most of the regressions were ambiguous in terms of their linearity. Two shortcomings of this study were that pooling of data across spiders for a general analysis was not possible due to statistical difference and data were too noisy to justify fitting higher degree models. Thus no clear conclusion about the general (non-spider-specific) scaling behavior could be reached. Given the mathematical n −n definition of the standardization factor sfac (lg/ls , compare equation 2.2.6, p. 25 for abbreviations) and results of previous studies that suggest cubic scaling (power exponent value n = 3; Prange, 1977; Karner, 1999) a non-linear relationship would have been expected on theoretical grounds. Further research is needed to identify the correct scaling relationship for D. aquaticus in order to model the spider’s leg segments by scaling a template to the corresponding dimensional properties.

2.4.6 Angle-volume characteristic of leg joints

2.4.6.1 Volume-shift in diﬀerent leg joints

The examination of standardized mean angle-volume characteristics for leg joints in D. aquaticus revealed that volume-shift over the range of movement varied with joint type and leg position. This indicates that the amount of haemolymph shifted during joint deflection depends on the type of joint and the position of the leg it belongs to. Comparing the influence of joint flexion on haemolymph volume change between different joint types revealed that in femur-patella joints a volume shift of approx. 2.5 µl occurred over the range of movement while in tibia-metatarsus joints a volume-shift of only approx. 0.6 µl (apart from joints in leg 4 with approx. 1.2 µl) occurred.

Comparing angle-volume characteristics of femur-patella joints from the fourth leg of D. aquaticus with those from T. atrica (Parry and Brown, 1959a) and C. salei (Karner, 1999) revealed a close similarity (Fig. 2.4.1). To compare leg joints of the three species, angle-volume characteristics for D. aquaticus were standardized to the estimated joint width of T. atrica. Parry and Brown (1959a) reported the distance between the femur- patella and tibia-metatarsus joints (11 mm) but failed to report the actual joint width. Based on the standardization applied by Karner (1999), who did not state the joint

41 Acquisition of angle-volume characteristics 2.4 Discussion

0.6

0.5 l)

µ 0.4

0.3

0.2 Joint volume (

0.1

0 40 60 80 100 120 140 160 180 Joint angle Θ (°)

Figure 2.4.1: Comparison of angle-volume characteristics for femur-patella joints of three species. Black markers: T. atrica (Parry and Brown, 1959a, leg position and joint width not reported), blue dot-and-dashed line: C. salei (Karner, 1999, 4th leg, joint width not reported), red lines: D. aquaticus (4th leg), solid line corresponds to estimated joint width of 0.75 mm, dashed lines: 0.8 mm (upper line) and 0.7 mm (lower line). Standardized joint width was estimated based on the standardization applied by Karner (1999) and measurements on preserved specimens of T. atrica. width either, and measurements on preserved specimens of T. atrica,3 a joint width of 0.75 ± 0.05 mm was estimated. No attempt was made to compare tibia-metatarsus joints due to the fact that the ventral hinge stop of about 85◦ in D. aquaticus did not permit comparisons with the measurements of 40◦ and 60◦ reported by Parry and Brown (1959a). Differences between the femur-patella characteristics of the three spiders might be caused by variation in joint anatomy among these species (ratio of joint width to cross sectional area) as concluded by Karner (1999). Another factor previously not addressed is the application of different hydrostatic pressures during the experiment. While internal fluid pressure was applied during observations on T. atrica and D. aquaticus, Karner (1999) did not report any pressure settings and presumably did not apply a hydrostatic pressure. As described in section 2.4.2, different hemolymph pressures influence the angle-volume characteristics for a given joint. This might account for the lower course of the angle-volume characteristic reported by Karner (1999).

3Femur-patella joint width and corresponding distance between femur-patella and tibia-metatarsus joint axes was measured for four diﬀerent legs of a male and female spider, respectively.

42 Acquisition of angle-volume characteristics 2.4 Discussion

Blickhan and Barth (1985) showed that torque (M) can be developed by the leg joint at a given angle (θ) when a certain hemolymph pressure (P) is applied and deﬂection of the joint (∆Θ) causes the internal volume to change (∆V ).

∆V M = · P (2.4.1) ∆Θ

The authors noted that experimental findings by Parry and Brown (1959a) verified this equation. Thus, given equal internal pressure throughout all legs, the generated torque can be explained by the volume-shift taking place during deflection of the joints. Given this relationship, femur-patella joints appear to contribute considerably more towards generation of propulsion torques/forces than tibia-metatarsus joints.

The results of this study show that tibia-metatarsus joint width increased with more posterior leg position. The smallest joint width was found in the first leg (0.817 mm) which was followed by the second (0.846) and third (0.882 mm) leg. The joint of the fourth leg was the widest (0.962 mm). Angle-volume characteristics for these joints also revealed a continuous increase in volume-shift with more posterior position of the leg indicated by the increasing slope angle. This characteristic was very pronounced in the fourth leg, resulting in approximately twice as much volume-shift for the same range of movement compared to the first leg. Given equation 2.4.1 higher torques are developed in the hind legs’ tibia-metatarsus joints during extension. Ehlers (1939) stated that due to the arched arrangement of the legs along the prosoma the angular orientation of the long axes of leg one and four are almost converse resulting in a contraction of the first leg and extension of the forth leg during the stance phase while leg two and three show an intermediate movement. Thus during terrestrial locomotion in spiders, propulsion forces due to hydraulic extension seem to be most important for more posterior legs. Weihmann et al. (2010) pointed out that due to the viscose nature of hemolymph the pressure in the joints does not build up instantly because hemolymph has to be provided by the fine lacunae. Thus, the resulting flow impedance limits the speed of fast joint deflection. The authors point out that joints which require more hemolymph because of a greater size might benefit from the fact that the supplying lacunae have a greater diameter as well. Zentner (2003) used Poiseuille’s equation (Eq. 2.4.2) to simulate laminar pipe flow for lacunae in a spider leg.

∆V πr4 ∆P V˙ = = · =(πr2)rϕ˙ (2.4.2) ∆t 8η l

43 Acquisition of angle-volume characteristics 2.4 Discussion

The volumetric flow rate (V˙ ) of the hemolymph in equation 2.4.2 is defined by the change of volume (∆V ) per unit time (∆t) and depends on the fourth power of the radius (r) of the lacunae, the dynamic viscosity (η) of the hemolymph, the length (l) of the supplying lacunae, and the pressure drop (∆P ). The author also stated that the volumetric flow rate can also be seen as a function of the angular velocity (ϕ ˙) which according to Blickhan and Barth (1985) expresses the volume change caused by the articular membrane of a joint with the radius r. Results from experiments conducted concurrently on legs of Phrixotrichus roseus (tarantula) verified the derived equation of motion for this model and the importance of the cross section area of the lacunae. This confirmed earlier findings and conclusions of Sens (1996) who measured increasing cross sectional area of the lacunae in more posterior leg position in Grammostola spatulata (tarantula) using sequential sectioning techniques. This, according to equation 2.4.2, results in decreasing flow impedance for lacunae in more posterior legs. Increases in joint width and slope of angle-volume characteristics for tibia-metatarus joints documented in this study confirm the important role of hydraulic extension in the hind legs during locomotion in D. aquaticus.

Joint width and slope of angle-volume characteristics for femur-patella joints did not follow the same pattern observed in tibia-metatarsus joints. While the characteristic of the fourth leg was still the most pronounced, the characteristic of the third leg showed the least volume-shift over the range of movement. In contrast to tibia-metatarsus joints, the characteristic for the second leg was almost equal to that of the fourth leg whereas the characteristic of the first leg indicated slightly more volume-shift than that of the third leg. According to equation 2.4.1, the fourth and second leg develop the greatest torques during extension. The width of femur-patella joints revealed the same pattern with the fourth joint being the widest (1.329 mm). The second widest was the joint of the second leg (1.297 mm) which was followed by that of the first (1.262 mm) and third (1.213 mm) legs. The fact that the second leg has such a pronounced characteristic cannot be explained satisfactorily by Ehlers’s, 1939 argument about leg arrangement and extension versus flexion of different legs during the stance phase. According to Ehler’s observations the second leg should generate propulsion by flexion and high extension torques generated by hemolymph pressure should result in even less torque generated by the flexing muscles. Suter and Wildman (1999) analysed video images showing D. triton galloping across the water surface. The results revealed that this species uses the anterior three leg pairs to generate thrust. Since D. aquaticus is closely related to D. triton, analogous galloping behavior can be expected. However, these quantitative

44 Acquisition of angle-volume characteristics 2.4 Discussion

findings contribute no further insight to the pronounced angle-volume characteristics of legs two and four. Quantitative data for D. aquaticus for slow locomotion on glass suggest that the second and third legs play a more dominant role in forward propulsion while the fourth leg is used for stabilisation (Pullar and Paulin, in prep.). However, the analysis was only conducted on two-dimensional dorsal images and therefore did not permit assessment of the contribution of the hydraulic joints which work dorso-ventrally (i.e. perpendicular to the recording plane). The results of this study do not seem to support the aforementioned findings by Ehlers (1939) and Suter and Wildman (1999) about leg contribution during locomotion since hydraulic extension of leg two appears to be able to generate as much torque as leg four, suggesting similar importance for torque generation. However, great dashes and very rapid leaps to capture flying insects have been observed in D. aquaticus (Williams, 1979). While video recordings of this behavior are not available for measurement, kinematic analysis of jumps by C. salei suggest that the main contribution to forward propulsion comes from extension of the fourth and second leg pair (Weihmann et al., 2010). In contrast, G. spatulata (tarantula), a much larger spider, used flexion of the front legs rather than extension of the hind legs for jumping (Sens, 1996). Based on findings by Parry and Brown (1959a) that geometrically similar spiders should have the ability to produce equal prosomal pressure, Weihmann et al. (2010) attributed this phenomenon to possible scaling effects. The size and scale of D. aquaticus appears more closely related to that of C. salei than to G. spatulata. In addition, C. salei, like Dolomedes, hunts insects using a sit-and-wait hunting strategy (Barth, 2002). Thus, the pronounced characteristics in femur-patella joints of the second and fourth leg pair in D. aquaticus is probably a result of the fact that rapid leaps and jumps are important for this species as well. The different patterns in angle-volume characteristics of femur-patella and tibia metatarsus joints cannot be explained satisfactorily by data collected as part of this study. Further research on three dimensional kinematics during locomotion and jumping in combination with measurements of ground reaction forces, is needed to clarify the contribution of certain leg joints to the generation of propulsive forces in D. aquaticus.

2.4.6.2 Scaling of angle-volume characteristics

To test for scaling eﬀects, a second analytical approach using the mean joint width of all joints for standardization of each joint was employed. Statistical analysis showed

45 Acquisition of angle-volume characteristics 2.4 Discussion no significant difference between characteristics of each joint type. Standardized angle- volume characteristics for femur-patella joints matched each other rather closely (Fig. 2.3.5b). Given that the joint axes were standardized to an equal width this indicates analogous active cross sectional areas causing the volume shift. Similarly, statistical differences could not be detected for standardized tibia-metatarsus joints (Fig. 2.3.6b). Close resemblance could be observed for legs one, two and three for tibia-metatarsus joints. However, even though no statistical difference could be detected, the standardized angle-volume characteristic of leg four did not appear to resemble the remaining characteristics as well as was the case for femur-patella joints. This might be due to other factors that alter the active cross sectional area and hence influence volume-shift. Karner (1999) found minor deviations in characteristics for C. salei when standardizing joint axes to equal width.

While Blickhan and Barth (1985) assumed that activation of muscles in live spiders might result in a change in the active cross sectional area and hence a decrease of generated torque, Karner (1999) argued the opposite, suggesting that muscles have to be understood as immobile elements of the hydraulic fluid. Karner concludes that due to the fact that the volume-shift caused by deflection of the joint is not altered by the activated muscles, the generated torque is not affected either (i.e. the active cross section area remains constant). Further explanations for the deviations between characteristics are still lacking. Anatomical comparisons of joints from different leg positions might provide insights into that phenomenon. The fact that standardizing angel-volume characteristics closely resembled each other suggests that joint volume in D. aquaticus scales according to geometric similarity. This is supported by data from Karner (1999) showing that in C. salei volume shift scaled according to geometric similarity as well.

46 Reconstruction of 3D spider model 3.1 Introduction

3 Reconstruction of 3D spider model using modern micro-CT technology

3.1 Introduction

3.1.1 Forward and inverse solutions in movement biomechanics

Biomechanics uses a cross-disciplinary approach to analyze and describe movement in animals and humans. Winter (2005) states that the application of mechanics to biological problems dates back to Leonardo DaVinci, Galileo, Lagrange, Bernoulli, Euler and Young. The author describes this discipline as a combination of life and physical sciences, where knowledge of physics, anatomy and engineering concepts are used to describe body segments and the forces acting in and upon them during movement.

Even though the course of motion appears to differ among animals with different anatomical blueprints (e.g. spider versus dog), the principles of locomotion are the same. Move- ment of body segments is caused by acting forces and torques. While gravitational and ground reaction forces (external forces) can be accurately quantified by available measuring technology, internal forces and torques are difficult to measure directly (Winter, 2005). They are subject to anatomical structures like muscles, tendons and bones and, in the case of spiders, the geometry of the exoskeleton and the acting hemolymph pressure. These forces and torques cause a complex movement behavior of multi-segmented systems (e.g. a leg where multiple joints allow movement of each body segment in various directions). However, through an approach called inverse-solution or inverse dynamics, net forces, and muscle torques causing the movement, can be predicted through measurements of body motion and external forces. On the other hand, these net forces and muscle torques can be used as input for the equations of motion to calculate the corresponding movement of body segments. This approach is called forward-solution or forward-dynamics. Analytical complexity is strongly correlated to the number of linkages in multi-segmented systems (Otten, 2003; Pandy, 2005).

To perform either of these analyzes both kinematic variables (e.g. displacement, joint angles, velocity and acceleration) and an accurate description of the body’s physical dimensions (e.g. size, shape, weight, and degrees of freedom) are required. The physical description then allows the construction of a reliable link-segment model. Furthermore, physical parameters like the mass distribution, the center of mass and the rotational

47 Reconstruction of 3D spider model 3.1 Introduction inertia (as measured by the segment’s resistance to changes in its rotation rate) are required.

Diﬀerent attempts to quantify these parameters have been made. Dempster and Gaugh- ran (1967) acquired properties of body segments by analyzing human cadavers. Ting et al. (1994) determined the rotational inertia of a cockroach’s body by analyzing the pendulum oscillation of the insect around an inserted pin. In addition to these inva- sive methods, general models have been established by representing limbs with simple geometric solids based on estimated shapes (e.g. for a human: Yeadon (1990); for a salamander: Ijspeert (2000). A more accurate estimate of the actual shape has been achieved by using a photogrammetric camera or a three-dimensional digitizer as a spatial measuring tool (e.g. Jensen, 1978; Hutchinson et al., 2005). To acquire shape estimates of external human body features on a higher resolution (approx. 4mm) the use of a 3D full-body laser scanner is currently being tested (K. Albracht, pers. comm.). How- ever, given the relatively small size of a spider, a much higher resolution is needed to acquire its external body geometry accurately. In this study, data from micro-computer tomography was used.

3.1.2 3D imaging using micro-CT

Computer tomography (CT) is a diagnostic imaging method that uses x-rays to create an image of an object. It was introduced into medical practice in the early 1970s (Housfield, 1973) and provides a fast and non destructive method for obtaining a high-resolution image of an object’s three-dimensional (3D) structure. These images allow the object to be viewed from virtually any perspective and thereby permit an examination of its interior in great detail by providing precise qualitative and quantitative information. Thus, CT offers an alternative method to traditional techniques like dissection or production of serial section from embedded specimens, both of which are time consuming and highly destructive (Dinley et al., 2010). Since its invention the resolution of CT has improved dramatically from approx. 1mm down to about 0.25 µm effective pixel sizes (Beltz et al., 2007). The use of X-ray microtomography (micro-CT) was pioneered in the 1980s by Feldkamp et al. (1989), who analyzed tissue samples at a microscopic level. Since then, micro-CT has been widely used in engineering and biological/medical sciences as a quantitative and a qualitative imaging technique. The application area ranges from examining engineered materials (Ho and Hutmacher, 2006; Madi et al., 2007) and geological samples (Ketcham and Carlson, 2001) to biological materials like

48 Reconstruction of 3D spider model 3.1 Introduction

Figure 3.1.1: Principle of computer tomography. Top from right to left: data acquisition. Detector screen (green bar) captures image of angular projection (2D radiograph) produced by X-ray beam. Bottom from left to right: Reconstruction of layers by numerically overlaying projections of each layer. Stack of all layers results in 3D structure (modiﬁed after Beltz et al., 2007, p. 56). teeth (Jung et al., 2005), bones (Jiang et al., 2000), and soft tissue such as embryonic tis- sues (Metscher, 2009) and mammalian nerves (Beckmann et al., 1999). The technology even allows in-vivo micro-CT of live animals (Postnov et al., 2002).

Micro-CT systems are available in two conﬁgurations: In-vivo imaging (X-ray source rotates) or in-vitro scanning (the specimen rotates). The spatial resolution for in-vivo scanners is limited since live animals might not tolerate high X-ray doses. Thus, higher spatial resolution is achieved by using the latter technique which provides very good information about 3D connectivity, topology and microachitecture (Holdsworth and Thornton, 2002). In in-vitro micro-CT imaging (Fig. 3.1.1), a ﬁxed X-ray source produces a beam which passes through the sample as it is rotated in equal steps through 180◦ or 360◦. For each step the resulting angular projection (2D radiograph) is captured as an image by a detector screen, where the brightness of each pixel is determined by the density of the material through which the beam passed. The acquired images are subsequently reconstructed numerically to create cross section slices of the object. Specialized volume graphics software is used for visualization. A detailed description is available elsewhere (Zollikofer and Ponce de León, 2005).

49 Reconstruction of 3D spider model 3.1 Introduction

One primary technique for creating three dimensional images is isocontouring. In order to find the boundaries of an object at least one surface must be defined. Mostly these boundaries are assumed to correspond to a certain threshold. Hence isocontours mark surfaces with the same attenuation. This is comparable to contours on a topographic map which mark lines of constant elevation. Analogous to the construction of topographic maps, surfaces are defined by interpolation between data points. Though this technique demands memory and CPU power, it provides high resolution images and detailed surface information (Ketcham and Carlson, 2001). Recently, X-ray CT has been used to determine surface area, for example, in corals (Laforsch et al., 2008), animal embryos (Hagadorn et al., 2006) and mechanical parts (Shammaa et al., 2008). However, X-ray microtomography has not yet been applied to determine the surface of an arthropod’s exoskeleton in order to create an accurate 3D model for biomechanical simulations.

50 Reconstruction of 3D spider model 3.2 Material and Methods

3.2 Material and Methods

3.2.1 Exoskeleton geometry acquisition

3.2.1.1 Preparation of specimen

To perform an in-vitro micro-CT scan an individual spider was haphazardly selected for imaging. The spider was gassed with ethyl acetate (May & Baker Ltd, Dagenham, England) by applying 1 ml of the chemical to 0.5 g cotton situated on the bottom of a 120 ml plastic container and covered with ﬁlter paper to prevent contact. After 20 minutes of exposure the dead spider was transferred to the specimen stage and positioned on top of a sticky dental wax ball. To ensure accurate imaging, the claws extending from the tarsi were hooked into pores of polystyrene foam to prevent the specimen from moving during the scanning procedure.

3.2.1.2 Micro-CT scan and numerical reconstruction

The specimen was scanned using a SkyScan-1172 high-resolution micro-CT system with a Hamamatsu 10Mp camera. (SkyScan, Kontich, Belgium). Beam accelerating voltage and current were set to 59 kV and 167 µA, respectively. The specimen was rotated through 188.3◦ by angular steps of 0.7◦. For settings of all parameters see log ﬁle in Appendix (pp. 89).

Digital cross-sections of the spider were generated numerically using the volumetric reconstruction software Nrecon (v. 1.5.1.4, Skyscan, Kontich, Belgium). The software uses a modiﬁed ﬁltered back-projection algorithm (Feldkamp et al., 1984) to create the cross-sections from the set of angular projections obtained as part of the scan.

3.2.1.3 Construction of Isosurface

Cross sectional images were imported into the three-dimensional (3D) visualization software Amira (v. 4.1.2 Mercury Computer Systems Inc., Chelmsford, MA, USA). Since identifying the internal structure of the spider was not the objective of this study a technique termed "isocontouring" by Ketcham and Carlson (2001) was used to obtain detailed information about surface structures. Given the high density of the rigid exoskeleton (Hillerton, 1984; Blickhan and Barth, 1985) and the low density of the surrounding air

51 Reconstruction of 3D spider model 3.2 Material and Methods

Figure 3.2.1: Segmentation of surface rendering dataset. Legs were segmented at the position of joint axes. Prosoma and abdomen were separated at the pedicel. Segments are depicted in diﬀerent colors. the spider’s boundary could be determined by choosing the corresponding threshold for surface rendering.

Threshold settings were adjusted to eliminate background noise as well as the dental wax support and the polystyrene foam. The generated surface model showing correct shape and topology using a optimized triangular-shaped mesh was saved as a *.wrl (Plane Text Virtual Reality Modeling Language File) ﬁle.

3.2.1.4 Exoskeleton segmentation

The surface model of the exoskeleton was imported into Autodesk 3D Studio Max, v. 2011 (Autodesk, Inc., San Rafael, CA, USA), a 3-D modelling and animation program. Prosoma and opisthosoma were separated at the joining narrow waist called the pedicel. Segmentation of the legs was performed by planes deﬁned using the position of joint axes in Dolomedes (Fig. 3.2.1). Planes were aligned perpendicular to the long axis of the leg and pedicel, respectively.

3.2.1.5 Body segment reconstruction

Further calculations to acquire parameters for the properties of body segments (e.g. center of mass and rotational inertia) require a deﬁned closed surface for each segment. However, holes in the mesh4 and the openings from the segmentation process caused 4Due to limitations of the implemented surface meshing algorithm in the 3D visualization software Amira it was not possible to generate a closed surface from the micro-CT data.

52 Reconstruction of 3D spider model 3.2 Material and Methods open surfaces for each body segment which did not permit further use for calculations. Thus, reconstruction of segments with deﬁned closed surfaces was done manually. No attempt was made to reconstruct segments automatically using meshing algorithms due to the fact that conventional triangulation methods for automated surface reconstruc- tions might require input data with uniform sampling rate or closed surfaces (Li et al., 2009).

Segments were reconstructed successively using Autodesk 3D Studio Max and Autodesk Maya v. 2011 (Autodesk, Inc., San Rafael, CA, USA) animation software. Each selected segment was duplicated and aligned to the reference axes (XYZ) for easier manipulation while all other segments were hidden. The shape of a GeoSphere or Capsule was adjusted to the segment’s mesh using the Object Deformation Tool (Stretch) and the Free Form Deformer (FFD 2x2x2). Finally, individual vertices were adjusted to align the new mesh with the segment. The falloff value, which defines how many neighboring vertices are influenced during the adjustment, was fine tuned until the two geometries closely matched (Fig. 3.2.2).

a b

Figure 3.2.2: Reconstruction of segment by approximated simple mesh geometries. Procedure shown exemplarily for tibia of the first left leg (comp. Fig. 3.2.1). a: Tibia segment (green) was duplicated (red) and aligned with the reference axes. The shape of a generated wire-frame object (Capsule) was modified to resemble the shape of the tibia. Modified vertices indicated in yellow. b: Modified wire-frame object superimposed on tibia duplicate.

53 Reconstruction of 3D spider model 3.3 Results

3.3 Results

3.3.1 Threshold adjustment

Visual comparison of the generated surface rendering dataset with the shape and topography of the scanned specimen allowed to determine the threshold for a close approximation. At a threshold value greater than 20,000 (Amira threshold range) distinct degeneration of the surface were clearly visible whereas threshold value below 8,000 resulted in distinct artefacts. Satisfactory concordance was achieved at threshold settings between 12,000 and 13,000 (Fig. 3.3.1).

3.3.2 Segmented 3D model

The file size of the generated 3D surface model from micro-CT data was about 62 MB containing 1,167,366 vertices and 1,029,696 faces. The fact that the model did not represent a closed surface (numerous vertices were not connected correctly) required reconstruction of segments with simple mesh geometries. Reconstructing the segments using defined closed surfaces resulted in a 3D model with a file size of about 5 MB containing

a b

Figure 3.3.1: Comparison of isosurfaces at diﬀerent threshold settings. a: A threshold value of 26,700 resulted in distinct degeneration. b: A threshold value of 5,500 resulted in distinct artefacts. c: Satis- factory concordance was achieved with a threshold value of 12,400.

54 Reconstruction of 3D spider model 3.3 Results

Table 3.3.1: Number of vertices and faces for master segments. Quantity states how often the segment is used in the model. Cox: coxa, tro: trochanter, fem: femur, pat: patella, tib: tibia, met: metatarsus, tar: tarsus, pro: prosoma, abd: abdomen.

cox tro fem pat tib met tar pro abd vertices 614 382 794 382 302 262 162 10520 1914 faces 615 400 816 400 320 280 180 11060 1984 quantity 8 8 8 8 8 8 8 1 1

35,618 vertices and 37,132 faces (compare table 3.3.1 for individual segments). The wire frame mesh geometries are shown exemplarily for the second right leg in Fig. 3.3.2. The reconstructed model consisted of 58 master segments with seven segments for each leg and one segment each for the prosoma and abdomen (Fig. 3.3.3). The master segment for the prosoma included sub-segments for eyes, labium, maxilla, chelicera, fangs, and pulps. The spinnerets were included as a sub-segment to the abdomen.

a b

Figure 3.3.2: Visual comparison of the wire frame mesh geometries with the shape of the respective second right spider leg. a: Wire frame mesh geometries, b: Spider leg

55 Reconstruction of 3D spider model 3.3 Results

a b

Figure 3.3.3: 3D model of D. aquaticus consisting of 58 master segments with seven segments for each leg and one segment each for the prosoma and abdomen. a: dorsal view, b: ventral view, c: perspective view.

56 Reconstruction of 3D spider model 3.4 Discussion

3.4 Discussion

The reconstruction method applied in this study represents a novel approach to describing the surface of an arthropod’s exoskeleton in order to create an accurate 3D model for biomechanical simulations. A close approximation of the body and limb geometry of D. aquaticus was achieved using micro-computer tomography and subsequent 3D-modelling. The surface rendering dataset generated from micro-CT data provided sufficient accuracy to reproduce the topography of the external geometry. The weight- bearing exoskeleton (cuticle) of arthropods is mostly made up of stiff protein matrix (Hillerton, 1984). The composition of this material causes the higher density of the cuticle in contrast to internal body parts. The clear contrast facilitated the selection of appropriate threshold settings for surface rendering. Visual comparison of the generated surface model and the scanned specimen proved sufficient for reproducing the topography.

The end product of the surface generation was a model deﬁned by a triangular shape mesh. While the shape and topography could be clearly depicted from this model the data were far from perfect for further analysis. The topographical resolution was so high that individual hairlines could still be distinguished which resulted in unnecessary information causing the huge ﬁle size. Holes and irregular orientation of individual vertices did not permit automated calculations of segment properties and contributed to the decisions to recreate the spider model manually. Manual alignment of mesh geometries (GeoSphere and Capsule) proved to be relatively simple and fairly accurate for reconstruction of the surface rendering obtained from micro-CT data. Visual comparison of superimposed segments from virtually every direction guaranteed close resemblance of the segmented exoskeleton. The resulting model provides a platform for further in-silico experiments.5

As a next step, the 3D model will be used to create a biomechanical model by linking the loose segments. Rigid linkages will be created between each segment according to the degrees-of-freedom of the corresponding joint. In addition, the reference frames of the resulting kinematic chain will be deﬁned using the Denevit-Hartenberg convention. This procedure is currently used in robotics to specify how the segments are linked to- gether and how each segment moves around any joint(s) it shares with adjacent segments (Sciavicco and Siciliano, 2000, pp. 42). A custom-made toolbox written in MATLAB (Paulin, unpublished data) will then automatically compute the mass and centre of

5And rendering it with hair makes it look really cool (compare picture on titlepage)

57 Reconstruction of 3D spider model 3.4 Discussion mass of the segments and a diagonal inertia tensor using a method proposed by Mirtich (1996).

The linked segments and their derived physical dimensions and parameters will provide the foundation for a fully functional biomechanical model of the spider D. aquaticus for further numerical simulations of inverse and forward-dynamics.

58 Discussion 4.1 Conclusion

4 Discussion

4.1 Conclusion

The principles of exploiting the natural interaction between the moving body and its mechanical coupling with its environment appear to be a key factor in locomotion (Dick- inson et al., 2000; Biewener, 2003). In order to minimize the cost of locomotion and recapture energy, continuous interaction occurs between the nervous system, the moving body and the environment. In theoretical, computational and robotic models, and in at least some animals, gait patterns clearly emerge from the mechanical design of the body, powered, tuned and stabilized by neuromuscular control, rather than from the nervous system alone. In this case, the brain acts to exploit, not to override, the natural dynamics of the organism and its interactions with the environment (Chiel and Beer, 1997; Iwasaki and Zheng, 2006). Most experimental studies have been done in vertebrates and insects. Certain spiders are agile predators, whose mechanical design and nervous system diﬀer markedly from vertebrates and, to a lesser but still substantial extent, from insects. The angle-volume characteristics measured in this study provide a quantitative description of volume shift in all hydraulic joints during movement. These results not only provide insights into the importance of hydraulic torque generation in each leg but could also facilitate investigations of interactions between these volume-shifting units during locomotion. Analysis and modelling of legged locomotion in spiders therefore should complement and extend our understanding of legged locomotion in other animals, humans, and robots. The generated 3D model of D. aquaticus from micro- CT images represents the ﬁrst attempt to create an accurate biomechanical model for further research. This model allows for new analytical methods and approaches to be undertaken in subsequent simulations of spider mobility. Thus the current study provides the basis for further theoretical, computational and experimental investigations of mechanical design, neural control and locomotor dynamics in spiders.

4.2 Suggestions for further research

Blickhan and Barth (1985) proposed that hemolymph pressure not only produces torques around the two hydraulic specialised joints examined in the study but is also able to induce torque at every joint if the internal volume of the leg changes during rotation of the limb. This hypothesis was supported by ﬁndings of Stewart and Martin (1974)

59 Discussion 4.2 Suggestions for further research who observed that the legs of a dead tarantula were lifted when fluid was injected into the prosoma. Even though the trochanter-femur joint responsible for that movement has an almost centred pivot and is operated by antagonistic muscles, they concluded that hydraulic-generated torques assist the flexor muscles. The apparatus and tracking algorithm developed for the present research provide an efficient method to detect and quantify hemolymph volume shift in all joints of arachnids. Experiments can be extended by measuring extension torques during joint rotation. Repeating measurements with different internal fluid pressures would provide a quantitative measure of its effect on hydraulically generated torques during locomotion.

Kinematic analyzes on D. aquaticus could reveal what ranges of movement are actually exploited in each joint during locomotion. These analyzes would provide information about the volume shift caused by all moving femur-patella and tibia-metatarsus joints during locomotion. Recent work on spider gait analysis revealed movement patterns of certain joints for D. aquaticus (Pullar and Paulin, in prep.). However, the markerless tracking method allowed only analysis of anteroposterior joint movement. Further research could provide insight into the gait patterns for the three dimensional multi-joint coordination in D. aquaticus during locomotion.

Further research is also needed to examine the direction and magnitude of the forces developed by the tarsi during locomotion. Analysis of ground reaction forces of moving spiders will provide insight into the importance of leg number and muscle forces (Blick- han and Full, 1993), as well as the accuracy of simple geometric scaling models involving a strength:weight ratio proposed by Full et al. (1991) on the basis of experimental results for cockroaches. To measure the ground reaction force vector induced by a spider leg, Blickhan and Barth (1985) used a force plate that allowed for the determination of dorsoventral, lateral, and axial force components during locomotion for one leg at a time. Applying a photoelastic method would provide simultaneous measurements of the forces generated in all legs of D. aquaticus. This approach was used previously in locomotion experiments involving insects (Harris, 1978; Harris and Ghiradella, 1980; Full et al., 1995).

Energy storage in elastically-deformable membranes has been demonstrated in hydraulically extended leg joints in different spider-like arachnids by Sensenig and Shultz (2003, 2004). These authors also investigated the effect of different internal fluid pressures on elastic recoil and showed that increased pressure in the joints acts synergetically with transarticular sclerites in some species but has little or no effect in others. They could

60 Discussion 4.2 Suggestions for further research not find evidence for elastic sclerites in true spiders (e.g. tarantula). Weihmann (2008) used kinematic analysis and data on ground reaction forces to investigate locomotion behavior of the wandering spider Ancylometes bogotensis. Based on his findings Weih- mann also concluded that this species does not use elastic mechanisms to store and recover energy during locomotion. However, Blickhan and Barth (1985) proposed the possibility of energy storage by elastic muscle rings and articular membranes in the tibia of the hunting spider C. salei. It is expected that further investigations on D. aquaticus using computational modelling will clarify whether interactions between internal fluid pressure and elastic energy storage during a step cycle exist. In addition, simulating the effect of the hemolymph volume shift during movement of hydraulically extended joints and the damping effect of hemolymph pressure will contribute to an integrative understanding of this mechanism.

These experiments will not only provide a better understanding of the unique locomotion strategy applied by spiders but also supply information and data for further simulation and technical applications in the field of robotics. For example, the current design of robots requires the placement of actuators at the joints. Future robots, inspired by spiders, could have powerful actuators placed within the body and use hydraulics and cables to drive lightweight legs. This would reduce the effect of inertia and make locomotion more efficient. Another advantage of using hydraulics could be that it causes hydrostatic stiffness in the walking legs. Thus robots with inflatable legs could be designed to make them small and light for transportation. To deploy these walking machines the legs would only have to be pressurized with fluid.

61 References

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72 Appendix

Appendix

Following is a section of figures showing the key components of the graphical user interface (p. 74) and the effect of the custom convolution filter and threshold setting (p. 75). The corresponding code can be found subsequently (pp. 76).

Furthermore, ﬁgures and tables which were not included into the result section are shown.

• Fig. A.2.1: Eﬀect of decreasing pressure on angle-volume characteristics (p. 85) • Fig. A.2.2: Angle-volume characteristics for femur-patella joints (p. 86) • Fig. A.2.3: Angle-volume characteristics for tibia-metatarsus joints (p. 87) • Table. A.2.1: Joint width (p. 88)

The Appendix ends with the log ﬁle of the micro-CT system reporting the settings of all parameters during scanning and volumetric reconstruction (pp. 89).

73 Appendix

Tracking Graphical User Interface

Figure A.1.1: Main display of tracking GUI. The image on the top shows the 200th video frame of glass capillary with superimposed tracked position of dyed fluid (red symbol). The image below shows cropped area of glass capillary (7 by 630 pixels) after image manipulation of corresponding image above (see code for details). The input field below allows selection of a specific frame (e.g. 200th) as well as manual scrolling by clicking on the arrows. The menu enables easy data input and output as well as changing the settings for image manipulation (functions listed in chronological order of usage): Load reads video stream into MATLAB, Convolution applies the filter algorithm, Threshold allows to set the threshold level for turning the area around the dyed fluid black, Crop determines the area shown in the lower image (visual check for threshold), Tracking direction changes the search behaviour of the tracking algorithm, Zoom allows to magnify the reference arrow in the upper image, pix2mm acti- vates the mouse tracker and returns the coordinates of the two reference arrow tips clicked on, Track runs the tracking algorithm, Check plot opens a new figure window with fluid position plotted against joint angle, Save opens a dialogue box to save the trial data. Corresponding source code can be found in Appendix A, pp. 76

74 Appendix

Figure A.1.2: Effect of custom convolution filter and threshold setting. a: Original image showing one frame of video stream, b: Image after applying convolution filter, ho- mogenising the lighting and enhancing edge contrast, c: Image after applying threshold setting, pixel values below the threshold were set to 0 (black).

75 Appendix

Source code for tracking algorithm

1 function varargout = capillarytrackgui1(varargin) 2 3 %Stefan Reussenzehn 2009 4 %Algorithm for tracking fluid displacement using a GUI. 5 %Images from video recordings are imported and subsequently analyzed. A convolution filter enhances the appearance of the dye in the glass capillary and a search algorithm finds the position of the dark pixel with the greatest x value. 6 7 % CAPILLARYTRACKGUI1 M-file for capillarytrackgui1.fig 8 % CAPILLARYTRACKGUI1, by itself, creates a new CAPILLARYTRACKGUI1 or raises the existing 9 % singleton*. 10 % 11 % H = CAPILLARYTRACKGUI1 returns the handle to a new CAPILLARYTRACKGUI1 or the handle to 12 % the existing singleton*. 13 % 14 % CAPILLARYTRACKGUI1(’CALLBACK’,hObject,eventData,handles,...) calls the local 15 % function named CALLBACK in CAPILLARYTRACKGUI1.M with the given input arguments. 16 % 17 % CAPILLARYTRACKGUI1(’Property’,’Value’,...) creates a new CAPILLARYTRACKGUI1 or raises the 18 % existing singleton*. Starting from the left, property value pairs are 19 % applied to the GUI before capillarytrackgui1_OpeningFcn gets called. An 20 % unrecognized property name or invalid value makes property application 21 % stop. All inputs are passed to capillarytrackgui1_OpeningFcn via varargin. 22 % 23 % *See GUI Options on GUIDE’s Tools menu. Choose "GUI allows only one 24 % instance to run (singleton)". 25 % 26 % See also: GUIDE, GUIDATA, GUIHANDLES 27 28 % Edit the above text to modify the response to help capillarytrackgui1 29 30 % Begin initialization code - DO NOT EDIT 31 gui_Singleton = 1; 32 gui_State = struct(’gui_Name’, mfilename, ... 33 ’gui_Singleton’, gui_Singleton, ... 34 ’gui_OpeningFcn ’, @capillarytrackgui1_OpeningFcn, ... 35 ’gui_OutputFcn ’, @capillarytrackgui1_OutputFcn, ... 36 ’gui_LayoutFcn’, [] , ... 37 ’gui_Callback’, []); 38 if nargin && ischar(varargin{1}) 39 gui_State.gui_Callback = str2func(varargin{1}); 40 end 41 42 if nargout 43 [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); 44 else 45 gui_mainfcn(gui_State, varargin{:}); 46 end

76 Appendix

47 % End initialization code - DO NOT EDIT 48 49 50 % --- Executes just before capillarytrackgui1 is made visible . 51 function capillarytrackgui1_OpeningFcn(hObject , eventdata, handles, varargin) 52 % This function has no output args, see OutputFcn. 53 % hObject handle to figure 54 % eventdata reserved - to be defined in a future version of MATLAB 55 % handles structure with handles and user data (see GUIDATA) 56 % varargin command line arguments to capillarytrackgui1 (see VARARGIN) 57 58 % Choose default command line output for capillarytrackgui1 59 handles.output = hObject; 60 61 % conv handles structure 62 guidata(hObject , handles); 63 64 % UIWAIT makes capillarytrackgui1 wait for user response (see UIRESUME) 65 % uiwait(handles.figure1); 66 67 68 % --- Outputs from this function are returned to the command line. 69 function varargout = capillarytrackgui1_OutputFcn(hObject, eventdata, handles) 70 % varargout cell array for returning output args (see VARARGOUT); 71 % hObject handle to figure 72 % eventdata reserved - to be defined in a future version of MATLAB 73 % handles structure with handles and user data (see GUIDATA) 74 75 % Get default command line output from handles structure 76 varargout{1} = handles.output; 77 78 79 % --- Executes on button press in LOAD. 80 function LOAD_Callback(hObject , eventdata, handles) 81 % hObject handle to LOAD (see GCBO) 82 % eventdata reserved - to be defined in a future version of MATLAB 83 % handles structure with handles and user data (see GUIDATA) 84 [handles.filename, handles.pathname] = uigetfile(’*.avi’, ’Load video’); 85 handles.fileinfo = aviinfo(handles.filename); 86 handles.filename = handles.filename(1:(length(handles .filename))-4); 87 handles.frame =1; 88 handles.frames = handles.fileinfo.NumFrames; 89 handles.thresh=640; 90 91 handles.roi=[1 handles.fileinfo.Height 1 handles.fileinfo.Width]; %dimensions of image 92 handles.roi(4)=str2double(get(handles.MAXX,’String ’)); 93 handles.roi(1)=str2double(get(handles.MINY,’String ’)); 94 handles.roi(2)=str2double(get(handles.MAXY,’String ’)); 95 handles.image = display_image(handles); 96 set(handles.RtoL, ’value’, 0); %default direction set as right to left 97 set(handles.LtoR, ’value’, 1); 98 handles.mask=[]; 99 guidata(hObject , handles);

77 Appendix

100 101 102 % --- Executes on button press in PREVIOUS. 103 function PREVIOUS_Callback(hObject, eventdata, handles ) 104 % hObject handle to PREVIOUS (see GCBO) 105 % eventdata reserved - to be defined in a future version of MATLAB 106 % handles structure with handles and user data (see GUIDATA) 107 if handles.frame > 1, 108 handles.frame = handles.frame - 1; 109 else 110 return 111 end 112 handles.image = display_image(handles); 113 handles.processedimage = display_processedimage(handles); 114 guidata(hObject , handles); 115 116 % --- Executes on button press in NEXT. 117 function NEXT_Callback(hObject , eventdata, handles) 118 % hObject handle to NEXT (see GCBO) 119 % eventdata reserved - to be defined in a future version of MATLAB 120 % handles structure with handles and user data (see GUIDATA) 121 if handles.frame < handles.frames, 122 handles.frame = handles.frame + 1; 123 else 124 return 125 end 126 handles.image = display_image(handles); 127 handles.processedimage = display_processedimage(handles); 128 guidata(hObject , handles); 129 130 131 function FRAME_Callback(hObject, eventdata, handles) 132 % hObject handle to FRAME (see GCBO) 133 % eventdata reserved - to be defined in a future version of MATLAB 134 % handles structure with handles and user data (see GUIDATA) 135 136 % Hints: get(hObject,’String’) returns contents of FRAME as text 137 % str2double(get(hObject,’String’)) returns contents of FRAME as a double 138 newframe = str2double(get(handles.FRAME,’String ’)); 139 if newframe

78 Appendix

153 % eventdata reserved - to be defined in a future version of MATLAB 154 % handles empty - handles not created until after all CreateFcns called 155 156 % Hint: edit controls usually have a white background on Windows. 157 % See ISPC and COMPUTER. 158 if ispc && isequal(get(hObject,’BackgroundColor ’), get(0,’ defaultUicontrolBackgroundColor’)) 159 set(hObject ,’BackgroundColor ’,’white’); 160 end 161 162 163 % --- Executes on button press in CONV. 164 function CONV_Callback(hObject , eventdata, handles) 165 % hObject handle to CONV (see GCBO) 166 % eventdata reserved - to be defined in a future version of MATLAB 167 % handles structure with handles and user data (see GUIDATA) 168 handles.mask = [0 1 0; 1 1 1; 0 1 0]; %mask for convolution 169 handles.conv = conv2(double(handles.image(:,:,1)),handles.mask, ’same’);%convolution of mask with image 170 handles.processedimage = display_processedimage(handles); 171 guidata(hObject , handles); 172 173 function THRESH_Callback(hObject , eventdata, handles) 174 % hObject handle to THRESH (see GCBO) 175 % eventdata reserved - to be defined in a future version of MATLAB 176 % handles structure with handles and user data (see GUIDATA) 177 178 % Hints: get(hObject,’String’) returns contents of THRESH as text 179 % str2double(get(hObject,’String’)) returns contents of THRESH as a double 180 handles.thresh=str2double(get(handles.THRESH ,’String ’)); 181 handles.processedimage = display_processedimage(handles); 182 guidata(hObject , handles); 183 184 % --- Executes during object creation, after setting all properties. 185 function THRESH_CreateFcn(hObject , eventdata, handles) 186 % hObject handle to THRESH (see GCBO) 187 % eventdata reserved - to be defined in a future version of MATLAB 188 % handles empty - handles not created until after all CreateFcns called 189 190 % Hint: edit controls usually have a white background on Windows. 191 % See ISPC and COMPUTER. 192 if ispc && isequal(get(hObject,’BackgroundColor ’), get(0,’ defaultUicontrolBackgroundColor’)) 193 set(hObject ,’BackgroundColor ’,’red’); 194 end 195 196 197 function MINX_Callback(hObject , eventdata, handles) 198 % hObject handle to MINX (see GCBO) 199 % eventdata reserved - to be defined in a future version of MATLAB 200 % handles structure with handles and user data (see GUIDATA) 201 202 % Hints: get(hObject,’String’) returns contents of MINX as text

79 Appendix

203 % str2double(get(hObject,’String’)) returns contents of MINX as a double 204 handles.roi(3)=str2double(get(handles.MINX,’String ’)); 205 handles.processedimage = display_processedimage(handles); 206 guidata(hObject , handles); 207 208 % --- Executes during object creation, after setting all properties. 209 function MINX_CreateFcn(hObject, eventdata, handles) 210 % hObject handle to MINX (see GCBO) 211 % eventdata reserved - to be defined in a future version of MATLAB 212 % handles empty - handles not created until after all CreateFcns called 213 214 % Hint: edit controls usually have a white background on Windows. 215 % See ISPC and COMPUTER. 216 if ispc && isequal(get(hObject,’BackgroundColor ’), get(0,’ defaultUicontrolBackgroundColor’)) 217 set(hObject ,’BackgroundColor ’,’white’); 218 end 219 220 221 function MAXX_Callback(hObject , eventdata, handles) 222 % hObject handle to MAXX (see GCBO) 223 % eventdata reserved - to be defined in a future version of MATLAB 224 % handles structure with handles and user data (see GUIDATA) 225 226 % Hints: get(hObject,’String’) returns contents of MAXX as text 227 % str2double(get(hObject,’String’)) returns contents of MAXX as a double 228 handles.roi(4)=str2double(get(handles.MAXX,’String ’)); 229 handles.processedimage = display_processedimage(handles); 230 guidata(hObject , handles); 231 232 % --- Executes during object creation, after setting all properties. 233 function MAXX_CreateFcn(hObject, eventdata, handles) 234 % hObject handle to MAXX (see GCBO) 235 % eventdata reserved - to be defined in a future version of MATLAB 236 % handles empty - handles not created until after all CreateFcns called 237 238 % Hint: edit controls usually have a white background on Windows. 239 % See ISPC and COMPUTER. 240 if ispc && isequal(get(hObject,’BackgroundColor ’), get(0,’ defaultUicontrolBackgroundColor’)) 241 set(hObject ,’BackgroundColor ’,’white’); 242 end 243 244 245 246 function MINY_Callback(hObject , eventdata, handles) 247 % hObject handle to MINY (see GCBO) 248 % eventdata reserved - to be defined in a future version of MATLAB 249 % handles structure with handles and user data (see GUIDATA) 250 251 % Hints: get(hObject,’String’) returns contents of MINY as text 252 % str2double(get(hObject,’String’)) returns contents of MINY as a double 253 handles.roi(1)=str2double(get(handles.MINY,’String ’));

80 Appendix

254 handles.processedimage = display_processedimage(handles); 255 guidata(hObject , handles); 256 257 % --- Executes during object creation, after setting all properties. 258 function MINY_CreateFcn(hObject, eventdata, handles) 259 % hObject handle to MINY (see GCBO) 260 % eventdata reserved - to be defined in a future version of MATLAB 261 % handles empty - handles not created until after all CreateFcns called 262 263 % Hint: edit controls usually have a white background on Windows. 264 % See ISPC and COMPUTER. 265 if ispc && isequal(get(hObject,’BackgroundColor ’), get(0,’ defaultUicontrolBackgroundColor’)) 266 set(hObject ,’BackgroundColor ’,’white’); 267 end 268 269 270 function MAXY_Callback(hObject , eventdata, handles) 271 % hObject handle to MAXY (see GCBO) 272 % eventdata reserved - to be defined in a future version of MATLAB 273 % handles structure with handles and user data (see GUIDATA) 274 275 % Hints: get(hObject,’String’) returns contents of MAXY as text 276 % str2double(get(hObject,’String’)) returns contents of MAXY as a double 277 handles.roi(2)=str2double(get(handles.MAXY,’String ’)); 278 handles.processedimage = display_processedimage(handles); 279 guidata(hObject , handles); 280 281 % --- Executes during object creation, after setting all properties. 282 function MAXY_CreateFcn(hObject, eventdata, handles) 283 % hObject handle to MAXY (see GCBO) 284 % eventdata reserved - to be defined in a future version of MATLAB 285 % handles empty - handles not created until after all CreateFcns called 286 287 % Hint: edit controls usually have a white background on Windows. 288 % See ISPC and COMPUTER. 289 if ispc && isequal(get(hObject,’BackgroundColor ’), get(0,’ defaultUicontrolBackgroundColor’)) 290 set(hObject ,’BackgroundColor ’,’white’); 291 end 292 293 294 % --- Executes on button press in RtoL. 295 function RtoL_Callback(hObject , eventdata, handles) 296 % hObject handle to RtoL (see GCBO) 297 % eventdata reserved - to be defined in a future version of MATLAB 298 % handles structure with handles and user data (see GUIDATA) 299 300 % Hint: get(hObject,’Value’) returns toggle state of RtoL 301 302 303 304 % --- Executes on button press in LtoR.

81 Appendix

305 function LtoR_Callback(hObject , eventdata, handles) 306 % hObject handle to LtoR (see GCBO) 307 % eventdata reserved - to be defined in a future version of MATLAB 308 % handles structure with handles and user data (see GUIDATA) 309 310 % Hint: get(hObject,’Value’) returns toggle state of LtoR 311 312 313 314 % --- Executes on button press in ZOOM. 315 function ZOOM_Callback(hObject , eventdata, handles) 316 % hObject handle to ZOOM (see GCBO) 317 % eventdata reserved - to be defined in a future version of MATLAB 318 % handles structure with handles and user data (see GUIDATA) 319 handles.zoom = zoom; 320 %Left click zoom in, right click zoom out 321 set(handles.zoom,’Enable’,’on’, ’Direction’, ’in’, ’RightClickAction ’, ’InverseZoom ’); 322 guidata(hObject , handles); 323 324 325 % --- Executes on button press in PIX2MM. 326 function PIX2MM_Callback(hObject , eventdata, handles) 327 % hObject handle to PIX2MM (see GCBO) 328 % eventdata reserved - to be defined in a future version of MATLAB 329 % handles structure with handles and user data (see GUIDATA) 330 clickData = gtrack(); 331 x = []; x = [x; clickData(:).x]; 332 y = []; y = [y; clickData(:).y]; 333 handles.distpix = sqrt((clickData(2).x-clickData(1).x)^2+(clickData (2).y-clickData (1).y )^2); 334 guidata(hObject , handles); 335 336 % --- Executes on button press in TRACK. 337 function TRACK_Callback(hObject, eventdata, handles) 338 % hObject handle to TRACK (see GCBO) 339 % eventdata reserved - to be defined in a future version of MATLAB 340 % handles structure with handles and user data (see GUIDATA) 341 handles.pos=[]; 342 handles.D=[]; 343 %check direction to track 344 rtol=get(handles.RtoL, ’value’); 345 if rtol==1 346 handles.dir=’RtoL’; 347 end 348 ltor=get(handles.LtoR, ’value’); 349 if ltor==1 350 handles.dir=’LtoR’; 351 end 352 353 for i= 1:handles.frames-1 354 disp = aviread([handles.pathname handles.filename], i); %reads the avi file 355 A = disp.cdata; 356 C = conv2(double(A(:,:,1)),handles.mask, ’same’);%convolution of mask with image

82 Appendix

357 CT = C.*(C0);%values in cropped image 360 % if handles.dir==’RtoL’ 361 % xn=x(length(x)); %find indices of x values corresponding to end points 362 % else xn=x(1); %find indices of x values corresponding to start 363 % end 364 365 if handles.dir==’RtoL’ 366 xn=x(1); %find indices of x values corresponding to end points 367 else xn=x(length(x)); %find indices of x values corresponding to start 368 end 369 370 ind = find(x==xn); 371 %use indices to take mean y values (is sometimes more than one y value for 372 %pixels furtheres to the right 373 yn=mean(y(ind(:))); 374 %convert back to full image coordintaes 375 X=xn+(handles.roi(3)-1); 376 Y=yn+(handles.roi(1)-1); 377 handles.pos=[handles.pos; X Y]; %saves list of positions 378 379 axes(handles.VIDEO) 380 %set up display and plot end point 381 imagesc(A); 382 axis equal 383 colormap(gray) 384 hold on 385 plot(X, Y, ’r.’) 386 hold off 387 end 388 handles.distanceMM = handles.D*(20/handles.distpix); % converts pixel distances to mm 389 390 guidata(hObject , handles); 391 392 % --- Executes on button press in SAVE. 393 function SAVE_Callback(hObject , eventdata, handles) 394 % hObject handle to SAVE (see GCBO) 395 % eventdata reserved - to be defined in a future version of MATLAB 396 % handles structure with handles and user data (see GUIDATA) 397 c = fix(clock); 398 %filename = sprintf(’%s_%02d-%02d-%4d%s’, [handles.filename ’_data’], c(3), c(2), c(1), ’.mat’);% 399 filename = sprintf(’%s’, [handles.filename ’_data’],’.mat’);% 400 prompt = {’Enter data file name:’}; 401 name = ’Save current data to a file’; 402 numlines = 1; 403 defaultanswer = {filename}; 404 filename2 = ’’; 405 filename2 = inputdlg(prompt,name,numlines,defaultanswer); 406 if isempty(filename2), return, end;

83 Appendix

407 save (filename, ’-struct’ ,’handles’, ’pos’, ’D’, ’distpix’, ’distanceMM’, ’thresh’, ’ roi’); 408 return 409 guidata(hObject , handles); 410 411 412 function i = display_image(handles) 413 cla(handles.VIDEO) 414 handles.video = aviread([handles.pathname handles.filename], [handles.frame]); 415 axes(handles.VIDEO) 416 i =handles.video.cdata; 417 imagesc(i); 418 colormap(handles.VIDEO,gray); 419 set(handles.VIDEO, ’xlimmode’, ’manual’, ’ylimmode’, ’manual ’); 420 axis equal 421 set(handles.FRAME, ’string’, num2str(handles.frame)); 422 set(handles.THRESH, ’string’, num2str(handles.thresh)); 423 return 424 425 function ip = display_processedimage(handles) 426 cla(handles.PLOT) 427 handles.video = aviread([handles.pathname handles.filename], [handles.frame]); 428 axes(handles.PLOT) 429 A = handles.video.cdata; 430 if ~isempty(handles.mask) 431 C = conv2(double(A(:,:,1)),handles.mask, ’same’);%convolution of mask with image 432 else ip=[]; 433 image(A) 434 return 435 end 436 CT = C.*(C

84 Appendix

Figures and tables

a b

Jointvolume( l)

Jointvolumeat120 ( l)

JointangleQ ( ° )

Figure A.2.1: Eﬀect of decreasing internal pressure on angle-volume characteristics. a: Angle- volume characteristics for femur-patella joint of second left leg. Pressure was decreased from trial to trial. Trial number position corresponds to joint volume at 120◦ (dashed line). b: Joint volume at 120◦ plotted against pressure for each trial. Numbers indicate trial numbers. Data were not included in further analyses because a) the trial for 19.6 kP could not be evaluated due to corrupted video ﬁle and b) the sudden increas of joint volume between trial 5 and 6 represents a measurement artefact. On physical grounds a continuous decrease of joint volume would have been expected.

85 Appendix

3.5 Spider1 3 2.5 2 1.5 1 0.5 0

3.5 Spider2 3

m 2.5 2 1.5 1

Jointvolume( l) 0.5 0

3.5 Spider3 3 2.5 2 1.5 1st leg 1 2nd leg 0.5 3rd leg th 0 4 leg 40 60 80 100 120 140 160 180 JointangleQ ( ° )

Figure A.2.2: Angle-volume characteristics for all femur-patella joints of three spiders determined by a polynomial model. Joint volume was set to zero at 40◦. Leg abbreviations: e.g. L1: left ﬁrst leg, R2: right second leg. Corresponding joint widths can be found in Table A.2.1

86 Appendix

1.5 Spider1

0.5

1.5 Spider2

m 1

0.5

Jointvolume( l)

1.5 Spider3

st 0.5 1 leg nd 2 leg rd 3 leg th 0 4 leg 80 100 120 140 160 180 200 JointangleQ ( ° )

Figure A.2.3: Angle-volume characteristics for all tibia-metatarsus joints of three spiders determined by a polynomial model. Joint volume was set to zero at 80◦. Leg abbreviations: e.g. L1: left ﬁrst leg, R2: right second leg. Corresponding joint widths can be found in Table A.2.1

87 Appendix

Table A.2.1: Width in mm for all femur-patella (fe-pa) and tibia-metatarsus (ti-me) joints of the three examined spiders in mm. Leg abbreviations: e.g. L1: left ﬁrst leg, R2: right second leg.

spider one spider two spider three fe-pa ti-me fe-pa ti-me fe-pa ti-me

L1 1.237 0.895 1.335 0.785 1.202 0.816 R1 1.263 0.908 1.311 0.751 1.225 0.745 L2 1.321 0.892 1.356 0.775 1.237 0.873 R2 1.318 0.914 1.374 0.793 1.178 0.828 L3 1.221 0.914 1.166 0.852 1.226 0.829 R3 1.242 0.953 1.189 0.879 1.234 0.869 L4 1.328 0.971 1.380 0.930 1.293 0.919 R4 1.292 1.005 1.353 1.004 1.331 0.941

88 Appendix

Log ﬁle of the micro-CT system

1 [System] 2 Scanner=Skyscan1172 3 Instrument S/N=031 4 Hardware version=A 5 Software=Version 1. 5 (build 1) 6 Home directory=C:\Skyscan1172 7 Tube=unknown 8 Camera=Hamamatsu 10Mp camera 9 Camera Pixel Size (um)= 11.57 10 CameraXYRatio=1.0020 11 Incl.in lifting (um/mm)=-1.8490 12 [Acquisition ] 13 Data directory=C:\results\Stefan\Dolomedes02 14 Filename Prefix=dolomedes02_ 15 Number of Files= 269 16 Source Voltage (kV)= 59 17 Source Current (uA)= 167 18 Number of Rows= 524 19 Number of Columns= 1000 20 Image Pixel Size (um)= 34.69 21 Object to Source (mm)=260.450 22 Camera to Source (mm)=347.379 23 Vertical Object Position (mm)=30.000 24 Optical Axis (line)= 233 25 Filter=No filter 26 Image Format=TIFF 27 Depth (bits)=16 28 Screen LUT=0 29 Exposure (ms)= 158 30 Rotation Step (deg)=0.700 31 Frame Averaging=ON (4) 32 Random Movement=ON (5) 33 Use 360 Rotation=NO 34 Geometrical Correction=ON 35 Median Filtering=ON 36 Flat Field Correction=ON 37 Rotation Direction=CC 38 Scanning Trajectory=ROUND 39 Type Of Motion=STEP AND SHOOT 40 Study Date and Time=May 07, 2009 13:12:52 41 Scan duration=00:13:15 42 [Reconstruction] 43 Reconstruction Program=NRecon 44 Program Version=Version: 1.5.1.4 45 Program Home Directory=C:\Skyscan1172 46 Dataset Origin=Skyscan1172 47 Dataset Prefix=dolomedes02_ 48 Dataset Directory=C:\results\Stefan\Dolomedes02 49 Time and Date=May 07, 2009 14:08:37 50 First Section=14 51 Last Section=503

89 Appendix

52 Reconstruction duration per slice (seconds)=1.659184 53 Postalignment=0.00 54 Section to Section Step=1 55 Sections Count=490 56 Result File Type=BMP 57 Result File Header Length (bytes)=1134 58 Result Image Width (pixels)=1000 59 Result Image Height (pixels)=1000 60 Pixel Size (um)=34.69933 61 Reconstruction Angular Range (deg)=188.30 62 Use 180+=OFF 63 Angular Step (deg)=0.7000 64 Smoothing =0 65 Ring Artifact Correction=10 66 Draw Scales=ON 67 Object Bigger than FOV=OFF 68 Reconstruction from ROI=OFF 69 Undersampling factor=1 70 Threshold for defect pixel mask (%)=0 71 Beam Hardening Correction (%)=50 72 CS Static Rotation (deg)=0.0 73 Mininum for CS to Image Conversion=0.0016 74 Maximum for CS to Image Conversion=0.0727 75 HU Calibration=OFF 76 BMP LUT=0 77 Cone-beam Angle Horiz.(deg)=7.622163 78 Cone-beam Angle Vert.(deg)=3.998291